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

arXiv: https://arxiv.org/abs/2504.12949 · HTML: https://mlsanity.com/paper/2504.12949/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 12 of its 27 references that are in the map.
- First posted on arXiv 17 Apr 2025.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 12 of 12)

- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems](https://mlsanity.com/paper/1710.00211/) (2017)
- [Solving high-dimensional partial differential equations using deep learning](https://mlsanity.com/paper/1707.02568/) (2017)
- [A comprehensive study of non-adaptive and residual-based adaptive sampling for physics-informed neural networks](https://mlsanity.com/paper/2207.10289/) (2022)
- [Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2103.01342/) (2021)
- [nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications](https://mlsanity.com/paper/2004.04276/) (2020)
- [A reinforcement learning approach to rare trajectory sampling](https://mlsanity.com/paper/2005.12890/) (2020)
- [Deep Reinforcement Learning for Adaptive Mesh Refinement](https://mlsanity.com/paper/2209.12351/) (2022)
- [A Provably Efficient Sample Collection Strategy for Reinforcement Learning](https://mlsanity.com/paper/2007.06437/) (2020)
- [Learning robust marking policies for adaptive mesh refinement](https://mlsanity.com/paper/2207.06339/) (2022)

## Built on by (most cited first, 2 of 2)

- [Iterative Training of Physics-Informed Neural Networks with Fourier-enhanced Features](https://mlsanity.com/paper/2510.19399/) (2025)
- [M3: Reframing Training Measures for Discretized Physical Simulations](https://mlsanity.com/paper/2605.08843/) (2026)

## Abstract (arXiv)

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.