A novel meta-learning initialization method for physics-informed neural networks

Abstract

Physics-informed neural networks (PINNs) have been widely used to solve various scientific computing problems. However, large training costs limit PINNs for some real-time applications. Although some works have been proposed to improve the training efficiency of PINNs, few consider the influence of initialization. To this end, we propose a New Reptile initialization based Physics-Informed Neural Network (NRPINN). The original Reptile algorithm is a meta-learning initialization method based on labeled data. PINNs can be trained with less labeled data or even without any labeled data by adding partial differential equations (PDEs) as a penalty term into the loss function. Inspired by this idea, we propose the new Reptile initialization to sample more tasks from the parameterized PDEs and adapt the penalty term of the loss. The new Reptile initialization can acquire initialization parameters from related tasks by supervised, unsupervised, and semi-supervised learning. Then, PINNs with initialization parameters can efficiently solve PDEs. Besides, the new Reptile initialization can also be used for the variants of PINNs. Finally, we demonstrate and verify the NRPINN considering both forward problems, including solving Poisson, Burgers, and Schrödinger equations, as well as inverse problems, where unknown parameters in the PDEs are estimated. Experimental results show that the NRPINN training is much faster and achieves higher accuracy than PINNs with other initialization methods.

References in corpus (4)

• Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains
• Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
• On the Poisson equation and diffusion approximation 3
• Accelerating Physics-Informed Neural Network Training with Prior Dictionaries

Cited by in corpus (5)

• Multi-Objective Loss Balancing for Physics-Informed Deep Learning
• Towards Foundation Model for Chemical Reactor Modeling: Meta-Learning with Physics-Informed Adaptation
• Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities
• Meta-Auto-Decoder: A Meta-Learning Based Reduced Order Model for Solving Parametric Partial Differential Equations
• Compositional Meta-Learning for Mitigating Task Heterogeneity in Physics-Informed Neural Networks