自适应融合物理与数据，提升小样本下的科学建模精度
Physics-Informed Neural Networks with Learnable Loss Balancing and Transfer Learning
- 用可学习的融合神经元动态调整物理约束与数据损失权重
- 仅用87个数据点实现热传导预测误差小于8%的优异表现
- 适合数据稀缺的流体、材料等科学建模场景
我们提出一种自监督物理信息神经网络（PINN）框架，在数据稀缺条件下自适应地平衡基于物理的监督与数据驱动的监督。不同于以往依赖固定或启发式权重的PINN，本方法引入可学习的融合神经元，根据各项不确定性动态调整物理残差与数据损失的相对贡献，实现稳定训练和更好泛化，无需人工调参。为提高效率，还集成迁移学习策略，复用相关领域的表征并适配新物理系统。在仅使用87个CFD数据点的液态金属微型散热器热传导预测任务中，自适应PINN误差低于8%，优于浅层神经网络、核方法及纯物理基线模型。该框架为在神经网络中自适应嵌入物理知识提供了通用方案，适用于流体动力学、材料建模等多个科学领域中的数据稀缺问题。
原文摘要 · Abstract (English)
We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or heuristic weighting of physics residuals and data loss, our approach introduces a learnable blending neuron that dynamically adjusts the relative contribution of each term based on their uncertainties. This mechanism enables stable training and improved generalization without manual tuning. To further enhance efficiency, we integrate a transfer learning strategy that reuses representations from related domains and adapts them to new physical systems with limited data. We validate the framework for the prediction of heat transfer in liquid-metal miniature heat sinks using only 87 CFD datapoints, where the adaptive PINN achieves an error <8%, outperforming shallow neural networks, kernel methods, and physics-only baselines. Our framework provides a general recipe for embedding physics adaptively into neural networks, offering a robust and reproducible approach for data-scarce problems across various scientific domains, including fluid dynamics and material modeling.
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