Bridging physics-based and data-driven modeling for learning dynamical systems

2021
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How can we learn a dynamical system to make forecasts, when some variables are unobserved? For instance, in COVID-19, we want to forecast the number of infected and death cases but we do not know the count of susceptible and exposed people. While mechanics compartment models are widely-used in epidemic modeling, data-driven models are emerging for disease forecasting. As a case study, we compare these two types of models for COVID-19 forecasting and notice that physics-based models significantly outperform deep learning models. We present a hybrid approach, AutoODE-COVID, which combines a novel compartmental model with automatic differentiation. Our method obtains a 57.4% reduction in mean absolute errors for 7-day ahead COVID19 forecasting compared with the best deep learning competitor. To understand the inferior performance of deep learning, we investigate the generalization problem in forecasting. Through systematic experiments, we found that deep learning models fail to forecast under shifted distributions either in the data domain or the parameter domain. This calls attention to rethink generalization especially for learning dynamical systems.
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Amazon.com strives to be Earth's most customer-centric company where customers can shop in our stores to find and discover anything they want to buy. We hire the world's brightest minds, offering them a fast paced, technologically sophisticated and friendly work environment. Economists at Amazon partner closely with senior management, business stakeholders, scientist and engineers, and economist leadership to solve key business problems ranging from Amazon Web Services, Kindle, Prime, inventory planning, international retail, third party merchants, search, pricing, labor and employment planning, effective benefits (health, retirement, etc.) and beyond. Amazon Economists build econometric models using our world class data systems and apply approaches from a variety of skillsets – applied macro/time series, applied micro, econometric theory, empirical IO, empirical health, labor, public economics and related fields are all highly valued skillsets at Amazon. You will work in a fast moving environment to solve business problems as a member of either a cross-functional team embedded within a business unit or a central science and economics organization. You will be expected to develop techniques that apply econometrics to large data sets, address quantitative problems, and contribute to the design of automated systems around the company. We are open to hiring candidates to work out of one of the following locations: Arlington, VA, USA | Bellevue, WA, USA | Boston, MA, USA | Los Angeles, CA, USA | New York, NY, USA | San Francisco, CA, USA | Seattle, WA, USA | Sunnyvale, CA, USA
US, WA, Seattle
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