Webinar Link: https://usc.zoom.us/webinar/register/WN_zyIBh_1gQLmKpMJG0GyLxw 

Abstract: The partial differential equations (PDEs) model several real-world setups of Physics, Engineering, biology, Epidemiology. The solution can be formulated as an operator map problem. We show that learning the operator kernels can be efficiently performed by exploiting the fundamental properties. We will discuss a novel multiwavelets-based neural operator approach to achieve a compressed representation and show applications on several benchmarks PDE datasets. Next, we also discuss a class of PDEs called 'Initial Value Problems,' which has applications in predictions and forecasting. We develop a compact non-linear neural operator which maps initial conditions to activities at a later time. The proposed approach yields data efficiency which is necessary to deal with scarce real-world datasets, and as a case study we formulate and solve urgent real-world problems like Epidemic forecasting (e.g., COVID19).

Biography: Gaurav Gupta is currently a researcher (Applied Scientist) at Amazon Web Services (AWS) AI labs. He completed his PhD from USC Viterbi. His research interests span the domain of time-series modeling, learning partial differential equations,  information theory for machine learning, fractional dynamical models, complex networks, brain EEG signals modeling. He is working on inter-disciplinary mathematical and applied problems on forecasting, PDEs, and has publications in top venues like Neurips, ICLR, Nature, IEEE Control Society, ACM cyber-physical society.

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Host: Pierluigi Nuzzo

Center for Cyber-Physical Systems and the Internet of Things (CCI) http://cci.usc.edu

Center for Autonomy and AI (AAI) https://aai.usc.edu