Physics-Informed Neural Operator for Learning Partial Differential Equations

• DOI: 10.1145/3648506
• Publication Date: 2024-02-21T12:06:51Z
• Authors: Zongyi Li; Hongkai Zheng; Nikola Kovachki; David Jin; Haoxuan Chen; Burigede Liu; Kamyar Azizzadene...; Anima Anandkumar
• Keywords: Operator (biology)

In this article, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family parametric Partial Differential Equations (PDE). PINO is first hybrid approach incorporating PDE at different resolutions operator. Specifically, in PINO, coarse-resolution with imposed higher resolution. The resulting model can accurately approximate ground-truth for many popular families shows no degradation accuracy even under zero-shot super-resolution, is, being able predict beyond resolution data. uses Fourier (FNO) framework guaranteed be universal approximator any continuous discretization convergent limit mesh refinement. By adding FNO resolution, obtain high-fidelity reconstruction Moreover, succeeds settings where available only are imposed, while previous approaches, such as Physics-Informed Neural Network (PINN), fail due optimization challenges, example, multi-scale dynamic systems Kolmogorov flows.