Two-Phase Optimization for PINN Training

TL;DR

This paper introduces a two-phase optimization algorithm for training Physics-Informed Neural Networks (PINNs) that decomposes the loss function and applies an adaptation of Inexact Restoration methods, demonstrating promising performance improvements.

Contribution

It presents a novel two-phase optimization algorithm based on Inexact Restoration techniques specifically designed for PINN training.

Findings

Effective in reducing PINN training loss

Improves convergence speed in experiments

Demonstrates robustness across different PINN problems

Abstract

This work presents an algorithm for training Neural Networks where the loss function can be decomposed into two non-negative terms to be minimized. The proposed method is an adaptation of Inexact Restoration algorithms, constituting a two-phase method that imposes descent conditions. Some performance tests are carried out in PINN training.