物理先验知识可让依赖数据下的学习速度达到独立同分布水平。
Physics-informed learning under mixing: How physical knowledge speeds up learning
- 引入物理先验正则化，提升依赖数据的学习效率
- 对齐的物理知识使学习率从Sobolev最坏情况提升至最优独立同分布水平
- 适合关注物理信息机器学习加速机制的研究者
在物理信息机器学习中，理解先验领域知识如何影响数据相关条件下的学习速率是一个主要挑战。本文聚焦于带物理信息正则化的经验风险最小化，推导了过剩风险在概率和期望意义上的复杂度相关界。证明当物理先验信息对齐时，学习速率可从（慢）Sobolev极小最大速率提升至（快）最优独立同分布速率，且无需因数据依赖而降低样本量。
原文摘要 · Abstract (English)
A major challenge in physics-informed machine learning is to understand how the incorporation of prior domain knowledge affects learning rates when data are dependent. Focusing on empirical risk minimization with physics-informed regularization, we derive complexity-dependent bounds on the excess risk in probability and in expectation. We prove that, when the physical prior information is aligned, the learning rate improves from the (slow) Sobolev minimax rate to the (fast) optimal i.i.d. one without any sample-size deflation due to data dependence.
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