Leveraging Physics Informed Neural Networks to Identify Signal Disruption Dynamics

Abstract

Physics informed neural networks (PINNs) have a long history of use in a variety of applications from engineering to the physical sciences such as biology or physics. PINNs allow for the incorporation of a priori understanding of a process’ structure into the neural network learning process. This allows for such models to incorporate the processes behind the data in a way that aligns with prior expectations for controlling dynamics. We attempt to leverage the physics informed neural network structure toward the evaluation of disruptions to classical dynamical models. We do so by incorporating elements of ordinary differential equations derived from the known process structure into the loss function of our neural network. We utilize this format to learn the structure of disruptions to exponential growth curves allowing us to forecast the resumption of growth post-disruption. As a case study, we consider the SPDR S&P 500 ETF Trust stock value from 2019 to 2021. This stock expresses an approximately exponential growth curve which is interrupted by the 2020 COVID-19 induced market crash. We aim to train a physics informed neural network on this data and forecast the resumption of growth during the recovery from the market crash. This serves as a proof of concept for this application of physics informed neural networks. We expect this endeavor to result in the identification of the functional structure of the COVID-19 market crash and the accurate forecasting of the resumption of growth. We additionally aim to expand this application post-proof of concept to evaluate Differential Delay Systems dynamics, an area of cutting-edge research.

Start Time

16-4-2025 9:00 AM

End Time

16-4-2025 11:30 AM

Presentation Type

Poster

Presentation Category

Science, Technology and Engineering

Student Type

Graduate Student - Masters

Faculty Mentor

Jeff Knisley

Faculty Department

Mathematics and Statistics

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Apr 16th, 9:00 AM Apr 16th, 11:30 AM

Leveraging Physics Informed Neural Networks to Identify Signal Disruption Dynamics

Physics informed neural networks (PINNs) have a long history of use in a variety of applications from engineering to the physical sciences such as biology or physics. PINNs allow for the incorporation of a priori understanding of a process’ structure into the neural network learning process. This allows for such models to incorporate the processes behind the data in a way that aligns with prior expectations for controlling dynamics. We attempt to leverage the physics informed neural network structure toward the evaluation of disruptions to classical dynamical models. We do so by incorporating elements of ordinary differential equations derived from the known process structure into the loss function of our neural network. We utilize this format to learn the structure of disruptions to exponential growth curves allowing us to forecast the resumption of growth post-disruption. As a case study, we consider the SPDR S&P 500 ETF Trust stock value from 2019 to 2021. This stock expresses an approximately exponential growth curve which is interrupted by the 2020 COVID-19 induced market crash. We aim to train a physics informed neural network on this data and forecast the resumption of growth during the recovery from the market crash. This serves as a proof of concept for this application of physics informed neural networks. We expect this endeavor to result in the identification of the functional structure of the COVID-19 market crash and the accurate forecasting of the resumption of growth. We additionally aim to expand this application post-proof of concept to evaluate Differential Delay Systems dynamics, an area of cutting-edge research.