Applied & Computational Mathematics seminar: PDE system identification using transport models

Speaker:  Gustavo Kunde Rohde, University of Virginia

Title:  PDE system identification using transport models 

Abstract:   The topic of PDE system identification from amplitude (acoustic) time series measurements obtained at specific locations in a spatial domain is an important problem with important applications in mechanical engineering and structural health monitoring. Model-based approaches based on PDE solutions are difficult to utilize in practice given the computational costs associated with inferring PDE parameters by finding which parameters yield solutions that are similar to the observed data. Learning-based methods are often preferred given their practicality. By utilizing a training dataset one can recover information about the state of a material by matching observed data to a trained model. However, the methodology is ad-hoc, opaque, and doesn't allow for understanding of when such approaches will work or fail. We describe a method to recover information about a PDE system based on sparse measurements that combines elements from both approaches. First, we show how an optimal transport-based approach can be used to model PDE solutions of certain traveling wave problems. We then demonstrate how to use training data to estimate an optimal transport-inspired model of the PDE solution at a particular location. We then use this model to recover information (i.e. PDE parameters) that generated a particular observed (test) time series sample. We show the results obtained by the proposed approach can outperform existing approaches for the same task including traditional detection/estimation approaches as well as more modern deep learning methods.

Time:  Friday, October 20, 2023 - 10:00am-11:00am

Place:  Exploratory Hall, Room 4106