[
  {
    "id": "kinetics-neural-ode",
    "title": "Kinetics parameter optimization of hydrocarbon fuels via neural ordinary differential equations",
    "authors": [
      "Xingyu Su",
      "Weiqi Ji",
      "Jian An",
      "Zhuyin Ren",
      "Sili Deng",
      "Chung K. Law"
    ],
    "year": 2023,
    "type": "journal-article",
    "venue": "Combustion and Flame",
    "volume": "251",
    "issue": null,
    "pages": "112732",
    "doi": "10.1016/j.combustflame.2023.112732",
    "topic": "sciml",
    "summary": "Treats kinetic parameter optimization as neural ODE training to calibrate hydrocarbon-fuel models against experimental targets.",
    "keywords": [
      "neural ODEs",
      "parameter optimization",
      "hydrocarbon fuels"
    ],
    "abstract": "Chemical kinetics mechanisms are essential for understanding, analyzing, and simulating complex combustion phenomena. In this study, a neural ordinary differential equation (Neural ODE) framework is employed to optimize the kinetics parameters of reaction mechanisms. Given experimental or high-cost simulated observations as training data, the proposed algorithm can optimally recover the hidden characteristics in the data. Different datasets of various sizes, types, and noise levels are systematically tested. A classic toy problem of stiff Robertson ODE is first used to demonstrate the learning capability, efficiency, and robustness of the Neural ODE approach. A 41-species, 232-reactions JP-10 skeletal mechanism and a 34-species, 121-reactions n-heptane skeletal mechanism are then optimized with species' temporal profiles and ignition delay times, respectively. Results show that the proposed algorithm can optimize stiff chemical models with sufficient accuracy, efficiency and robustness. It is noted that the trained mechanism not only fits the data perfectly but also retains its physical interpretability, which can be further integrated and validated in practical turbulent combustion simulations. In addition, as demonstrated with the stiff Robertson problem, it is promising to adopt Bayesian inference techniques with Neural ODE to estimate the kinetics parameter uncertainties from experimental data.",
    "sources": [
      "https://doi.org/10.1016/j.combustflame.2023.112732",
      "https://arxiv.org/abs/2209.01862",
      "https://hdl.handle.net/1721.1/156212",
      "https://github.com/DENG-MIT/ArrheniusOpt"
    ],
    "code_url": null,
    "arxiv_id": "2209.01862",
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/kinetics-neural-ode/paper.pdf",
      "source_url": "https://hdl.handle.net/1721.1/156212",
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    "fulltext_url": "https://jiweiqi.github.io/papers/kinetics-neural-ode/fulltext.txt",
    "repository_url": "https://hdl.handle.net/1721.1/156212",
    "related_code_url": "https://github.com/DENG-MIT/ArrheniusOpt"
  },
  {
    "id": "biomass-crnn",
    "title": "Autonomous kinetic modeling of biomass pyrolysis using chemical reaction neural networks",
    "authors": [
      "Weiqi Ji",
      "Franz Richter",
      "Michael J. Gollner",
      "Sili Deng"
    ],
    "year": 2022,
    "type": "journal-article",
    "venue": "Combustion and Flame",
    "volume": "240",
    "issue": null,
    "pages": "111992",
    "doi": "10.1016/j.combustflame.2022.111992",
    "topic": "sciml",
    "summary": "Learns biomass pyrolysis kinetics from thermogravimetric measurements with interpretable chemical reaction neural networks.",
    "keywords": [
      "CRNN",
      "biomass pyrolysis",
      "model discovery"
    ],
    "abstract": "Modeling the burning processes of biomass such as wood, grass, and crops is crucial for the modeling and prediction of wildland and urban fire behavior. Despite its importance, the burning of solid fuels remains poorly understood, which can be partly attributed to the unknown chemical kinetics of most solid fuels. Most available kinetic models were built upon expert knowledge, which requires chemical insights and years of experience. This work presents a framework for autonomously discovering biomass pyrolysis kinetic models from thermogravimetric analyzer (TGA) experimental data using the recently developed chemical reaction neural networks (CRNN). The approach incorporated the CRNN model into the framework of neural ordinary differential equations to predict the residual mass in TGA data. In addition to the flexibility of neural-network-based models, the learned CRNN model is interpretable, by incorporating the fundamental physics laws, such as the law of mass action and Arrhenius law, into the neural network structure. The learned CRNN model can then be translated into the classical forms of biomass chemical kinetic models, which facilitates the extraction of chemical insights and the integration of the kinetic model into large-scale fire simulations. We demonstrated the effectiveness of the framework in predicting the pyrolysis and oxidation of cellulose. This successful demonstration opens the possibility of rapid and autonomous chemical kinetic modeling of solid fuels, such as wildfire fuels and industrial polymers.",
    "sources": [
      "https://doi.org/10.1016/j.combustflame.2022.111992",
      "https://arxiv.org/abs/2105.11397",
      "https://hdl.handle.net/1721.1/156213"
    ],
    "code_url": "https://github.com/DENG-MIT/Biomass.jl",
    "arxiv_id": "2105.11397",
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/biomass-crnn/paper.pdf",
      "source_url": "https://hdl.handle.net/1721.1/156213",
      "version": "MIT repository copy",
      "sha256": "8fe24cba1d4d673c4588e6541fd6167d43e03686c3d91a7c5b412a66bcbfa29e",
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    "fulltext_url": "https://jiweiqi.github.io/papers/biomass-crnn/fulltext.txt",
    "repository_url": "https://hdl.handle.net/1721.1/156213"
  },
  {
    "id": "sgd-kinetics",
    "title": "SGD-based optimization in modeling combustion kinetics: Case studies in tuning mechanistic and hybrid kinetic models",
    "authors": [
      "Weiqi Ji",
      "Xingyu Su",
      "Bin Pang",
      "Yujuan Li",
      "Zhuyin Ren",
      "Sili Deng"
    ],
    "year": 2022,
    "type": "journal-article",
    "venue": "Fuel",
    "volume": "324",
    "issue": null,
    "pages": "124560",
    "doi": "10.1016/j.fuel.2022.124560",
    "topic": "sciml",
    "summary": "Uses differentiable simulation and stochastic gradient descent to optimize mechanistic and hybrid chemical kinetic models.",
    "keywords": [
      "SGD",
      "differentiable programming",
      "hybrid modeling"
    ],
    "abstract": "Chemical kinetic modeling is an integral part of combustion simulation, and extensive efforts have been devoted to developing high-fidelity yet computationally affordable models. Despite these efforts, modeling combustion kinetics is still challenging due to the demand for expert knowledge and high dimensional optimization against experiments. Therefore, data-driven approaches that enable efficient discovery and calibration of kinetic models have received much attention in recent years, the core of which is the high-dimensional optimization based on big data. Evolutionary algorithms are usually adopted for optimizing chemical kinetic models, although they usually suffer from high computational costs and are limited to a small number of parameters. Meanwhile, gradient-based optimizations, especially the stochastic gradient descent (SGD) methods, have shown success in developing complex models by training large-scale deep learning models. Therefore, this work explores the applications of SGD-based optimizations in tuning mechanistic kinetic models and learning hybrid kinetic models. We first showed that SGD-based optimizations could substantially save computational cost compared to evolutionary algorithms when the number of kinetic parameters in mechanistic models reached about one hundred. We then demonstrated that the SGD-based optimization enabled us to use a neural network model to represent the pyrolysis of the Hybrid Chemistry and optimize the associated hundreds of weights in the neural network. These proof-of-concept studies showed that the SGD-based optimization is more efficient than evolutionary algorithms, is a promising approach for developing chemical kinetic models with high dimensional parameters, and is capable of developing hybrid mechanistic-machine learning kinetic models.",
    "sources": [
      "https://doi.org/10.1016/j.fuel.2022.124560",
      "https://hdl.handle.net/1721.1/156214"
    ],
    "code_url": "https://github.com/DENG-MIT/Arrhenius.jl",
    "arxiv_id": null,
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/sgd-kinetics/paper.pdf",
      "source_url": "https://hdl.handle.net/1721.1/156214",
      "version": "MIT repository copy",
      "sha256": "96bcb12d678a1dcad35d88eccdf3ef9a41cf34674736dfcec5a8f0dea708af71",
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    "fulltext_url": "https://jiweiqi.github.io/papers/sgd-kinetics/fulltext.txt",
    "repository_url": "https://hdl.handle.net/1721.1/156214"
  },
  {
    "id": "arrhenius-jl",
    "title": "Arrhenius.jl: A Differentiable Combustion Simulation Package",
    "authors": [
      "Weiqi Ji",
      "Xingyu Su",
      "Bin Pang",
      "Séan J. Cassady",
      "Alison M. Ferris",
      "Yujuan Li",
      "Zhuyin Ren",
      "Ronald K. Hanson",
      "Sili Deng"
    ],
    "year": 2021,
    "type": "preprint",
    "venue": "arXiv",
    "volume": null,
    "issue": null,
    "pages": "",
    "doi": "10.48550/arxiv.2107.06172",
    "topic": "sciml",
    "summary": "Introduces differentiable combustion modeling in Julia for gradient-based sensitivity analysis, calibration, uncertainty quantification and model discovery.",
    "keywords": [
      "differentiable programming",
      "Julia",
      "Arrhenius.jl",
      "UQ"
    ],
    "abstract": "Combustion kinetic modeling is an integral part of combustion simulation, and extensive studies have been devoted to developing both high fidelity and computationally affordable models. Despite these efforts, modeling combustion kinetics is still challenging due to the demand for expert knowledge and optimization against experiments, as well as the lack of understanding of the associated uncertainties. Therefore, data-driven approaches that enable efficient discovery and calibration of kinetic models have received much attention in recent years, the core of which is the optimization based on big data. Differentiable programming is a promising approach for learning kinetic models from data by efficiently computing the gradient of objective functions to model parameters. However, it is often challenging to implement differentiable programming in practice. Therefore, it is still not available in widely utilized combustion simulation packages such as CHEMKIN and Cantera. Here, we present a differentiable combustion simulation package leveraging the eco-system in Julia, including DifferentialEquations.jl for solving differential equations, ForwardDiff.jl for auto-differentiation, and Flux.jl for incorporating neural network models into combustion simulations and optimizing neural network models using the state-of-the-art deep learning optimizers. We demonstrate the benefits of differentiable programming in efficient and accurate gradient computations, with applications in uncertainty quantification, kinetic model reduction, data assimilation, and model discovery.",
    "sources": [
      "https://doi.org/10.48550/arxiv.2107.06172",
      "https://arxiv.org/abs/2107.06172"
    ],
    "code_url": "https://github.com/DENG-MIT/Arrhenius.jl",
    "arxiv_id": "2107.06172",
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/arrhenius-jl/paper.pdf",
      "source_url": "https://arxiv.org/abs/2107.06172",
      "version": "Author preprint",
      "sha256": "f77d9770e2017708c176dac62259bb58d57a6884484b5983aed1272d8782540c",
      "bytes": 1149769
    },
    "fulltext_url": "https://jiweiqi.github.io/papers/arrhenius-jl/fulltext.txt"
  },
  {
    "id": "crnn",
    "title": "Autonomous Discovery of Unknown Reaction Pathways from Data by Chemical Reaction Neural Network",
    "authors": [
      "Weiqi Ji",
      "Sili Deng"
    ],
    "year": 2021,
    "type": "journal-article",
    "venue": "The Journal of Physical Chemistry A",
    "volume": "125",
    "issue": "4",
    "pages": "1082-1092",
    "doi": "10.1021/acs.jpca.0c09316",
    "topic": "sciml",
    "summary": "Infers interpretable reaction pathways and kinetic parameters from concentration time series using a neural architecture based on mass-action and Arrhenius laws.",
    "keywords": [
      "CRNN",
      "reaction discovery",
      "neural ODEs",
      "interpretable models"
    ],
    "abstract": "Chemical reactions occur in energy, environmental, biological, and many other natural systems, and the inference of the reaction networks is essential to understand and design the chemical processes in engineering and life sciences. Yet, revealing the reaction pathways for complex systems and processes is still challenging because of the lack of knowledge of the involved species and reactions. Here, we present a neural network approach that autonomously discovers reaction pathways from the time-resolved species concentration data. The proposed chemical reaction neural network (CRNN), by design, satisfies the fundamental physics laws, including the law of mass action and the Arrhenius law. Consequently, the CRNN is physically interpretable such that the reaction pathways can be interpreted, and the kinetic parameters can be quantified simultaneously from the weights of the neural network. The inference of the chemical pathways is accomplished by training the CRNN with species concentration data via stochastic gradient descent. We demonstrate the successful implementations and the robustness of the approach in elucidating the chemical reaction pathways of several chemical engineering and biochemical systems. The autonomous inference by the CRNN approach precludes the need for expert knowledge in proposing candidate networks and addresses the curse of dimensionality in complex systems. The physical interpretability also makes the CRNN capable of not only fitting the data for a given system but also developing knowledge of unknown pathways that could be generalized to similar chemical systems.",
    "sources": [
      "https://doi.org/10.1021/acs.jpca.0c09316",
      "https://arxiv.org/abs/2002.09062"
    ],
    "code_url": "https://github.com/DENG-MIT/CRNN",
    "arxiv_id": "2002.09062",
    "repository_url": "https://hdl.handle.net/1721.1/138715.2",
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/crnn/paper.pdf",
      "source_url": "https://doi.org/10.1021/acs.jpca.0c09316",
      "version": "Published version",
      "sha256": "7eed4bfc41e65ed830f2494f806aba3d31a592c6fd3e76155a4821078a87146b",
      "bytes": 4115532
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    "fulltext_url": "https://jiweiqi.github.io/papers/crnn/fulltext.txt"
  },
  {
    "id": "hychem",
    "title": "Data-Driven Approaches to Learn HyChem Models",
    "authors": [
      "Weiqi Ji",
      "Julian Zanders",
      "Ji-Woong Park",
      "Sili Deng"
    ],
    "year": 2021,
    "type": "conference-paper",
    "venue": "ASME ICEF 2021",
    "volume": null,
    "issue": null,
    "pages": "",
    "doi": "10.1115/icef2021-67925",
    "topic": "sciml",
    "summary": "Applies stochastic gradient descent to calibrate lumped HyChem fuel models against ignition-delay measurements across temperature regimes.",
    "keywords": [
      "SGD",
      "HyChem",
      "kinetic calibration",
      "jet fuels"
    ],
    "abstract": "The HyChem (Hybrid Chemistry) approach has recently been proposed for modeling high-temperature combustion of real, multi-component fuels. The approach combines lumped reaction steps for fuel thermal and oxidative pyrolysis with detailed chemistry for the oxidation of the resulting pyrolysis products. Determining the pyrolysis submodel requires extensive experimentation on speciation measurements. Recent work has been directed to learn HyChem from an existing HyChem model for a similar fuel, which requires less data. However, the approach usually shows substantial discrepancies with experimental data within the Negative Temperature Coefficient (NTC) regime, as the low-temperature chemistry is more fuel-specific than high-temperature chemistry. This paper proposes a machine learning approach to learn the HyChem models that can cover both high-temperature and low-temperature regimes. Specifically, we develop a HyChem model using the experimental datasets of ignition delay times covering a wide range of temperatures and equivalence ratios. The chemical kinetic model is treated as a neural network model, and we then employ stochastic gradient descent (SGD), a technique that was developed for deep learning, for the training. We demonstrate the approach in learning the HyChem model for F-24, which is a Jet-A derived fuel, and compare the results with previous work employing genetic algorithms. The results show that the SGD approach can achieve comparable model performance with genetic algorithms but the computational cost is reduced by 1000 times. In addition, with regularization in SGD, the SGD approach changes the kinetic parameters from their original values much less than genetic algorithm and is thus more likely to retrain mechanistic meanings. Finally, our approach is built upon open-source packages and can be applied to the development and optimization of chemical kinetic models for internal combustion engine simulations.",
    "sources": [
      "https://doi.org/10.1115/icef2021-67925",
      "https://arxiv.org/abs/2104.07875",
      "https://hdl.handle.net/1721.1/150935",
      "https://github.com/DENG-MIT/Arrhenius.jl"
    ],
    "code_url": "https://github.com/DENG-MIT/Arrhenius.jl",
    "arxiv_id": "2104.07875",
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/hychem/paper.pdf",
      "source_url": "https://hdl.handle.net/1721.1/150935",
      "version": "MIT repository copy",
      "sha256": "a5773abd62d239f1102cc6c0f66d0a3632cf5bcf57ed8c5258a82db59324a5dd",
      "bytes": 1465743
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    "fulltext_url": "https://jiweiqi.github.io/papers/hychem/fulltext.txt",
    "repository_url": "https://hdl.handle.net/1721.1/150935"
  },
  {
    "id": "cellbox-adjoint",
    "title": "Inference of cell dynamics on perturbation data using adjoint sensitivity",
    "authors": [
      "Weiqi Ji",
      "Bo Yuan",
      "Ciyue Shen",
      "Aviv Regev",
      "Chris Sander",
      "Sili Deng"
    ],
    "year": 2021,
    "type": "workshop-paper",
    "venue": "ICLR 2021 Workshop on Deep Learning for Simulation (SimDL)",
    "volume": null,
    "issue": null,
    "pages": "",
    "doi": "10.48550/arxiv.2104.06467",
    "topic": "sciml",
    "summary": "Uses adjoint sensitivity and differentiable programming to infer cell-network dynamics from simulated perturbation-response data.",
    "keywords": [
      "adjoint sensitivity",
      "CellBox",
      "network inference",
      "systems biology"
    ],
    "abstract": "Data-driven dynamic models of cell biology can be used to predict cell response to unseen perturbations. Recent work (CellBox) had demonstrated the derivation of interpretable models with explicit interaction terms, in which the parameters were optimized using machine learning techniques. While the previous work was tested only in a single biological setting, this work aims to extend the range of applicability of this model inference approach to a diversity of biological systems. Here we adapted CellBox in Julia differential programming and augmented the method with adjoint algorithms, which has recently been used in the context of neural ODEs. We trained the models using simulated data from both abstract and biology-inspired networks, which afford the ability to evaluate the recovery of the ground truth network structure. The resulting accuracy of prediction by these models is high both in terms of low error against data and excellent agreement with the network structure used for the simulated training data. While there is no analogous ground truth for real life biological systems, this work demonstrates the ability to construct and parameterize a considerable diversity of network models with high predictive ability. The expectation is that this kind of procedure can be used on real perturbation-response data to derive models applicable to diverse biological systems.",
    "sources": [
      "https://doi.org/10.48550/arxiv.2104.06467",
      "https://arxiv.org/abs/2104.06467",
      "https://simdl.github.io/papers/"
    ],
    "code_url": "https://github.com/jiweiqi/CellBox.jl",
    "arxiv_id": "2104.06467",
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/cellbox-adjoint/paper.pdf",
      "source_url": "https://arxiv.org/abs/2104.06467",
      "version": "Author preprint",
      "sha256": "c2b252c4a9f543bae78a7605dd1a741b05fcf23f706261cc30cdb010d86ef617",
      "bytes": 1045523
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    "fulltext_url": "https://jiweiqi.github.io/papers/cellbox-adjoint/fulltext.txt"
  },
  {
    "id": "kinet",
    "title": "KiNet: A Deep Neural Network Representation of Chemical Kinetics",
    "authors": [
      "Weiqi Ji",
      "Sili Deng"
    ],
    "year": 2021,
    "type": "preprint",
    "venue": "arXiv",
    "volume": null,
    "issue": null,
    "pages": "",
    "doi": "10.48550/arxiv.2108.00455",
    "topic": "sciml",
    "summary": "Represents time-stepping chemical kinetics with a residual neural network and multi-step training, with ignition-delay gradients for model refinement.",
    "keywords": [
      "KiNet",
      "neural surrogates",
      "BPTT",
      "ignition delay"
    ],
    "abstract": "Deep learning is a potential approach to automatically develop kinetic models from experimental data. We propose a deep neural network model of KiNet to represent chemical kinetics. KiNet takes the current composition states and predicts the evolution of the states after a fixed time step. The long-period evolution of the states and their gradients to model parameters can be efficiently obtained by recursively applying the KiNet model multiple times. To address the challenges of the high-dimensional composition space and error accumulation in long-period prediction, the architecture of KiNet incorporates the residual network model (ResNet), and the training employs backpropagation through time (BPTT) approach to minimize multi-step prediction error. In addition, an approach for efficiently computing the gradient of the ignition delay time (IDT) to KiNet model parameters is proposed to train the KiNet against the rich database of IDT from literature, which could address the scarcity of time-resolved species measurements. The KiNet is first trained and compared with the simulated species profiles during the auto-ignition of H2/air mixtures. The obtained KiNet model can accurately predict the auto-ignition processes for various initial conditions that cover a wide range of pressures, temperatures, and equivalence ratios. Then, we show that the gradient of IDT to KiNet model parameters is parallel to the gradient of the temperature at the ignition point. This correlation enables efficient computation of the gradient of IDT via backpropagation and is demonstrated as a feasible approach for fine-tuning the KiNet against IDT. These demonstrations shall open up the possibility of building data-driven kinetic models autonomously. Finally, the trained KiNet could be potentially applied to kinetic model reduction and chemistry acceleration in turbulent combustion simulations.",
    "sources": [
      "https://doi.org/10.48550/arxiv.2108.00455",
      "https://arxiv.org/abs/2108.00455"
    ],
    "code_url": null,
    "arxiv_id": "2108.00455",
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/kinet/paper.pdf",
      "source_url": "https://arxiv.org/abs/2108.00455",
      "version": "Author preprint",
      "sha256": "440b59a46f54285268d881956aa96e549736d4e8dccc8e107c898ef074a1e081",
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    "fulltext_url": "https://jiweiqi.github.io/papers/kinet/fulltext.txt"
  },
  {
    "id": "inverse-combustors",
    "title": "Neural Differential Equations for Inverse Modeling in Model Combustors",
    "authors": [
      "Xingyu Su",
      "Weiqi Ji",
      "Long Zhang",
      "Wantong Wu",
      "Zhuyin Ren",
      "Sili Deng"
    ],
    "year": 2021,
    "type": "conference-paper",
    "venue": "ASME IMECE 2021",
    "volume": null,
    "issue": null,
    "pages": "",
    "doi": "10.1115/imece2021-69657",
    "topic": "sciml",
    "summary": "Infers unknown inlet composition and flow fluctuations from sparse combustor-temperature measurements using neural differential equations.",
    "keywords": [
      "inverse problems",
      "neural differential equations",
      "combustor dynamics"
    ],
    "abstract": "Abstract Monitoring the dynamics processes in combustors is crucial for safe and efficient operations. However, in practice, only limited data can be obtained due to limitations in the measurable quantities, visualization window, and temporal resolution. This work proposes an approach based on neural differential equations to approximate the unknown quantities from available sparse measurements. The approach tackles the challenges of nonlinearity and the curse of dimensionality in inverse modeling by representing the dynamic signal using neural network models. In addition, we augment physical models for combustion with neural differential equations to enable learning from sparse measurements. We demonstrated the inverse modeling approach in a model combustor system by simulating the oscillation of an industrial combustor with a perfectly stirred reactor. Given the sparse measurements of the temperature inside the combustor, upstream fluctuations in compositions and/or flow rates can be inferred. Various types of fluctuations in the upstream, as well as the responses in the combustor, were synthesized to train and validate the algorithm. The results demonstrated that the approach can efficiently and accurately infer the dynamics of the unknown inlet boundary conditions, even without assuming the types of fluctuations. Those demonstrations shall open a lot of opportunities in utilizing neural differential equations for fault diagnostics and model-based dynamic control of industrial power systems.",
    "sources": [
      "https://doi.org/10.1115/imece2021-69657",
      "https://arxiv.org/abs/2107.11510",
      "https://github.com/DENG-MIT/NN-PSR"
    ],
    "code_url": "https://github.com/DENG-MIT/NN-PSR",
    "arxiv_id": "2107.11510",
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/inverse-combustors/paper.pdf",
      "source_url": "https://arxiv.org/abs/2107.11510",
      "version": "Author preprint",
      "sha256": "e018da89187861fb4c2e5620491e473997820e5b7b1db2c01678ef9f8b7fc964",
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    "fulltext_url": "https://jiweiqi.github.io/papers/inverse-combustors/fulltext.txt"
  },
  {
    "id": "stiff-neural-ode",
    "title": "Stiff neural ordinary differential equations",
    "authors": [
      "Suyong Kim",
      "Weiqi Ji",
      "Sili Deng",
      "Yingbo Ma",
      "Christopher Rackauckas"
    ],
    "year": 2021,
    "type": "journal-article",
    "venue": "Chaos: An Interdisciplinary Journal of Nonlinear Science",
    "volume": "31",
    "issue": "9",
    "pages": "093122",
    "doi": "10.1063/5.0060697",
    "topic": "sciml",
    "summary": "Studies stiff neural ODE training using scale-aware architectures, output and loss scaling, and stabilized gradient calculations.",
    "keywords": [
      "neural ODEs",
      "stiff systems",
      "differentiable simulation"
    ],
    "abstract": "Neural Ordinary Differential Equations (ODE) are a promising approach to learn dynamic models from time-series data in science and engineering applications. This work aims at learning Neural ODE for stiff systems, which are usually raised from chemical kinetic modeling in chemical and biological systems. We first show the challenges of learning neural ODE in the classical stiff ODE systems of Robertson's problem and propose techniques to mitigate the challenges associated with scale separations in stiff systems. We then present successful demonstrations in stiff systems of Robertson's problem and an air pollution problem. The demonstrations show that the usage of deep networks with rectified activations, proper scaling of the network outputs as well as loss functions, and stabilized gradient calculations are the key techniques enabling the learning of stiff neural ODE. The success of learning stiff neural ODE opens up possibilities of using neural ODEs in applications with widely varying time-scales, like chemical dynamics in energy conversion, environmental engineering, and the life sciences.",
    "sources": [
      "https://doi.org/10.1063/5.0060697",
      "https://arxiv.org/abs/2103.15341",
      "https://hdl.handle.net/1721.1/138719"
    ],
    "code_url": "https://github.com/DENG-MIT/StiffNeuralODE",
    "arxiv_id": "2103.15341",
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/stiff-neural-ode/paper.pdf",
      "source_url": "https://hdl.handle.net/1721.1/138719",
      "version": "MIT repository copy",
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    "fulltext_url": "https://jiweiqi.github.io/papers/stiff-neural-ode/fulltext.txt",
    "repository_url": "https://hdl.handle.net/1721.1/138719"
  },
  {
    "id": "stiff-pinn",
    "title": "Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics",
    "authors": [
      "Weiqi Ji",
      "Weilun Qiu",
      "Zhiyu Shi",
      "Shaowu Pan",
      "Sili Deng"
    ],
    "year": 2021,
    "type": "journal-article",
    "venue": "The Journal of Physical Chemistry A",
    "volume": "125",
    "issue": "36",
    "pages": "8098-8106",
    "doi": "10.1021/acs.jpca.1c05102",
    "topic": "sciml",
    "summary": "Examines PINN failure on stiff chemical kinetics and uses quasi-steady-state reduction to make the studied systems tractable.",
    "keywords": [
      "PINNs",
      "stiff systems",
      "QSSA",
      "chemical kinetics"
    ],
    "abstract": "The recently developed physics-informed neural network (PINN) has achieved success in many science and engineering disciplines by encoding physics laws into the loss functions of the neural network such that the network not only conforms to the measurements and initial and boundary conditions but also satisfies the governing equations. This work first investigates the performance of the PINN in solving stiff chemical kinetic problems with governing equations of stiff ordinary differential equations (ODEs). The results elucidate the challenges of utilizing the PINN in stiff ODE systems. Consequently, we employ quasi-steady-state assumption (QSSA) to reduce the stiffness of the ODE systems, and the PINN then can be successfully applied to the converted non-/mild-stiff systems. Therefore, the results suggest that stiffness could be the major reason for the failure of the regular PINN in the studied stiff chemical kinetic systems. The developed stiff-PINN approach that utilizes QSSA to enable the PINN to solve stiff chemical kinetics shall open the possibility of applying the PINN to various reaction-diffusion systems involving stiff dynamics.",
    "sources": [
      "https://doi.org/10.1021/acs.jpca.1c05102",
      "https://arxiv.org/abs/2011.04520",
      "https://hdl.handle.net/1721.1/138718"
    ],
    "code_url": "https://github.com/DENG-MIT/Stiff-PINN",
    "arxiv_id": "2011.04520",
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/stiff-pinn/paper.pdf",
      "source_url": "https://hdl.handle.net/1721.1/138718",
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    "repository_url": "https://hdl.handle.net/1721.1/138718"
  },
  {
    "id": "flamelet-subspace",
    "title": "Kinetic subspace investigation using neural network for uncertainty quantification in nonpremixed flamelets",
    "authors": [
      "Benjamin C. Koenig",
      "Weiqi Ji",
      "Sili Deng"
    ],
    "year": 2023,
    "type": "journal-article",
    "venue": "Proceedings of the Combustion Institute",
    "volume": "39",
    "issue": "4",
    "pages": "5229-5238",
    "doi": "10.1016/j.proci.2022.07.226",
    "topic": "uq",
    "summary": "Uses a neural-network surrogate to identify multidimensional kinetic subspaces for uncertainty propagation across nonpremixed flamelet profiles.",
    "keywords": [
      "active subspaces",
      "neural surrogates",
      "flamelets",
      "uncertainty quantification"
    ],
    "abstract": "Propagating uncertainties in kinetic models through turbulent combustion simulations to properly quantify the uncertainties in the simulation results remains a challenging and numerically expensive problem. Efficient approaches have been proposed for certain flames in the flamelet region by reducing their uncertainty input from a high-dimensional kinetic parameter space to a one-dimensional variable. However, this one-dimensional assumption does not apply to all flamelet regimes. In the current work, we developed a systematic approach to discover low-dimensional active subspace reductions that apply to the entire mixture fraction space of the flamelet, and that function even in cases where the uncertainty response is not uniform across the entire solution domain and the one-dimensional assumption does not apply. In doing so, we are able to achieve uncertainty quantification with a tunable tradeoff between high accuracy and low computational cost through careful selection of subspace dimensionality. We facilitated computation in this method using a specifically designed deep neural network based surrogate model to compute the temperature gradients of the flamelet profile to the kinetic parameters. We presented, as a proof-of-concept, a two-stage active subspace reduction on the kinetic parameter space of a nonpremixed methane flamelet. In doing so we demonstrated that its uncertainty response cannot be represented by a one-dimensional kinetic variable due to its uncorrelated behavior across the mixture fraction domain. We instead proposed a four-dimensional active subspace that captures 98% of the uncertainty response in the flame profile at largely reduced computational cost compared to the full kinetic parameter space. The tunability, generality, and reduced computational cost of this method demonstrate its potential to facilitate uncertainty quantification of complex and large-scale combustion problems.",
    "sources": [
      "https://doi.org/10.1016/j.proci.2022.07.226",
      "https://hdl.handle.net/1721.1/156211"
    ],
    "code_url": null,
    "arxiv_id": null,
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/flamelet-subspace/paper.pdf",
      "source_url": "https://hdl.handle.net/1721.1/156211",
      "version": "MIT repository copy",
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    "fulltext_url": "https://jiweiqi.github.io/papers/flamelet-subspace/fulltext.txt",
    "repository_url": "https://hdl.handle.net/1721.1/156211"
  },
  {
    "id": "shock-tube-bayes",
    "title": "Using shock tube species time-histories in Bayesian parameter estimation: Effective independent-data number and target selection",
    "authors": [
      "Huaibo Chen",
      "Weiqi Ji",
      "Séan J. Cassady",
      "Alison M. Ferris",
      "Ronald K. Hanson",
      "Sili Deng"
    ],
    "year": 2023,
    "type": "journal-article",
    "venue": "Proceedings of the Combustion Institute",
    "volume": "39",
    "issue": "4",
    "pages": "5299-5308",
    "doi": "10.1016/j.proci.2022.08.118",
    "topic": "uq",
    "summary": "Examines effective independent-data counts and target selection when using shock-tube species time histories for Bayesian kinetic parameter estimation.",
    "keywords": [
      "Bayesian inference",
      "parameter estimation",
      "shock tubes",
      "data correlation"
    ],
    "abstract": "Species time-histories in shock tube experiments provide rich kinetic information for parameter estimation, but there are two problems in using these data in Bayesian approaches. First, the effective independent-data number is not equal to the number of data points in a curve, so brute multiplication of all data points in likelihood function can weaken the constraints from prior information. Second, taking all points of a curve as targets can lead to results different from that of taking several representative points in the curve. In this paper, we employed maximum a posteriori estimation combined with a neural network response surface to optimize a propane mechanism against multispecies time-histories of propane pyrolysis in a shock tube. Three methods of calculating the likelihood function are used: multiplying all points in a curve (C-160), taking the averaged likelihood in each point (C-1), and taking the likelihood of last points (LastP). The influence of effective independent-data number was studied by comparing C-1 and C-160. It was found that C-160 performed slightly better in fitting experimental data, but brute multiplication overtuned the rate constants beyond a reasonable range. The larger the effective independent-data number, the more severe the overtuning, leading to only a slight improvement of model predictions. The influence of target selection is investigated by comparing LastP and C-1. LastP outperformed C-1 slightly, which can be attributed to the fact that larger discrepancies observed between experimental data and model predictions of the last point can increase the weights of likelihood functions. This further implies that several critical points can represent the entire line for point estimation. This paper can provide a reference both for modelers about reasonable utilization of species time-histories, and for experimentalists about the importance of a detailed probability distribution of measurement error, as well as experiment design with emphasis on critical points.",
    "sources": [
      "https://doi.org/10.1016/j.proci.2022.08.118",
      "https://hdl.handle.net/1721.1/156218"
    ],
    "code_url": null,
    "arxiv_id": null,
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/shock-tube-bayes/paper.pdf",
      "source_url": "https://hdl.handle.net/1721.1/156218",
      "version": "MIT repository copy",
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    "fulltext_url": "https://jiweiqi.github.io/papers/shock-tube-bayes/fulltext.txt",
    "repository_url": "https://hdl.handle.net/1721.1/156218"
  },
  {
    "id": "mechanism-reduction-uq",
    "title": "Uncertainty analysis in mechanism reduction via active subspace and transition state analyses",
    "authors": [
      "Xingyu Su",
      "Weiqi Ji",
      "Zhuyin Ren"
    ],
    "year": 2021,
    "type": "journal-article",
    "venue": "Combustion and Flame",
    "volume": "227",
    "issue": null,
    "pages": "135-146",
    "doi": "10.1016/j.combustflame.2020.12.053",
    "topic": "uq",
    "summary": "Combines active subspaces with an intermediate reduction state to separate uncertainty changes caused by parameter truncation and reaction coupling.",
    "keywords": [
      "active subspaces",
      "mechanism reduction",
      "uncertainty analysis"
    ],
    "abstract": "A systematic approach is formulated for the uncertainty analysis of kinetic parameters on combustion characteristics during skeletal reduction. The active subspace method together with sensitivity analysis is first employed to identify extreme low-dimensional active subspace of input parameter space and to facilitate the construction of response surfaces with small size of samples. An intermediate transition state during reduction is then defined such that the uncertainty change arising from uncertainty parameter truncation and reaction coupling during reduction can be decoupled and quantified. The approach is demonstrated in the reduction of a 55-species, 290-reaction dimethyl ether (DME) mechanism, with the rate constants characterized by independent lognormal distribution. Three representative skeletal mechanisms are identified for the uncertainty analysis, with each of the subsequent reduction yielding significant errors in the single-stage and/or two-stage DME-air auto-ignition process. Results show that sensitivity analysis can reduce the number of kinetic parameters from 290 down to 32, and the active subspace method can further identify a dominant active direction within this 32-dimensional subspace, which greatly facilitates the polynomial fitting for constructing the response surface of the ignition delay times. The uncertainty analysis with the polynomial chaos expansion method shows that the reduction from DME42 with 42 species to DME40 with 40 species has influential effect on the high-temperature reaction pathway; while the reduction from DME55 to DME42 and from DME40 to DME30 mainly affects the low-temperature pathway. In addition, the uncertainty change associated with parameter truncation is shown to be proportional to the change in the most active direction, which could further accelerate uncertainty analysis.",
    "sources": [
      "https://doi.org/10.1016/j.combustflame.2020.12.053",
      "https://suxy15.github.io/assets/downloads/papers/X.Su_2021_CNF.pdf",
      "https://github.com/SuXY15/CanteraUq"
    ],
    "code_url": "https://github.com/SuXY15/CanteraUq",
    "arxiv_id": null,
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/mechanism-reduction-uq/paper.pdf",
      "source_url": "https://suxy15.github.io/assets/downloads/papers/X.Su_2021_CNF.pdf",
      "version": "Published version",
      "sha256": "b54bc2135600d33f9afe1913e1adfbfa56d33e493f6fae1447c4c37c4a80723e",
      "bytes": 3344293
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    "fulltext_url": "https://jiweiqi.github.io/papers/mechanism-reduction-uq/fulltext.txt"
  },
  {
    "id": "premixed-sensitivity",
    "title": "Dependence of kinetic sensitivity direction in premixed flames",
    "authors": [
      "Weiqi Ji",
      "Tianwei Yang",
      "Zhuyin Ren",
      "Sili Deng"
    ],
    "year": 2020,
    "type": "journal-article",
    "venue": "Combustion and Flame",
    "volume": "220",
    "issue": null,
    "pages": "16-22",
    "doi": "10.1016/j.combustflame.2020.06.027",
    "topic": "uq",
    "summary": "Investigates how kinetic sensitivity directions vary through premixed flame structures and their connection to laminar flame speed and extinction.",
    "keywords": [
      "sensitivity analysis",
      "premixed flames",
      "flame speed",
      "extinction"
    ],
    "abstract": "The sensitivities of turbulent combustion simulations to chemical kinetic parameters can be analyzed to understand the controlling reactions in turbulent flames and to quantify the uncertainties in simulations. However, computing the sensitivity of turbulent combustion simulations to a large number of kinetic parameters is still challenging. A promising approach is to estimate the sensitivity from laminar flames, especially for cases where the flamelet model is applicable. Under these conditions, the underlying hypothesis is that the sensitivity direction of the flamelet profiles is independent of the strain rate and the flame coordinate, which is the progress variable for premixed flames. In the present work, this hypothesis was tested in laminar premixed counterflow flames. We first studied the sensitivity directions of two extreme cases, the near-extinction strained flames and the freely propagating unstretched flames. It was found that the sensitivity directions of the extinction strain rate and the laminar flame speed are aligned with each other for various fuels, equivalence ratios, and pressures. We then studied the dependence of the sensitivity direction of the maximum flame temperature on the strain rate as well as the dependence of the sensitivity direction of the species profiles on the progress variable. It was found that the sensitivity direction of maximum temperature was largely independent of the strain rate. Moreover, the sensitivity directions of the temperature and species profiles were independent of the progress variable, and they were all similar to the sensitivity direction of the extinction strain rate. These findings suggest that there is a universal sensitivity direction for turbulent premixed flames and the direction can be estimated by the sensitivity direction of extinction strain rate. These conclusions will enable efficient sensitivity analysis of turbulent combustion simulations when the hypothesis is valid.",
    "sources": [
      "https://doi.org/10.1016/j.combustflame.2020.06.027",
      "https://arxiv.org/abs/2001.05367"
    ],
    "code_url": null,
    "arxiv_id": "2001.05367",
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/premixed-sensitivity/paper.pdf",
      "source_url": "https://doi.org/10.1016/j.combustflame.2020.06.027",
      "version": "Published version",
      "sha256": "c78ef8ec9009fdc2860bf9c3d3626c5cd95f66b9a1dbbdc2da0d45c779d8e2cc",
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    "fulltext_url": "https://jiweiqi.github.io/papers/premixed-sensitivity/fulltext.txt"
  },
  {
    "id": "ignition-sensitivity",
    "title": "Evolution of sensitivity directions during autoignition",
    "authors": [
      "Weiqi Ji",
      "Zhuyin Ren",
      "Chung K. Law"
    ],
    "year": 2019,
    "type": "journal-article",
    "venue": "Proceedings of the Combustion Institute",
    "volume": "37",
    "issue": "1",
    "pages": "807-815",
    "doi": "10.1016/j.proci.2018.07.005",
    "topic": "uq",
    "summary": "Relates the sensitivity directions of temperature, species and ignition delay, enabling efficient evaluation of ignition-delay sensitivities.",
    "keywords": [
      "sensitivity analysis",
      "ignition delay",
      "chemical kinetics"
    ],
    "abstract": "Sensitivity analysis of the ignition delay time and species profiles to kinetic parameters has been widely used to identify the rate-limiting steps during the autoignition process, providing insights for the optimization of the reaction mechanism. This work studies the time evolution of the sensitivity directions of the temperature and species concentration during autoignition. The direction is represented by a unit vector along the gradient of the simulation output to the kinetic parameters, and the alignment between the two directions are measured by the inner product between the corresponding unit vectors. We use evolution of the sensitivity directions to reveal changes in the rate-limiting steps and the correlation among species at different phases of the ignition delay period. It is found that the sensitivity directions of temperature and the concentrations of the major intermediate species are similar to each other during the entire ignition delay period. In particular, they converge to the same direction when approaching the ignition state, and the direction is the same as the one for the ignition delay time. The correlation is validated for various fuels across a wide range of pressures and temperatures, and works for both single-stage ignition and two-stage ignition. Consequently the sensitivity of the ignition delay time can be efficiently evaluated based on the temperature sensitivity at the ignition point, for which a single run of the simulation can produce the sensitivity to all parameters, as otherwise the sensitivity of the ignition delay time has to be evaluated through finite difference, in which the number of runs equals to the number of parameters. It can also significantly reduce the computation cost of gradient-based algorithms for the purpose of mechanism optimization and uncertainty quantification.",
    "sources": [
      "https://doi.org/10.1016/j.proci.2018.07.005",
      "https://collaborate.princeton.edu/en/publications/evolution-of-sensitivity-directions-during-autoignition/"
    ],
    "code_url": "https://github.com/jiweiqi/IgnSens",
    "arxiv_id": null,
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/ignition-sensitivity/paper.pdf",
      "source_url": "https://doi.org/10.1016/j.proci.2018.07.005",
      "version": "Published version",
      "sha256": "d5fa307e302f459e5bc0cce1d44333d1109b04a53af251dffa99b1092159becb",
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    "fulltext_url": "https://jiweiqi.github.io/papers/ignition-sensitivity/fulltext.txt"
  },
  {
    "id": "turbulent-uq",
    "title": "Quantifying kinetic uncertainty in turbulent combustion simulations using active subspaces",
    "authors": [
      "Weiqi Ji",
      "Zhuyin Ren",
      "Youssef Marzouk",
      "Chung K. Law"
    ],
    "year": 2019,
    "type": "journal-article",
    "venue": "Proceedings of the Combustion Institute",
    "volume": "37",
    "issue": "2",
    "pages": "2175-2182",
    "doi": "10.1016/j.proci.2018.06.206",
    "topic": "uq",
    "summary": "Uses active subspaces and response surfaces to propagate kinetic uncertainty to the liftoff height of a turbulent Cabra hydrogen jet flame.",
    "keywords": [
      "active subspaces",
      "turbulent combustion",
      "uncertainty propagation"
    ],
    "abstract": "Uncertainty quantification in expensive turbulent combustion simulations usually adopts response surface techniques to accelerate Monte Carlo sampling. However, it is computationally intractable to build response surfaces for high-dimensional kinetic parameters. We employ the active subspaces approach to reduce the dimension of the parameter space, such that building a response surface on the resulting low-dimensional subspace requires many fewer runs of the expensive simulation, rendering the approach suitable for various turbulent combustion models. We demonstrate this approach in simulations of the Cabra H 2 /N 2 jet flame, propagating the uncertainties of 21 kinetic parameters to the liftoff height. We identify a one-dimensional active subspace for the liftoff height using 84 runs of the simulations, from which a response surface with a one-dimensional input is built; the probability distribution of the liftoff height is then characterized by evaluating a large number of samples using the inexpensive response surface. In addition, the active subspace provides a global sensitivity metric for determining the most influential reactions. Comparison with autoignition tests reveals that the sensitivities to the HO 2 -related reactions in the Cabra flame are promoted by the diffusion processes. The present work demonstrates the capability of active subspaces in quantifying uncertainty in turbulent combustion simulations and provides physical insights into the flame via the active subspace-based sensitivity metric.",
    "sources": [
      "https://doi.org/10.1016/j.proci.2018.06.206",
      "https://hdl.handle.net/1721.1/126335",
      "https://github.com/DENG-MIT/ArrheniusActiveSubspace"
    ],
    "code_url": null,
    "arxiv_id": null,
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/turbulent-uq/paper.pdf",
      "source_url": "https://hdl.handle.net/1721.1/126335",
      "version": "MIT repository copy",
      "sha256": "c0237384bdd1920d8aa5633805e42105066b967e0f0b935d4b20dfeb893990c5",
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    "fulltext_url": "https://jiweiqi.github.io/papers/turbulent-uq/fulltext.txt",
    "repository_url": "https://hdl.handle.net/1721.1/126335",
    "related_code_url": "https://github.com/DENG-MIT/ArrheniusActiveSubspace"
  },
  {
    "id": "neural-network-uq",
    "title": "Uncertainty Propagation in Deep Neural Network Using Active Subspace",
    "authors": [
      "Weiqi Ji",
      "Zhuyin Ren",
      "Chung K. Law"
    ],
    "year": 2019,
    "type": "preprint",
    "venue": "arXiv",
    "volume": null,
    "issue": null,
    "pages": "",
    "doi": "10.48550/arxiv.1903.03989",
    "topic": "uq",
    "summary": "Builds response surfaces in gradient-based active subspaces to propagate uncertain neural-network inputs at reduced computational cost.",
    "keywords": [
      "active subspaces",
      "neural networks",
      "input uncertainty",
      "surrogate models"
    ],
    "abstract": "The inputs of deep neural network (DNN) from real-world data usually come with uncertainties. Yet, it is challenging to propagate the uncertainty in the input features to the DNN predictions at a low computational cost. This work employs a gradient-based subspace method and response surface technique to accelerate the uncertainty propagation in DNN. Specifically, the active subspace method is employed to identify the most important subspace in the input features using the gradient of the DNN output to the inputs. Then the response surface within that low-dimensional subspace can be efficiently built, and the uncertainty of the prediction can be acquired by evaluating the computationally cheap response surface instead of the DNN models. In addition, the subspace can help explain the adversarial examples. The approach is demonstrated in MNIST datasets with a convolutional neural network. Code is available at: https://github.com/jiweiqi/nnsubspace.",
    "sources": [
      "https://doi.org/10.48550/arxiv.1903.03989",
      "https://arxiv.org/abs/1903.03989"
    ],
    "code_url": "https://github.com/jiweiqi/nnsubspace",
    "arxiv_id": "1903.03989",
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/neural-network-uq/paper.pdf",
      "source_url": "https://arxiv.org/abs/1903.03989",
      "version": "Author preprint",
      "sha256": "8db67d80315f39b2e8d92029673e8eafd6db065d8bc929bd2cb1f22fd9b1eafe",
      "bytes": 446223
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    "fulltext_url": "https://jiweiqi.github.io/papers/neural-network-uq/fulltext.txt"
  },
  {
    "id": "shared-subspaces",
    "title": "Shared low-dimensional subspaces for propagating kinetic uncertainty to multiple outputs",
    "authors": [
      "Weiqi Ji",
      "Jiaxing Wang",
      "Olivier Zahm",
      "Youssef M. Marzouk",
      "Bin Yang",
      "Zhuyin Ren",
      "Chung K. Law"
    ],
    "year": 2018,
    "type": "journal-article",
    "venue": "Combustion and Flame",
    "volume": "190",
    "issue": null,
    "pages": "146-157",
    "doi": "10.1016/j.combustflame.2017.11.021",
    "topic": "uq",
    "summary": "Combines single-output active subspaces into a shared low-dimensional representation for propagating kinetic uncertainty to multiple quantities of interest.",
    "keywords": [
      "active subspaces",
      "dimension reduction",
      "multiple outputs",
      "HCCI"
    ],
    "abstract": "Forward propagation of kinetic uncertainty in combustion simulations usually adopts response surface techniques to accelerate Monte Carlo sampling. Yet it is computationally challenging to build response surfaces for high-dimensional input parameters and expensive combustion models. This study uses the active subspace method to identify a low-dimensional subspace of the input space, within which response surfaces can be built. Active subspace methods have previously been developed only for single (scalar) model outputs, however. This paper introduces a new method that can simultaneously approximate the marginal probability density functions of multiple outputs using a single low-dimensional shared subspace. We identify the shared subspace by solving a least-squares system to compute an appropriate combination of single-output active subspaces. Because the identification of the active subspace for each individual output may require a significant number of samples, this process may be computationally intractable for expensive models such as turbulent combustion simulations. Instead, we propose a heuristic approach that learns the relevant subspaces from cheaper combustion models. The performance of the active subspace for a single output, and of the shared subspace for multiple outputs, is first demonstrated with the ignition delay times and laminar flame speeds of hydrogen/air, methane/air, and dimethyl ether (DME)/air mixtures. Then we demonstrate extrapolatory performance of the shared subspace: using a shared subspace trained on the ignition delays at constant volume, we perform forward propagation of kinetic uncertainties through zero-dimensional HCCI simulations—in particular, single-stage ignition of a natural gas/air mixture and two-stage ignition of a DME/air mixture. We show that the shared subspace can accurately reproduce the probability of ignition failure and the probability density of ignition crank angle conditioned on successful ignition, given uncertainty in the kinetics.",
    "sources": [
      "https://doi.org/10.1016/j.combustflame.2017.11.021",
      "https://uqgroup.mit.edu/publications/",
      "https://github.com/DENG-MIT/ArrheniusActiveSubspace"
    ],
    "code_url": null,
    "arxiv_id": null,
    "related_code_url": "https://github.com/DENG-MIT/ArrheniusActiveSubspace"
  },
  {
    "id": "surrogate-subspace",
    "title": "Propagation of Kinetic Uncertainty through Surrogate Subspace in Combustion Simulations",
    "authors": [
      "Weiqi Ji",
      "Jiaxing Wang",
      "Bin Yang",
      "Zhuyin Ren",
      "Chung K. Law"
    ],
    "year": 2017,
    "type": "conference-paper",
    "venue": "10th U.S. National Combustion Meeting",
    "volume": null,
    "issue": null,
    "pages": null,
    "doi": null,
    "topic": "uq",
    "summary": "Explores a low-rank surrogate subspace for propagating kinetic uncertainty, using neural response surfaces and genetic optimization.",
    "keywords": [
      "surrogate subspaces",
      "uncertainty propagation",
      "dimension reduction"
    ],
    "abstract": "",
    "sources": [
      "https://www.researchgate.net/publication/321028260_Propagation_of_Kinetic_Uncertainty_through_Surrogate_Subspace_in_Combustion_Simulations",
      "https://rotavera.uga.edu/Documents/Program-a.pdf",
      "https://orcid.org/0000-0002-7097-0219"
    ],
    "code_url": null,
    "arxiv_id": null
  },
  {
    "id": "machine-learning-combustion",
    "title": "Machine learning for combustion",
    "authors": [
      "Lei Zhou",
      "Yuntong Song",
      "Weiqi Ji",
      "Haiqiao Wei"
    ],
    "year": 2022,
    "type": "journal-article",
    "venue": "Energy and AI",
    "volume": "7",
    "issue": null,
    "pages": "100128",
    "doi": "10.1016/j.egyai.2021.100128",
    "topic": "applications",
    "summary": "Reviews machine-learning approaches to combustion modeling, experiments and computational prediction.",
    "keywords": [
      "review",
      "machine learning",
      "combustion"
    ],
    "abstract": "Combustion science is an interdisciplinary study that involves nonlinear physical and chemical phenomena in time and length scales, including complex chemical reactions and fluid flows. Combustion widely supplies energy for powering vehicles, heating houses, generating electricity, cooking food, etc. The key to study combustion is to improve the combustion efficiency with minimum emission of pollutants. Machine learning facilitates data-driven techniques for handling large amounts of combustion data, either obtained through experiments or simulations under multiple spatiotemporal scales, thereby finding the hidden patterns underlying these data and promoting combustion research. This work presents an overview of studies on the applications of machine learning in combustion science fields over the past several decades. We introduce the fundamentals of machine learning and its usage in aiding chemical reactions, combustion modeling, combustion measurement, engine performance prediction and optimization, and fuel design. The opportunities and limitations of using machine learning in combustion studies are also discussed. This paper aims to provide readers with a portrait of what and how machine learning can be used in combustion research and to inspire researchers in their ongoing studies. Machine learning techniques are rapidly advancing in this era of big data, and there is high potential for exploring the combination between machine learning and combustion research and achieving remarkable results.",
    "sources": [
      "https://doi.org/10.1016/j.egyai.2021.100128"
    ],
    "code_url": null,
    "arxiv_id": null
  },
  {
    "id": "mobility-demand",
    "title": "Machine learning model to project the impact of COVID-19 on US motor gasoline demand",
    "authors": [
      "Shiqi Ou",
      "Xin He",
      "Weiqi Ji",
      "Wei Chen",
      "Lang Sui",
      "Yu Gan",
      "Zifeng Lu",
      "Zhenhong Lin",
      "Sili Deng",
      "Steven Przesmitzki",
      "Jessey Bouchard"
    ],
    "year": 2020,
    "type": "journal-article",
    "venue": "Nature Energy",
    "volume": "5",
    "issue": "9",
    "pages": "666-673",
    "doi": "10.1038/s41560-020-0662-1",
    "topic": "applications",
    "summary": "Combines pandemic scenarios, mobility data and machine learning to project US motor-gasoline demand during COVID-19.",
    "keywords": [
      "machine learning",
      "energy demand",
      "mobility",
      "scenario analysis"
    ],
    "abstract": "Owing to the global lockdowns that resulted from the COVID-19 pandemic, fuel demand plummeted and the price of oil futures went negative in April 2020. Robust fuel demand projections are crucial to economic and energy planning and policy discussions. Here we incorporate pandemic projections and people’s resulting travel and trip activities and fuel usage in a machine-learning-based model to project the US medium-term gasoline demand and study the impact of government intervention. We found that under the reference infection scenario, the US gasoline demand grows slowly after a quick rebound in May, and is unlikely to fully recover prior to October 2020. Under the reference and pessimistic scenario, continual lockdown (no reopening) could worsen the motor gasoline demand temporarily, but it helps the demand recover to a normal level quicker. Under the optimistic infection scenario, gasoline demand will recover close to the non-pandemic level by October 2020.",
    "sources": [
      "https://doi.org/10.1038/s41560-020-0662-1",
      "https://hdl.handle.net/1721.1/130586"
    ],
    "code_url": "https://github.com/jiweiqi/covid19-mobility",
    "arxiv_id": null,
    "correction_url": "https://doi.org/10.1038/s41560-020-00711-7",
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/mobility-demand/paper.pdf",
      "source_url": "https://hdl.handle.net/1721.1/130586",
      "version": "MIT repository copy",
      "sha256": "743623bff527d210650176f1e8e59156ae9ed90b0477d2204cee009ffd89dd44",
      "bytes": 1346516
    },
    "fulltext_url": "https://jiweiqi.github.io/papers/mobility-demand/fulltext.txt",
    "repository_url": "https://hdl.handle.net/1721.1/130586"
  },
  {
    "id": "naphtha-ignition",
    "title": "Ignition delay measurements of light naphtha: A fully blended low octane fuel",
    "authors": [
      "Tamour Javed",
      "Ehson F. Nasir",
      "Ahfaz Ahmed",
      "Jihad Badra",
      "Khalil Djebbi",
      "Mohamed Beshir",
      "Weiqi Ji",
      "S. Mani Sarathy",
      "Aamir Farooq"
    ],
    "year": 2017,
    "type": "journal-article",
    "venue": "Proceedings of the Combustion Institute",
    "volume": "36",
    "issue": "1",
    "pages": "315-322",
    "doi": "10.1016/j.proci.2016.05.043",
    "topic": "kinetics",
    "summary": "Measures ignition delays of a fully blended low-octane light naphtha fuel.",
    "keywords": [
      "ignition delay",
      "naphtha",
      "fuel kinetics"
    ],
    "abstract": "",
    "sources": [
      "https://doi.org/10.1016/j.proci.2016.05.043"
    ],
    "code_url": null,
    "arxiv_id": null
  },
  {
    "id": "rcm-rate-constants",
    "title": "Measurement of reaction rate constants using RCM: A case study of decomposition of dimethyl carbonate to dimethyl ether",
    "authors": [
      "Peng Zhang",
      "Shuang Li",
      "Yingdi Wang",
      "Weiqi Ji",
      "Wenyu Sun",
      "Bin Yang",
      "Xin He",
      "Zhi Wang",
      "Chung K. Law",
      "Feng Zhang"
    ],
    "year": 2017,
    "type": "journal-article",
    "venue": "Combustion and Flame",
    "volume": "183",
    "issue": null,
    "pages": "30-38",
    "doi": "10.1016/j.combustflame.2017.05.006",
    "topic": "kinetics",
    "summary": "Studies rapid-compression-machine measurement of a reaction rate using dimethyl carbonate decomposition as a case study.",
    "keywords": [
      "reaction rates",
      "RCM",
      "dimethyl carbonate"
    ],
    "abstract": "",
    "sources": [
      "https://doi.org/10.1016/j.combustflame.2017.05.006"
    ],
    "code_url": null,
    "arxiv_id": null
  },
  {
    "id": "ntc-lower-turnover",
    "title": "On the crossover temperature and lower turnover state in the NTC regime",
    "authors": [
      "Weiqi Ji",
      "Peng Zhao",
      "Peng Zhang",
      "Zhuyin Ren",
      "Xin He",
      "Chung K. Law"
    ],
    "year": 2017,
    "type": "journal-article",
    "venue": "Proceedings of the Combustion Institute",
    "volume": "36",
    "issue": "1",
    "pages": "343-353",
    "doi": "10.1016/j.proci.2016.05.046",
    "topic": "kinetics",
    "summary": "Investigates crossover temperature and the lower turnover state of negative-temperature-coefficient ignition behavior.",
    "keywords": [
      "NTC",
      "autoignition",
      "reaction pathways"
    ],
    "abstract": "",
    "sources": [
      "https://doi.org/10.1016/j.proci.2016.05.046"
    ],
    "code_url": null,
    "arxiv_id": null
  },
  {
    "id": "first-stage-ntc",
    "title": "First-stage ignition delay in the negative temperature coefficient behavior: Experiment and simulation",
    "authors": [
      "Peng Zhang",
      "Weiqi Ji",
      "Tanjin He",
      "Xin He",
      "Zhi Wang",
      "Bin Yang",
      "Chung K. Law"
    ],
    "year": 2016,
    "type": "journal-article",
    "venue": "Combustion and Flame",
    "volume": "167",
    "issue": null,
    "pages": "14-23",
    "doi": "10.1016/j.combustflame.2016.03.002",
    "topic": "kinetics",
    "summary": "Combines experiments and simulations to investigate negative-temperature-coefficient behavior in first-stage ignition delay.",
    "keywords": [
      "two-stage ignition",
      "NTC",
      "RCM"
    ],
    "abstract": "",
    "sources": [
      "https://doi.org/10.1016/j.combustflame.2016.03.002"
    ],
    "code_url": null,
    "arxiv_id": null
  },
  {
    "id": "ntc-upper-turnover",
    "title": "On the controlling mechanism of the upper turnover states in the NTC regime",
    "authors": [
      "Weiqi Ji",
      "Peng Zhao",
      "Tanjin He",
      "Xin He",
      "Aamir Farooq",
      "Chung K. Law"
    ],
    "year": 2016,
    "type": "journal-article",
    "venue": "Combustion and Flame",
    "volume": "164",
    "issue": null,
    "pages": "294-302",
    "doi": "10.1016/j.combustflame.2015.11.028",
    "topic": "kinetics",
    "summary": "Studies the kinetic mechanisms controlling the upper turnover states in the negative-temperature-coefficient regime.",
    "keywords": [
      "NTC",
      "autoignition",
      "chemical kinetics"
    ],
    "abstract": "Using n-butane, n-heptane and iso-octane as representative fuels exhibiting NTC (negative temperature coefficient) behavior, comprehensive computational studies with detailed mechanisms and theoretical analysis were performed to investigate the upper stationary point, denoted as turnover states, on the NTC curve near the higher temperature regime, where the ignition delay τ exhibits a local maximum. It is found that the global behavior of the turnover states exhibits distinctive thermodynamic and kinetic characteristics under different pressures, in that the ignition delay at the turnover states shows an Arrhenius dependence on the temperature T and an approximate inverse quadratic power law dependence on the pressure P. These global behaviors imply that the temperature and pressure of the turnover states are not independent and can be correlated by an Arrhenius dependence, as ln P ∝ 1/T. Further theoretical analyses demonstrate that such turnover states result from the competition between the low-temperature chain branching reactions and the decomposition of the intermediate species, and therefore correspond to a critical value, α, of the ratio of OH production from low-temperature chemistry. In addition, the ignition delay at the turnover state can be well correlated by the analytical expression derived by Peters et al., with the further demonstration that the pressure dependence of the turnover ignition delay mainly result from the H2O2 decomposition reaction. Comparison of the present results with the literature experimental data of n-heptane ignition delay time shows very good agreement.",
    "sources": [
      "https://doi.org/10.1016/j.combustflame.2015.11.028",
      "https://www.osti.gov/biblio/1249644"
    ],
    "code_url": null,
    "arxiv_id": null,
    "pdf": {
      "url": "https://jiweiqi.github.io/papers/ntc-upper-turnover/paper.pdf",
      "source_url": "https://www.osti.gov/biblio/1249644",
      "version": "Repository manuscript",
      "sha256": "1e6b0d9fd1c12e92e7c1f0a8f06be88be10983976d3babf9acdd240591689f07",
      "bytes": 5277652
    },
    "fulltext_url": "https://jiweiqi.github.io/papers/ntc-upper-turnover/fulltext.txt"
  },
  {
    "id": "isobutanol-intermediates",
    "title": "Intermediate species measurement during iso-butanol auto-ignition",
    "authors": [
      "Weiqi Ji",
      "Peng Zhang",
      "Tanjin He",
      "Zhi Wang",
      "Ling Tao",
      "Xin He",
      "Chung K. Law"
    ],
    "year": 2015,
    "type": "journal-article",
    "venue": "Combustion and Flame",
    "volume": "162",
    "issue": "10",
    "pages": "3541-3553",
    "doi": "10.1016/j.combustflame.2015.06.010",
    "topic": "kinetics",
    "summary": "Measures intermediate species during iso-butanol autoignition to examine the underlying oxidation pathways.",
    "keywords": [
      "iso-butanol",
      "species measurements",
      "autoignition"
    ],
    "abstract": "",
    "sources": [
      "https://doi.org/10.1016/j.combustflame.2015.06.010"
    ],
    "code_url": "https://github.com/jiweiqi/Isobutanol_Mechanism",
    "arxiv_id": null
  }
]