Adaptive Data Harvesting for Efficient Neural Network Learning with Universal Constraints

2026-05-10

AI Summary

This work addresses the challenge of training neural networks under universal constraints—such as Lyapunov or physics-informed conditions—over continuous domains, where conventional sampling strategies rely on fixed heuristics and struggle to balance convergence speed, stability, and solution quality. To overcome these limitations, the study introduces, for the first time, a reinforcement learning–based adaptive sampling mechanism that dynamically optimizes sample selection according to the model’s current learning state. This approach transcends handcrafted sampling rules by automatically learning an optimal sampling distribution from data and training experience. Experimental results on Lyapunov neural networks and physics-informed neural networks (PINNs) demonstrate that the proposed framework substantially improves both constraint satisfaction accuracy and training efficiency, highlighting its broad applicability in scenarios 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.

Problem

• universal constraints
• sample selection
• neural network training
• adaptive data harvesting
• continuous domains

Innovation

• adaptive sampling
• reinforcement learning
• universal constraints
• physics-informed neural networks
• Lyapunov neural networks