Machine learning model to project the impact of COVID-19 on
U.S. motor gasoline demand
Shiqi Oua, Xin Heb *, Weiqi Jic, Wei Chend, Lang Suib, Yu Gane, Zifeng Lue, Zhenhong Lina, Sili
Dengc, Steven Przesmitzkib, Jessey Bouchardb
a. Energy and Transportation Science Division, Oak Ridge National Laboratory. 2360 Cherahala Blvd,
Knoxville, Tennessee 37932, USA.
b. Aramco Services Company: Aramco Research Center – Detroit, 46535 Peary Ct, Novi, Michigan 48377,
USA.
c. Department of Mechanical Engineering, Massachusetts Institute of Technology. 77 Massachusetts
Avenue, Cambridge, Massachusetts 02139, USA.
d. Michigan Department of Transportation. 18101 W Nine Mile Rd., Southfield, MI 48075, USA.
e. Energy Systems Division, Argonne National Laboratory, Lemont, Illinois 60439, USA.
*

Corresponding Author; xin.he@aramcoamericas.com, ORCID: 0000-0003-2492-4454

Citation:
Ou, S., He, X., Ji, W. et al. Machine learning model to project the impact of
COVID-19 on US motor gasoline demand. Nature Energy (2020): 1-8.
https://doi.org/10.1038/s41560-020-0662-1

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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.

Keywords: Gasoline demand, Projection, COVID-19 pandemic, Mobility behaviors, Machine
Learning

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Introduction
Since December 2019, the infectious coronavirus disease 2019 (COVID-19) quickly swept the
world and reached pandemic status in just a few months 1,2. Of the over 7.5 million cases
reported worldwide, about 25% are in the United States (U.S.), making it the country with the
largest number of confirmed cases in the world so far 3. Bendavid et al.(2020) implies that the
actual infections could be more widespread than indicated by the number of confirmed cases 4.
To cope with the pandemic, public health policies were implemented to slow the spread of
COVID-19 by “flattening the curve” using “stay-at-home” policies. The unanticipated reduction
in mobility, and therefore fuel demand, resulted in a glut of oil in the market and the West
Texas Intermediate oil price plunged to an unprecedented negative value in April 2020 5,6. For
the oil market, the U.S. is one of the largest energy consumers and oil producers in the world.
Fluctuations and uncertainties in U.S. oil consumption impacts the petroleum supply chain and
trends of the broader energy economy 7. Beyond temporary and local oil price and demand
shocks, U.S. gasoline demand alone is significant enough to impact longer-term investments in
the global energy industry, which impacts the world economy as a whole.
While the value of oil has somewhat recovered since April, uncertainties in the U.S.
economy persist because of the lingering pandemic. The International Monetary Fund
estimated the annual change in real Gross Domestic Product (GDP) in the U.S. could be -5.9% in
2020 and the global economy could contract by 3%. To effectively reduce uncertainties,
multiple models were developed by researchers to project the trend of the COVID-19 pandemic
8. Projections of the evolution of COVID-19 pandemic trends show that lock-downs help reduce
COVID-19 transmissions by 90% compared to the baseline in Austin, TX 9. However, this
unprecedented phenomenon could last for a few years: Kissler et al. (2020) suggested that,
even after the pandemic peaked, COVID-19 surveillance should be continued since a resurgence
in contagion could be possible as late as 2024 8. Therefore, beyond immediate economic
responses, the longer-term impact on the U.S. economy may persist well beyond 2020.
Therefore, an effective forecast or estimate of the pandemic impacts could help people well
prepare and navigate around unknown risks. More specifically, reliably projecting the oil
demand, a critical leading indicator of the state of the U.S. economy, is beneficial to related
business activities and investment decisions.
There are studies that discuss the impacts of unexpected natural hazards/disasters on
energy demand/consumption 10,11, or studies that evaluate impacts of occurred pandemic on
tourism 12 and economics 13. However, few studies have quantified and forecasted the oil
demands under multiple pandemic scenarios, and this research is desperately needed. To date,
studies focused on energy impacts of COVID-19 pandemic are limited to the short-term Energy
Outlook released by the U.S. Energy Information Administration (EIA); this outlook uses a

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simplified evolution of COVID-19 pandemic to forecast the U.S. GDP, energy supplies, demands
and prices until the fourth quarter of 2021 14. In this work, we develop a model that combines
personal mobility with motor gasoline demand and uses a neural network to correlate personal
mobility with the evolution of the COVID-19 pandemic, the government policies, and the
demographic information.
In this study we extend the understanding of the COVID-19 impact on medium-term fuel
demand as the pandemic evolves. This would be useful to both policy makers and stakeholders
in balancing the COVID-19 spread and economic recovery. Some key findings are: under the
reference infection scenario, the growth of motor gasoline demand in the U.S. is slow after a
quick rebound in May, and it is unlikely that demand will recover to a non-pandemic level prior
to October 2020; under both the reference and pessimistic infection scenarios, a continual
lockdown (no-reopening) policy could worsen the motor gasoline demand temporarily, but it
helps the demand recover to a normal level quicker due to its impact on infection rate; under
the optimistic infection scenario, the projected trend of motor gasoline demand will recover to
about 95% of the non-pandemic gasoline level (almost fully recover) by late September 2020;
however, under the pessimistic infection scenario, the second wave of infections in mid-June to
August could significantly lower the gasoline demand once more, but it will not be worse than it
was in April. These results imply that government intervention, and its impact on infection rate,
does influence infection rate which thereby impacts mobility and fuel demand.

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Mobility and Pandemic
A result of policies aimed at “flattening the curve” is an unprecedented restriction to mobility.
Beginning in March and through April, at least 316 million people in the U.S. lived in regions
with some form of stay-at-home policy 15. U.S. Department of Transportation data shows travel
on all roads and streets in March 2020 decreased by 18.6%, an equivalent of 50.6 billion fewer
vehicle miles compared with travel in March 2019 16. Subsequently, U.S. on-road transportation
fuel consumption in April 2020 was 30% lower than it was in April 2019 17.
Widespread availability of personal mobile devices has allowed us to quantitatively measure
people’s confinement. Since the onset of the pandemic, Google and Apple released mobility
reports or webpages using aggregated map data to help better quantify the correlation
between reduction in mobility and the spread of COVID-19 18–20. Figure 1(a)-(c) shows changes
in mobility in the U.S. reported by Google for the period between February 15 and June 4, 2020
for work, retail and recreation, and grocery and pharmacy 18. The U.S. shutdown policies are
governed at the state or more localized levels instead of a federal level, and there is
considerable variation of mobility decrease among states. Although all three categories
experience widespread decrease in mobility starting March 26, at the onset of many stay-athome orders, the decrease is heterogeneous across the states and categories. Figure 1(d)
shows the 7-day average for daily COVID-19 cases and deaths during the same period 21.
Although the daily number of cases of COVID-19 increased between March 16 and April 20,
during a period of which much of the country was shut down, this increase is primarily due to
the long incubation period of COVID-19 22. Likewise, an increase in the daily number of deaths
occurred roughly two weeks after confirmed cases. The data clearly shows that the changes in
mobility and pandemic data are highly non-linear. A sharp change in mobility is observed in the
first two weeks after the pandemic reaches a threshold, then mobility plateaus and becomes
insensitive to further increases in confirmed cases or deaths. We conduct a detailed correlation
analysis between mobility and pandemic data to identify the key parameters being considered
in the model development. The results of the correlation analysis are presented in
Supplementary Figure 1 and Supplementary Note 1.
Since the change in mobility implies the change in vehicle miles traveled (VMT), the mobility
data provides a solid foundation to analyze the fuel demand change in each travel category.
This also means that a reliable fuel demand projection model can be created if the future
mobility can be predicted based on the projected evolution of the pandemic.

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Figure 1. Changes in mobility in various sectors and number of cases. Percentage changes in Google
mobility between February 15 and June 4, 2020 for (a) workplaces; (b) grocery and pharmacy; (c) retail
and recreations 18. (d) 7-day average of the number of COVID-19 cases and deaths in the U.S. 3 Please
note the boxplots represent the interquartile range (IQR) where the lower and upper whiskers represent
1.5×IQR. Each yellow data point represents the mobility of outlier states that do not fall into the
1.5xIQR.

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Pandemic Oil Demand Analysis (PODA) Model
Motor gasoline is the main U.S. transportation fuel, accounting for about 58% of total
transportation sector energy consumption and 45% of total petroleum consumption 23. In this
work, a machine-learning based PODA model is developed to project the U.S. gasoline demand
using COVID-19 pandemic data, government policies, and demographic information. As shown
in Figure 2, the model contains two major modules: a Mobility Dynamic Index Forecast Module
and a Motor Gasoline Demand Estimation Module. The Mobility Dynamic Index Forecast
Module identifies the changes in travel mobility caused by the evolution of COVID-19 pandemic
and government orders, and it projects the changes in travel mobility indices relative to the
pre-COVID-19 period in the U.S. Notably, the change in travel mobility, which affects the
frequency of human contact or the level of social distancing, can reciprocally impact the
evolution of the pandemic to some extent, as the black dashed line shows in Figure 2. The
Motor Gasoline Demand Estimation Module estimates VMT on pandemic days while
considering the dynamic indices of travel mobility, and it quantifies motor gasoline demands by
coupling the gasoline demands and VMT. The neural network model, which is the core of the
PODA model, has 42 inputs, 2 layers, and 25 hidden nodes for each layer, with rectified linear
units as the activation function (see the “Methods” section for details). The data sets used for
model training, calibration, and validation are provided in Supplementary Note 2. In the PODA
model, the potential induced travel demand due to the lower oil prices under the COVID-19
pandemic is not explicitly considered.

Figure 2. The structure of the PODA model.

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The pandemic data used to project future motor gasoline demand is taken from the
Youyang Gu (YYG) COVID-19 projection model, which is one of few models referenced by the
U.S. Centers for Disease Control and Prevention (CDC) that offers a medium-term (threemonth) forecast of infections and deaths for each state under multiple scenarios 8,24. The model
is updated daily providing new projections for the next three months. The YYG model generates
three new infection cases (mean, lower, and upper) under a 95% confidence interval and
uncertainties. Therefore, we divide our study into three scenarios that align with these
projections: reference (mean), optimistic (lower) and pessimistic (upper). In addition, the
pandemic data forecasted by the MIT model 8,25 is used to project the gasoline demand, which
is compared against the projection based on inputs from the YYG model. The details of these
scenarios are provided in Supplementary Note 3 and Supplementary Figures 5-7. We also
provide the fuel demand of the “Non-pandemic” scenario for comparison. For this scenario, we
use the four-year average from 2016 to 2019 to reflect the seasonal change in gasoline demand
(see Supplementary Figures 8 and 9 for details).

Projections of Motor Gasoline Demand Under COVID-19 Pandemic
Figure 3 shows U.S. motor gasoline demand projections and state-level mobility projections up
to September 21, 2020 under the reference pandemic scenario. The historical mobility and
gasoline demand data for simulation in the model is from March 1 to June 5, and the pandemic
data is from the YYG model projection as of June 10, 2020. Shown in Figure 3 the projected
motor gasoline demands from the PODA model fit well with the historical motor gasoline
demand from EIA as of June 5, 2020. As the reopening was successively implemented by states,
the U.S. motor gasoline demand gradually recovered from its low point during the first weeks of
April. By the week of June 5, 2020, the gasoline demand reached 7.9 million barrels per day
(BPD), growing nearly 56% compared to the April 3 low point 17.
This study adopts the mobility trend data from Google 18 into the PODA model for
projecting future motor gasoline demand, and uses the mobility data from Apple 19 as inputs for
projected fuel demand comparison. The value deviations between the projected motor gasoline
demands based on mobility trends from these two data sources are shown in Figure 3. For
predictions after May, the projected gasoline demands based on Apple mobility data tend to be
about 10% higher than the projections based on Google mobility data. Thus, though the
mobility trends from Google and Apple are estimated using different methodologies—Google
estimates mobility using location and visit duration data 18, and Apple uses route map requests
19—these collection methods have a relatively limited effect on the projected motor gasoline
demand. However, the Apple mobility data offers only the aggregated changes of mobility,
which do not differentiate mobility among detailed trip activities/purposes and may not well
represent some trip categories. Therefore, the gasoline demand projections based on Apple

8

mobility data could result in a larger error. As a result, this study uses the inputs from Google
mobility data for projection and scenario discussion.
The PODA model can also be used to project the mobility level. In addition to motor
gasoline demand, Figure 3 also exhibits the projected mobility levels in each individual state
from March to September 2020. Clearly, the mobility levels in all states are much lower in April
than in March, and the differences are much larger for states that have more COVID-19
infections, such as New York and California. However, in May when many states start
reopening, the mobility levels in most states increase dramatically. Especially in states from the
Midwest and South, such as North Dakota and Alabama, mobility levels are already higher than
they were in January 2020 when the baseline mobility level was low partially due to the cold
weather. However, if this disease evolves as the reference scenario suggests—shown in Figure
5(a)—the mobility levels and gasoline demand in these states could stay low in mid-June to
early August 2020 as the pandemic resurges. After that, the mobility and gasoline demand
slowly recover as the daily confirmed cases gradually decline.

Figure 3. The projection of gasoline demand and mobility level in the U.S. under the reference
pandemic scenario. (a) Comparison of gasoline demand projections based on the Apple mobility data
and Google mobility data 18,19, EIA weekly motor gasoline supply and non-pandemic gasoline demands
are provided for comparison 17; (b) State-level mobility projections. “Apple” means the inputs for
projection are from Apple, and “Google” means the inputs for projection are from Google. Mobility level
at 0% in the legend bar for Apple mobility refers to the baseline on January 13, 2020 19. Mobility level at
0% in the legend bar for Google mobility refers to the baseline of the median value for the
corresponding days of the weeks from January 3 to February 6, 2020 18.

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Dynamics of Future Motor Gasoline Demand
The knowledge deficit of this disease magnifies the uncertainty of the projections on motor
gasoline demand. Figure 4 gives the corresponding motor gasoline demands under three
different scenarios. To present the weekly changes to better show the trend and clear
comparison between different scenarios, the projected values of gasoline demands shown in
Figure 4 are all given as 7- day moving averages. The scenario details are described in
Supplementary Note 3. Analyzing the medium-term projected motor gasoline demand to
October 2020 under the reference scenario, it can be seen that, although the motor gasoline
demand will grow rapidly after April recovery, it is expected to remain fairly flat from mid-May
until October. The projected motor gasoline demand by the end of September will be about
8.342 million BPD. Compared to the demands under non-pandemic scenario, the projected
gasoline demand in late September 2020 under the reference pandemic scenario is about 90%
of the demand under the non-pandemic scenario. The motor gasoline demand is about 78% of
the demand under the non-pandemic scenario on May 8, 2020; and it is about 82% on June 5,
2020 17. Therefore, the motor gasoline demand in the U.S. is unlikely to recover to a nonpandemic level in the medium-term (before October 2020) under the current reference
pandemic scenario. This is primarily because the YYG model projects that the pandemic will
continue to evolve, and a new smaller wave of infections could occur in mid-June to August,
which could lessen people’s desire to travel or prompt the government to adjust its
intervention measures.
The projections of optimistic and pessimistic scenarios expand the probabilities of the
motor gasoline demands in the medium-term. In the optimistic scenario, the reproduction
values are believed to be smaller than at the beginning of the pandemic period, and people are
assumed to be more willing to travel. Thus, the motor gasoline demand after April continues
rapidly growing till October. The projected motor gasoline demand in late September 2020
under the optimistic scenario is about 98% of the demand under the non-pandemic scenario,
which means the U.S. gasoline demand is almost normal by then. In the pessimistic scenario,
the pandemic response measures are assumed to deteriorate, and a more serious wave of daily
new infections are projected. This would result in more social distancing measures by
governments, companies, and individuals, as well as increased concerns about travel. Thus, the
motor gasoline demand after April declines to about 6.1 million BPD before it starts recovering
by mid-August, but the demand will not be worse than it was in April. The projected motor
gasoline demand in late September 2020 under the pessimistic pandemic scenario is about 78%
of the demand projected for the non-pandemic scenario. Although results as of June 10, 2020,
are presented in this work, the PODA model is updated regularly with the evolution of the
pandemic (https://covid19-mobility.com/).

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This study is also able to project the motor gasoline demands with pandemic inputs from
other pandemic projection models. Considering the forecast period, and availability of model
source codes, this study chooses the pandemic projections from the MIT model as an example
8,25. The purple curve in Figure 4 shows the projected gasoline demands in the U.S. based on
inputs from the MIT model, which is very close to the demand projected using the optimistic
scenario from the YYG model. This is because the evolution of the COVID-19 pandemic
projected by the MIT model is similar to that projected by the YYG model under the optimistic
scenario 24,25, as shown in Supplementary Figure 5.

Figure 4. Gasoline demand under different scenarios (projected by June 10, 2020). Gasoline demand
projections are based on the three scenarios of the YYG model and MIT model 24,25. EIA weekly motor
gasoline supply and non-pandemic gasoline demands are provided for comparison 17 .

Gasoline Demand Under Reopening and No-Reopening Policies
With the reopening of many states in late April and early May 2020, the motor gasoline
demand has clearly increased, even though the pandemic is far from over. Some researchers
have warned that too early reopening in some states could result in more infections and deaths
26, while a continuation of shutdown measures, or postponing reopening, will mean continued
reduction in mobility. To further explore the potential impact of reopening and no-reopening

11

policies on motor gasoline demand, we create a hypothetical scenario (the “no-reopening”
scenario) in which the reopening policy is postponed by four weeks (i.e., the reopening is not
implemented until late May and early June 2020). Here, the travel mobility and motor gasoline
demand on April 24 – May 21 (four weeks) is assumed to be postponed by four weeks to May
22 – June 18. Travel mobility and motor gasoline demand on April 24 – May 21 are assumed to
be linearly extended from April 23. In addition, the study by Fowler et al. shows that, in the
U.S., a strict stay-at-home order can help to a 30.2% reduction of confirmed infection cases
after one week, a 40.0% reduction after two weeks, and a 48.6% reduction after three weeks 27.
These reduction rates are built into the no-reopening scenario in comparison to the scenarios
with the YYG model under the facts with reopening 24. In the no-reopening scenarios, the
reciprocal effect of mobility on the evolution of the pandemic is not considered.
Figure 5 shows the differences in motor gasoline demand resulting from reopening and noreopening policies under the reference, optimistic, and pessimistic scenarios. Under the
reference scenario with a no-reopening policy, the four-week delay causes the motor gasoline
demand to recover much slower than it would be with a reopening policy during this period.
However, after the reopening in late May and early June, the rebound in gasoline demand is
more prominent than it is in late April and early May. The cumulative motor gasoline demand
during the period from April 23 to September 21, 2020, under both reopening and noreopening policies are calculated in these three pairs of scenarios, as shown in Figure 5. Under
the reference scenario, the cumulative motor gasoline demand with the no-reopening policy is
approximately 6.4 million barrels more than the motor gasoline demand with the reopening
policy. Under the optimistic scenario, the cumulative motor gasoline demand resulting from the
no-reopening policy is about 40.0 million barrels less than that resulting from the reopening
policy. Under the pessimistic scenario, the cumulative motor gasoline demand resulting from
the no-reopening policy is about 109.5 million barrels more than that resulting from the
reopening policy. In summary, under the reference and pessimistic scenarios, the no-reopening
policy could worsen the motor gasoline demand in the short-term, but it might help the motor
gasoline demand recover to a normal level sooner, and therefore the cumulative gasoline
demand during this period would be higher. Comparatively, under the optimistic scenarios, the
reopening policy could result in a quicker recovery of the motor gasoline demand in the
medium-term.

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Figure 5. Projections of motor gasoline demands under reopening and no-reopening policies. (a) Three
scenarios of daily number of newly infected cases projected by the YYG model 24; (b) Gasoline demand
projection comparing reopening and no-reopening policies under the reference YYG scenario; (c)
Gasoline demand projection comparing reopening and no-reopening policies under the optimistic YYG
scenario; (d) Gasoline demand projection comparing reopening and no-reopening policies under the
pessimistic scenario.

Conclusions
A machine learning model, PODA, was developed to predict travel mobility in combination
with motor gasoline demand. This model allows review of the mobility trends from Google
and Apple, compares with the non-pandemic period, analyzes the historical weekly motor
gasoline demand published by EIA, and projects the future motor gasoline demand. By
projecting the motor gasoline demand under different pandemic and policy scenarios and
combined with the pandemic models referenced by the CDC, this paper provides several
insights of interest to stakeholders.

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Under the current reference pandemic scenario, the growth of motor gasoline demand is
slow from mid-May until August. It is unlikely that motor gasoline demand in the U.S. will
reach a non-pandemic level in the medium-term (before October 2020). Under the optimistic
pandemic scenario, the motor gasoline demand (using the PODA model with Google mobility
as input) is expected to continue growing and will recover to about 98% of the demand under
the non-pandemic scenario by late September 2020, which means the gasoline demand
would be almost fully recover by then. Under the pessimistic infection scenario, the second
wave of infections in mid-June to August could significantly lower the gasoline demand again,
but it would not be worse than it was in April.
With a reopening policy, the mobility level in the states from the Midwest and South
have rebounded near or back to a normal level already. However, under the reference
pandemic scenario, if infections increase in these states, their mobility levels could still
decrease by mid-June to early August 2020. Under the reference and pessimistic scenarios, a
no-reopening policy could lower the motor gasoline demand temporarily, but it might also
help demand increase to a normal level quicker. However, under the optimistic scenarios, a
reopening policy recovers motor gasoline demand sooner.
The contribution of this study is the creation of a framework for investigating and
projecting motor gasoline demand based on COVID-19 pandemic impacts, changes in
mobility, and demographic information in each individual state. This study can contribute to
evaluate the effects of pandemic on energy industry and economy, to outlook
macroeconomics and social activities. However, the model has some limitations that should
be addressed. First, the model assumes the gasoline demands from non-light-duty vehicles
and other sectors, which accounts for 8% of the total gasoline consumption in the U.S., are
constant during the pandemic 23,28. Second, the model does not consider the dynamic impact
of travel mobility on the evolution of the COVID-19 pandemic. As more is learned about both
the pandemic model and the reciprocal effects of mobility on model results, the analysis and
the model will be updated and improved.
The motor gasoline demand projections by the PODA model are updated and released
regularly on a publicly available website (https://covid19-mobility.com). With appropriate
modification, the PODA model will be applied to project other transportation-related fuel
demand (such as for freight trucks) and to study fuel demand changes in other countries in
the near future.

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Methods
The Mobility Dynamic Index Forecast Module
For the Mobility Dynamic Index Forecast Module, we develop a method using the machinelearning neural network that uses pandemic data, policies, and demographic data as inputs to
predict variations in mobility. The historical COVID-19 pandemic data, government policies, and
demographic data are used as the model inputs, which are listed in Supplementary Note 2.
These inputs are selected based on the correlation analysis between the pandemic and the
mobility data 18–20, which are presented in Supplementary Figure 1. The neural network model
has 5 outputs related to the Google and Apple mobilities. The complete list of data used as
inputs and outputs in the Mobility Dynamic Index Forecast Module is provided in
Supplementary Table 1.
Data preprocessing is applied to the datasets to accelerate training and improve the model
performance: both the network inputs and outputs are centered by the mean values and
normalized by the standard deviations. The loss function is specified as the mean square error
of the standardized outputs. The neural network model has 42 inputs (listed in Supplementary
Table 1 with descriptive statistics shown in Supplementary Figures 2-4), 2 hidden layers, and 25
hidden nodes for each hidden layer, with rectified linear units as the activation function. In
addition, the mode is implemented with the deep learning framework of PyTorch 29. The
network is optimized using Adam 30, with a default learning rate of 1e-3 and a batch size of 64.
To avoid potential overfitting, the L2 regularization is applied with a weight decay factor of 1e-4.
In addition, the rolling-window cross-validation is adopted to search the optimal network
structure, which is detailed in Supplementary Note 5. Out-of-sample testing is also performed
for the selected neural network structure to estimate the performance of the model in
predicting future mobility. Specifically, the number of hidden layers and nodes are chosen to
maximize the accuracy of both training and test datasets, the performance of different number
of layers and nodes is compared in Supplementary Table 4. Normally, the network reaches a
good performance after 5,000 epochs. The results of neural network model validation are
provided in Supplementary Figures 10 and 11, and described by Supplementary Note 5.
The future evolution of COVID-19 pandemic is needed to project the future gasoline fuel
demand. In this study, we adopt the pandemic projection of the YYG model and use the
projection from the MIT model for comparison 8,24,25. The YYG model parameters are constantly
calibrated against newly reported data using machine learning; thus, they can capture the
effect of state policies. In addition, this model predicts the number of newly infected people,
newly recovered people, and new deaths for the coming three months. It should be clarified
that the Mobility Dynamic Index Forecast Module uses the number of U.S. daily confirmed
cases as an input rather than the daily newly infected cases, as the confirmed cases have more

15

impacts on people’s mobility decisions. However, the YYG model projects daily new infection
cases, but not the daily new confirmed cases. And the confirmed cases is only a portion of the
infection cases as a lot of asymptomatic cases are not tested. We then convert the number of
newly infected cases to the number of newly confirmed cases by recognizing the following
relationship:
(1)
𝑁𝑖𝑛𝑓𝑒𝑐𝑡𝑒𝑑,𝑑 = 𝜂 ∗ 𝑁𝑐𝑜𝑛𝑓𝑖𝑟𝑚𝑒𝑑,𝑑+16
where η is calculated so that it best fits the total U.S. confirmed cases with the historically
projected total infected cases from the YYG model for the reference, lower, and upper
scenarios, respectively. d+16 means the confirmed cases value has a time delay of 16 days
compared to the newly infected cases. Supplementary Figure 5 shows the calculated daily
number of confirmed cases based on the newly infected cased projected by YYG on June 10,
2020.

The Motor Gasoline Demand Estimation Module
Travel mobility is fairly stable under normal conditions, and the estimated driving miles by
trip activity for each individual state from the National Household Travel Survey (NHTS) 2017
are used as a benchmark 31. Estimated miles of travel by trip activities from the NHTS are
presented in Supplementary Table 2, and the calculation method is described by
Supplementary Note 6. Normally, the gasoline demand from personal travel mobility is
comparatively inelastic 7. However, the motor gasoline demand decreases due to a decrease in
out-of-home trips during the pandemic. Therefore, it is important to decompose personal outof-home trips and connect them to the evolution of the pandemic for the Dynamic Mobility
Index Forecast module. We denote dynamic mobility indices for people in state (n) on date (d)
as a vector 𝑄𝑛,𝑑 ∈ ℝ𝐾 :
1
𝑞𝑛,𝑑
2
𝑄𝑛,𝑑 = 𝑞𝑛,𝑑 ,
…
𝐾
[𝑞𝑛,𝑑 ]

𝑛 ∈ {1,2, … 𝑁}

(2)

where N denotes the total number of states in the U.S. In the case where the historical mobility
data in the PODA model are from Google, then K = 4, and the dynamic indices of mobility
include “workplaces”, “grocery and pharmacy,” “retail and recreation,” and “parks.” In case
where the historical mobility data are from Apple, then K = 1, and the dynamic index of mobility
is “driving.” This study uses the Google mobility data as an example. Due to the tracking errors
of mobility (e.g., Google uses the locational and duration data instead of actual route distance
data for quantifying the mobility trend) and the partial mismatching in definitions of trip
activities between Google and NHTS. Using the Google data as an example, the indices of
1
2
dynamic mobility include the activities: workplaces (𝑞𝑛,𝑑
), grocery and pharmacy (𝑞𝑛,𝑑
), retail

16

3
4
and pharmacy (𝑞𝑛,𝑑
), and parks (𝑞𝑛,𝑑
). The changes of mobility by trip activity, based on NHTS
trip activities and used for projecting the motor gasoline demand, include the activities: work
2
3
(𝑚1𝑛,𝑑 ), school/daycare/religious activity (𝑚𝑛,𝑑
), medical/dental services (𝑚𝑛,𝑑
),
4
5
6
7
shopping/errands (𝑚𝑛,𝑑 ), recreational/social (𝑚𝑛,𝑑 ), transport someone (𝑚𝑛,𝑑 ), meals (𝑚𝑛,𝑑
),
1
2
9
8
and something else (𝑚𝑛,𝑑 ). The vector of the mobility adjustment factor 𝑋 = [𝑥 𝑥 ⋯ 𝑥 ]
must be used for better calibration and projection. The indices of dynamic mobility from Google
𝑝
𝑘
- 𝑞𝑛,𝑑
need adjustments with X before they are converted to 𝑚𝑛,𝑑
, which represents the

mobility changes for trip activity (p) in state (n) on date (d). The changes in mobility by trip
activity are presented in Eq. (3).
𝑚1𝑛,𝑑
2
𝑀𝑛,𝑑 = 𝑚𝑛,𝑑 ,
…
𝑃
𝑚
[ 𝑛,𝑑 ]

𝑛 ∈ {1,2, … 𝑁}

(3)

Through the mobility adjustment factor 𝑋 = [𝑥1 𝑥 2 ⋯ 𝑥 9 ], we can connect the changes of
mobility (Mn,d) by trip activity and the indices of dynamic mobility (Qn,d) based on their
definitions of trip activities, respectively 18,31. The conversion equations are shown in Eq. (4).
1
𝑚1𝑛,𝑑 = 𝑞𝑛,𝑑
∙ 𝑥1
2
1
𝑚𝑛,𝑑
= 𝑞𝑛,𝑑
∙ 𝑥2
3
2
𝑚𝑛,𝑑
= 𝑞𝑛,𝑑
∙ 𝑥3
4
2
𝑚𝑛,𝑑
= 𝑞𝑛,𝑑
∙ 𝑥4
5
3
4
𝑚𝑛,𝑑
= [𝑥 9 ∙ 𝑞𝑛,𝑑
+ (1 − 𝑥 9 ) ∙ 𝑞𝑛,𝑑
] ∙ 𝑥5

{

(4)

6
3
𝑚𝑛,𝑑
= 𝑞𝑛,𝑑
∙ 𝑥6
3
7
𝑚𝑛,𝑑
= 𝑞𝑛,𝑑
∙ 𝑥7
8
3
𝑚𝑛,𝑑
= 𝑞𝑛,𝑑
∙ 𝑥8

𝑝
Using the changes in mobility for trip activity (p) in state (n) on date (d) - 𝑚𝑛,𝑑
, we can

estimate the miles traveled for different trip activities listed in Supplementary Table 2. They are
calculated by Eq. (5).
𝑝
𝑝
𝑡𝑛,𝑑
= 𝑆𝑛𝑝 ∙ (1 + 𝑚𝑛,𝑑
),

𝑝 ∈ {1, 2, … , 𝑃}

(5)

𝑝
where P denotes the total number of NHTS trip activities; 𝑡𝑛,𝑑
is the estimated miles traveled

for an average household for trip activity (p) in state (n) on date (d); and 𝑆𝑛𝑝 is the average miles
traveled for each trip activity (p) in state (n) on normal days of a year. The baseline for mobility
changes in Google is travel during the 5-week period from January 3 to February 6, 2020 18.

17

Lastly, the estimated total miles traveled 𝑇𝑛,𝑑 of people in state (n) on date (d) is shown in
Eq. (6).
𝑃
𝑝
𝑇𝑛,𝑑 = ∑ 𝑡𝑛,𝑑
+𝐶

(6)

𝑝=1
𝑝
where ∑𝑃𝑝=1 𝑡𝑛,𝑑
denotes the total miles traveled by an average household in state (n) on date

(d), and C is a constant that denotes the “miles” converted from non-household activities.
Correspondingly, the motor gasoline demand in state (n) on date (d) should be roughly
proportionally related to the total miles traveled by people in the same state on the same date,
as shown in Eq. (7).
𝑁

𝐺𝑑 = ∑ (𝑇𝑛,𝑑
𝑛=1

𝐺𝐵
∙𝑦 )
𝑇 𝑛

(7)

where 𝐺𝑑 denotes the nationwide motor gasoline demand in the U.S. on date (d); GB is the
medium value of motor gasoline demand in the U.S. during the 5-week period from January 3
to February 6, 2020; and T denotes the total miles traveled by people on normal days. This
period is used as a benchmark for mobility change by Google 18. Finally, 𝑦𝑛 denotes the on-road
demand share in state (n) in the U.S, which is shown in Supplementary Table 3.
We solve Eq. (8) to calibrate the values of the adjustment factor vector 𝑋 and constant 𝐶.
2

̅̅̅̅
min ∑ (|𝐺𝐸𝐼𝐴,𝑊 − 𝐺
𝑑 |⁄𝐺𝐸𝐼𝐴,𝑊 ) ,

𝑠. 𝑡. 𝑋, 𝐶 ∈ ℝ+

(8)

where Eq. (8) is used to minimize the sum of squared absolute percentage error. 𝐺𝐸𝐼𝐴,𝑊
denotes the weekly motor gasoline demand in the U.S., which is published by the U.S. EIA every
week. ̅̅
𝐺̅̅
𝑑 is the average weekly value of daily estimated motor gasoline demand (𝐺𝑑 ).
EIA provides values of weekly finished motor gasoline supplies, which are used to estimate
gasoline demand in the U.S. 32. For this study, we use this data to calibrate in the Motor
Gasoline Demand Estimation Module. A quadratic equation is adopted to fit the seasonality of
weekly motor gasoline demands in 2016–2019, as discussed in Supplementary Note 4, and it
will be used as a “normal days” benchmark to compare with the motor gasoline demand in
2020 under the pandemic. In addition, the information on the shares of motor gasoline
consumed by the transportation sector by state in 2017 and 2018 are presented in
Supplementary Table 3. The state shares of motor gasoline consumption are pretty stable in
2017-2018 33, and therefore it assumes that the state shares of motor gasoline consumption
before the pandemic remain the same in 2020. What’s more, the transportation sector

18

accounts for 94%-98% of motor gasoline consumption 33. Therefore, this study does not
consider the motor gasoline consumed by the commercial and industrial sectors as the inputs in
the model but calibrates the potential differences as a “constant” in the model.

19

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22

Acknowledgement
This research was financially supported by Aramco Services Company and used resources at
the National Transportation Research Center at Oak Ridge National Laboratory and Systems
Assessment Center of Energy Systems Division at Argonne National Laboratory. This manuscript
has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 and UChicago
Argonne, LLC under Contract DE-AC02-06CH11357 with the U.S. Department of Energy. The
authors would like to thank the developer of the YYG model, Mr. Youyang Gu, for his feedback
on the COVID-19 projections used in this study. The authors are solely responsible for the views
expressed in this study.

Author Contributions
PODA model concept and methodologies were structured by S.O., X.H., W.J., and W.C.
Python codes were developed by X.H. and W.J. Data was collected by S.O., X.H., W.J., Z.L., L.S.,
and Y.G. Data Analyses were performed by S.O., X.H., L.S., W.J., W.C., J.B., Z.L., and S.D. The
manuscript was written by the combination of S.O., L.S., S.P., X.H., W.J., and Z. L.

Data Availability
The data used for model development are either provided in Supplementary Information or
publicly available at:
(1) EIA weekly gasoline demand: https://www.eia.gov/dnav/pet/pet_cons_wpsup_k_w.htm
(2) U.S. pandemic data: https://usafacts.org/visualizations/coronavirus-covid-19-spread-map/
(3) YYG pandemic projection model: https://github.com/youyanggu/covid19_projections
(4) MIT pandemic projection model: https://github.com/COVIDAnalytics/DELPHI
(5) Apple Mobility: https://www.apple.com/covid19/mobility
(6) Google Mobility: https://www.google.com/covid19/mobility/
(7) Government policy:
https://github.com/COVID19StatePolicy/SocialDistancing/blob/master/data/USstatesCov1
9distancingpolicy.csv
(8) National Household Travel Survey 2017: https://nhts.ornl.gov/
(9) EIA State Energy Data System: https://www.eia.gov/state/seds/
The results that support the findings of this study are provided in the main text and
Supplementary Information. The source data underlying all figures in the main manuscript and

23

Supplementary Information are provided as a Source Data file. With the evolution of the
pandemic, the U.S. motor gasoline demand and mobility level projection is updated periodically
and posted at https://covid19-mobility.com and https://teem.ornl.gov/poda.shtml.

Code Availability
The code of the PODA model is deposited and managed on GitHub
(https://github.com/jiweiqi/covid19-mobility).

Competing interests
We declare that none of the authors have competing financial or non-financial interests.

Figure Legends
Figure 1. Changes in mobility in various sectors and number of cases. Percentage changes in Google
mobility between February 15 and June 4, 2020 for (a) workplaces; (b) grocery and pharmacy; (c) retail
and recreations 18. (d) 7-day average of the number of COVID-19 cases and deaths in the U.S. 3 Please
note the boxplots represent the interquartile range (IQR) where the lower and upper whiskers represent
1.5×IQR. Each yellow data point represents the mobility of outlier states that do not fall into the
1.5xIQR.
Figure 2. The structure of the PODA model.
Figure 3. The projection of gasoline demand and mobility level in the U.S. under the reference
pandemic scenario. (a) Comparison of gasoline demand projections based on the Apple mobility data
and Google mobility data 18,19, EIA weekly motor gasoline supply and non-pandemic gasoline demands
are provided for comparison 17; (b) State-level mobility projections. “Apple” means the inputs for
projection are from Apple, and “Google” means the inputs for projection are from Google. Mobility level
at 0% in the legend bar for Apple mobility refers to the baseline on January 13, 2020 19. Mobility level at
0% in the legend bar for Google mobility refers to the baseline of the median value for the
corresponding days of the weeks from January 3 to February 6, 2020 18.
Figure 4. Gasoline demand under different scenarios (projected by June 10, 2020). Gasoline demand
projections are based on the three scenarios of the YYG model and MIT model 24,25. EIA weekly motor
gasoline supply and non-pandemic gasoline demands are provided for comparison 17 .

24

Figure 5. Projections of motor gasoline demands under reopening and no-reopening policies. (a) Three
scenarios of daily number of newly infected cases projected by the YYG model 24; (b) Gasoline demand
projection comparing reopening and no-reopening policies under the reference YYG scenario; (c)
Gasoline demand projection comparing reopening and no-reopening policies under the optimistic YYG
scenario; (d) Gasoline demand projection comparing reopening and no-reopening policies under the
pessimistic scenario.

25