Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems using Transfer Learning

• URL: http://arxiv.org/abs/2401.02810v2
• Date: Mon, 15 Jan 2024 13:10:12 GMT
• Title: Physics-Informed Neural Networks for High-Frequency and Multi-Scale Problems using Transfer Learning
• Authors: Abdul Hannan Mustajab, Hao Lyu, Zarghaam Rizvi, Frank Wuttke
• Abstract summary: Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs) We propose using transfer learning to boost the robustness and convergence of training PINN. We elaborately described our training strategy, including selection, and suggested guidelines for using transfer learning to train neural networks for solving more complex problems.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Physics-informed neural network (PINN) is a data-driven solver for partial and ordinary differential equations(ODEs/PDEs). It provides a unified framework to address both forward and inverse problems. However, the complexity of the objective function often leads to training failures. This issue is particularly prominent when solving high-frequency and multi-scale problems. We proposed using transfer learning to boost the robustness and convergence of training PINN, starting training from low-frequency problems and gradually approaching high-frequency problems. Through two case studies, we discovered that transfer learning can effectively train PINN to approximate solutions from low-frequency problems to high-frequency problems without increasing network parameters. Furthermore, it requires fewer data points and less training time. We elaborately described our training strategy, including optimizer selection, and suggested guidelines for using transfer learning to train neural networks for solving more complex problems.

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