MURI 21 LEARNING AND META-LEARNING OF PARTIAL DIFFERENTIAL EQUATIONS VIA PHYSICS-INFORMED NEURAL NETWORKS: THEORY,ALGORITHMS, AND APPLICATIONS
Abstract
Despite the significant progress over the last 50 years in simulating multiphysics problems using numerical discretization of partial differential equations (PDEs), we still cannot incorporate seamlessly noisy data into existing algorithms, mesh-generation is complex, and we cannot tackle high-dimensional problems governed by parametrized PDEs. Moreover, solving inverse problems is often prohibitively expensive and requires different formulations and new computer codes. We propose to overcome these obstacles by introducing physics-informed learning, integrating seamlessly data and mathematical models, and implementing them using physics-informed neural networks (PINNs) and other new physics informed networks (PINs). We will blend knowledge on existing methods, e.g. domain decomposition and uncertainty quantification, with the new concepts in deep neural networks and more general networks and regressions. Inversely, we will employ synergistically the lessons learned from PINNs/PINs to enhance the performance of existing numerical methods, e.g., for low-dimensional modeling and high-dimensional PDEs.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Aug 12, 2021
- Source ID
- FA95502010358
Entities
People
- George Karniadakis
Organizations
- Air Force Office of Scientific Research
- Brown University
- United States Air Force