物理引导机器学习外推框架的开发与验证：以经典瞬态扩散基准为例
Development and Validation of a Physics-Guided Machine Learning Extrapolation Framework Using a Classical Transient Diffusion Benchmark
- Indian Institute of Technology Jodhpur（印度理工学院焦特布尔分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究提出一种物理引导机器学习外推框架，结合BiLSTM和PINN，利用经典瞬态扩散基准验证，通过坐标变换与递归扩展策略，实现训练域外准确且物理一致的预测。
AI中文摘要：
工程中使用的机器学习模型通常在有限的操作范围内进行训练，然而，在这些领域之外往往需要可靠的预测。因此，主要挑战是外推而非插值。由于训练范围之外的数据稀缺，严格的验证受到阻碍。为解决这一局限性，提出了一种新颖的外推框架，并与成熟的机器学习架构相结合，以实现在训练域之外准确且物理一致的预测。该框架通过系统评估两种物理引导架构建立：双向长短期记忆（BiLSTM）网络和物理信息神经网络（PINN）。采用经典的一维瞬态扩散问题作为基准，因为其精确解析解在时空域内提供了无限且可靠的数据，从而实现严格的定量验证。该问题特别具有挑战性，因为解从初始奇点演化，经历强非线性瞬态过程，最终接近稳态线性分布。当训练数据仅限于该演化的中间部分时，向奇点的反向外推尤为困难。为提高可靠性，引入了物理引导的坐标变换、边界感知学习策略和增强稳定性的时间推进方法。外推通过“训练-预测-验证-扩展”策略进行评估，其中经过验证的预测被递归添加到训练集中，以逐步扩展预测范围。结果表明，该方法在训练域之外实现了准确且物理一致的预测，突显了该框架在数据有限工程应用中的潜力。
英文摘要：
Machine learning models used in engineering are typically trained within limited operating ranges, yet reliable predictions are often required beyond these domains. Consequently, the primary challenge is extrapolation rather than interpolation. Rigorous validation is hindered by the scarcity of data outside the training range. To address this limitation, a novel extrapolation framework is integrated with established machine learning architectures to enable accurate and physically consistent predictions beyond the training domain. The framework is established by systematically evaluating two physics-guided architectures: a Bidirectional Long Short-Term Memory (BiLSTM) network and a Physics-Informed Neural Network (PINN). A classical one-dimensional transient diffusion problem is adopted as a benchmark because its exact analytical solution provides unlimited, reliable data across the spatio-temporal domain, enabling rigorous quantitative validation. The problem is particularly challenging because the solution evolves from an initial singularity through a strongly nonlinear transient regime before approaching a steady-state linear profile. When training data are confined to an intermediate portion of this evolution, backward extrapolation toward the singularity becomes especially demanding. To improve reliability, physics-guided coordinate transformations, boundary-aware learning strategies, and stability-enhancing temporal marching are incorporated. Extrapolation is evaluated using a train-predict-validate-extend strategy, in which validated predictions are recursively added to the training set to progressively extend the prediction horizon. The results demonstrate accurate and physically consistent predictions beyond the training domain, highlighting the framework's potential for engineering applications where data availability is limited.
