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

• URL: http://arxiv.org/abs/2211.00214v1
• Date: Tue, 1 Nov 2022 01:50:00 GMT
• Title: Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows
• Authors: Rapha\"el Pellegrin, Blake Bullwinkel, Marios Mattheakis, Pavlos Protopapas
• Abstract summary: Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations. We adopt a recently developed transfer learning approach for PINNs and introduce a multi-head model. We show that our methods provide significant computational speedups in comparison to standard PINNs trained from scratch.
• Score: 1.1470070927586016
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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