Contact Name

Scott Holan

Contact Email

Holans@missouri.edu

Speaker(s) Information

Prof. Stefano Castruccio, University of Notre Dame

 

 

 

•  

 

Additional Event Information

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.