DeepAI AI Chat
Log In Sign Up

Physics-Informed Neural Operator for Learning Partial Differential Equations

by   Zongyi Li, et al.

Machine learning methods have recently shown promise in solving partial differential equations (PDEs). They can be classified into two broad categories: approximating the solution function and learning the solution operator. The Physics-Informed Neural Network (PINN) is an example of the former while the Fourier neural operator (FNO) is an example of the latter. Both these approaches have shortcomings. The optimization in PINN is challenging and prone to failure, especially on multi-scale dynamic systems. FNO does not suffer from this optimization issue since it carries out supervised learning on a given dataset, but obtaining such data may be too expensive or infeasible. In this work, we propose the physics-informed neural operator (PINO), where we combine the operating-learning and function-optimization frameworks. This integrated approach improves convergence rates and accuracy over both PINN and FNO models. In the operator-learning phase, PINO learns the solution operator over multiple instances of the parametric PDE family. In the test-time optimization phase, PINO optimizes the pre-trained operator ansatz for the querying instance of the PDE. Experiments show PINO outperforms previous ML methods on many popular PDE families while retaining the extraordinary speed-up of FNO compared to solvers. In particular, PINO accurately solves challenging long temporal transient flows and Kolmogorov flows where other baseline ML methods fail to converge.


page 8

page 10


Generic bounds on the approximation error for physics-informed (and) operator learning

We propose a very general framework for deriving rigorous bounds on the ...

Fourier Continuation for Exact Derivative Computation in Physics-Informed Neural Operators

The physics-informed neural operator (PINO) is a machine learning archit...

NeurOLight: A Physics-Agnostic Neural Operator Enabling Parametric Photonic Device Simulation

Optical computing is an emerging technology for next-generation efficien...

Fourier-RNNs for Modelling Noisy Physics Data

Classical sequential models employed in time-series prediction rely on l...

A Physics Informed Neural Network for Time-Dependent Nonlinear and Higher Order Partial Differential Equations

A physics informed neural network (PINN) incorporates the physics of a s...

Meta Learning of Interface Conditions for Multi-Domain Physics-Informed Neural Networks

Physics-informed neural networks (PINNs) are emerging as popular mesh-fr...