Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows

TL;DR

This paper introduces a transfer learning approach with multi-head PINNs to efficiently simulate stochastic branched flows, significantly reducing computation time compared to traditional PINNs.

Contribution

The paper develops a multi-head transfer learning framework for PINNs and demonstrates its effectiveness in simulating complex stochastic branched flows.

Findings

Multi-head PINNs achieve faster convergence than standard PINNs.

Transfer learning reduces training time for nonlinear differential equations.

GAN-based PINNs outperform feedforward PINNs in transfer tasks.

Abstract

Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning approach for PINNs and introduce a multi-head model to efficiently obtain accurate solutions to nonlinear systems of ordinary differential equations with random potentials. In particular, we apply the method to simulate stochastic branched flows, a universal phenomenon in random wave dynamics. Finally, we compare the results achieved by feed forward and GAN-based PINNs on two physically relevant transfer learning tasks and show that our methods provide significant computational speedups in comparison to standard PINNs trained from scratch.