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<p>In physics-informed neural networks (PINNs for short), the selection of observation points plays a critical role in model accuracy and convergence. Most existing sampling strategies rely on heuristic or problem-specific rules, and lack a unified optimization framework with theoretical guarantees. This paper proposes a submodular sampling framework applicable to various task settings in PINNs, including forward problems, inverse problems, and system identification. By exploiting the information coverage and diversity properties of submodular functions, the proposed framework provides a principled approach for selecting informative observation points under limited data budgets. Numerical experiments on benchmark partial differential equation (PDE for short) problems demonstrate that the proposed method consistently improves prediction accuracy and generalization compared with random and heuristic sampling strategies, while maintaining favorable computational efficiency. Overall, this work introduces a theoretically grounded and practically effective sampling paradigm for physics-informed learning across diverse PINN applications.</p>

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Submodular sampling framework applicable to various tasks of physics-informed neural networks

  • 期刊论文

  • 发表日期：

    2026年2月23日

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  • Hao Zhong,
  • Qi Zhang

摘要

In physics-informed neural networks (PINNs for short), the selection of observation points plays a critical role in model accuracy and convergence. Most existing sampling strategies rely on heuristic or problem-specific rules, and lack a unified optimization framework with theoretical guarantees. This paper proposes a submodular sampling framework applicable to various task settings in PINNs, including forward problems, inverse problems, and system identification. By exploiting the information coverage and diversity properties of submodular functions, the proposed framework provides a principled approach for selecting informative observation points under limited data budgets. Numerical experiments on benchmark partial differential equation (PDE for short) problems demonstrate that the proposed method consistently improves prediction accuracy and generalization compared with random and heuristic sampling strategies, while maintaining favorable computational efficiency. Overall, this work introduces a theoretically grounded and practically effective sampling paradigm for physics-informed learning across diverse PINN applications.