Adaptive Data Harvesting for Efficient Neural Network Learning with Universal Constraints

TL;DR

This paper introduces a reinforcement learning-based method to adaptively select samples during neural network training, enhancing efficiency and constraint satisfaction in models like Lyapunov NNs and PINNs.

Contribution

It proposes a novel adaptive sampling strategy learned from data, outperforming fixed heuristics in training neural networks with universal constraints.

Findings

Reinforcement learning improves constraint satisfaction in test problems.

Adaptive sampling significantly enhances training efficiency.

Method is applicable to various domains requiring adaptive input selection.

Abstract

Training neural networks to satisfy universal constraints over continuous domains poses unique challenges. Common examples include Lyapunov Neural Networks (Lyapunov NNs) and Physics-Informed Neural Networks (PINNs), where analytical solutions are generally either unavailable or overly restrictive. Sample-based methods are therefore commonly used to enforce these constraints, and the choice of samples has a substantial impact on convergence speed, stability, and solution quality. Most existing methods rely on fixed heuristics or handcrafted rules, and are suboptimal in practice. In this paper, we aim to improve upon them by learning, from data and experience, how to dynamically and iteratively adjust the samples in response to the model's evolving learning performance. Trained by reinforcement learning, the learned policy improves empirical constraint satisfaction on test problems while significantly improving efficiency. We validate the approach on both Lyapunov NNs and PINNs, and demonstrate its broader applicability to domains where adaptive input selection is essential for effective training.