A local, low-dimensional Machine Learning based PDE Solver for modeling engineering applications
Presenter
March 23, 2024
Abstract
In this talk, I will introduce a semi-supervised Machine Learning (ML) approach to model PDEs across a variety of engineering applications. The local, low-dimensional ML-Solver solves PDEs on multi-resolution meshes which are significantly coarser than the computational meshes used in typical engineering simulations. A coarse ML-Solver element, known as a subdomain, is representative of hundreds or even thousands of computational elements. The PDE solutions as well as other PDE conditions such as geometry, source terms and BCs are represented by n-dimensional latent vectors on each subdomain. The transformations between latent vectors and solution or condition fields on computational elements within a subdomain are learnt using field neural networks. Additionally, spatial, and temporal flux relationships between neighboring subdomains are learnt in the latent space using flux conservation neural networks and time integration neural networks. All the NNs are trained using data generated from engineering simulations. This talk will delve further into the nuts and bolts of the ML-Solver and demonstrate it across a variety of engineering use cases from fluids, thermal and mechanical applications. Finally, this talk will also demonstrate a use case of the ML-Solver that shows the potential of development towards a foundation model which can be used across a wide range of applications with consistent physics.