Speaker: Adar Kahana (Tel Aviv University)
Title: Solving PDE related problems using deep-learning
Abstract: In this talk I will present our work on PDE related problems and how integrating deep-learning can help achieve better results. We discuss the accelerating topic of physically-informed neural networks: a method for solving PDEs with neural networks. With this in mind, we present our work in this field and present two interesting variants of this method. Motivated by the physical experiment of acoustic waves propagating in an underwater homogeneous domain, we discuss the inverse problem: Simulating the physical experiment, we solve the acoustic wave equation and save the data at a small number of sensors over many time steps and given these sensor measurements we aim to find and identify the shape of an obstacle inside the domain. We cast it to a data-driven problem by building an image segmentation of the domain where the segment is an arbitrary polygon (the obstacle). We improve the model using a physically-informed loss term designed based on the wave equation. After that we switch to a completely different area - we discuss an explicit nonlinear numerical scheme for the 1D wave equation that remains stable when violating the CFL condition. We create a data-set based on a stable wave propagation process and train a network to infer a non-stable process. We incorporate a physically-informed loss term here as well to achieve better accuracy (lower deviation from the analytic solution) for our scheme.