February 21, 2025

Stefano Castruccio - University of Notre Dame

[Castruccio Talk Recording] [Castruccio Talk Slides]

Location: Zoom 
Title: New Perspectives on Balancing Physics with Data-Driven Models: the Case for Physics Informed Neural Networks in Environmental Statistics

Abstract: The idea of performing data analysis by leveraging physical information with a data-driven model has a long history in environmental Statistics. Physical-Statistical models are predicated on the idea that hierarchical Bayesian models could have a spatio-temporal process informed by a partial differential equation (PDE) which expresses some well-known physical information about the system. The machine learning literature has recently focused on the same problem by proposing a different yet related solution: instead of devising a purely data-driven neural network, inference can be penalized by means of PDE expressing the physics of the system. This approach allows for “soft” constraints on the model instead of a “hard” specification of the process dynamics in physical-statistical models. In this talk, I will discuss two of my recent works on this topic developed by my research group, and discuss the relative merits of this new approach from the perspective of a statistician. The first work will focus on a deep double reservoir model informed by two-dimensional incompressible Navier Stokes, while the second one will discuss the link between a PDE-driven penalty and physics-informed priors. I will also briefly discuss some of my recent work on physics informed convolutional autoencoders and transformers with attention mechanisms. 

Bio: Stefano Castruccio is the Notre Dame Collegiate Associate Professor in Statistics at the University of Notre Dame. He obtained his PhD in 2013 at the University of Chicago, and he was later postdoctoral fellow King Abdullah University of Science and Technology (Saudi Arabia), Lecturer at Newcastle University (UK), before moving to his current institution. He works in spatio-temporal models for complex environmental problems, from air pollution to climate change.