RL-PINNs: Reinforcement Learning-Driven Adaptive Sampling for Efficient Training of PINNs

• URL: http://arxiv.org/abs/2504.12949v1
• Date: Thu, 17 Apr 2025 13:50:55 GMT
• Title: RL-PINNs: Reinforcement Learning-Driven Adaptive Sampling for Efficient Training of PINNs
• Authors: Zhenao Song,
• Abstract summary: Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs)<n>Their performance heavily relies on the strategy used to select training points.<n>We propose RL-PINNs, a reinforcement learning-driven adaptive sampling framework that enables efficient training with only a single round of sampling.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs). However, their performance heavily relies on the strategy used to select training points. Conventional adaptive sampling methods, such as residual-based refinement, often require multi-round sampling and repeated retraining of PINNs, leading to computational inefficiency due to redundant points and costly gradient computations-particularly in high-dimensional or high-order derivative scenarios. To address these limitations, we propose RL-PINNs, a reinforcement learning(RL)-driven adaptive sampling framework that enables efficient training with only a single round of sampling. Our approach formulates adaptive sampling as a Markov decision process, where an RL agent dynamically selects optimal training points by maximizing a long-term utility metric. Critically, we replace gradient-dependent residual metrics with a computationally efficient function variation as the reward signal, eliminating the overhead of derivative calculations. Furthermore, we employ a delayed reward mechanism to prioritize long-term training stability over short-term gains. Extensive experiments across diverse PDE benchmarks, including low-regular, nonlinear, high-dimensional, and high-order problems, demonstrate that RL-PINNs significantly outperforms existing residual-driven adaptive methods in accuracy. Notably, RL-PINNs achieve this with negligible sampling overhead, making them scalable to high-dimensional and high-order problems.

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