[论文] Efficient Closure Learning in Dynamical Systems: A Comparison of Data-...

论文概要

研究领域: ML 作者: Rileigh Bandy, Teresa Portone, Mohammad Khalil, Eric Crislip, Kyle Neal 发布时间: 2026-11-02 arXiv: 2611.03612

中文摘要

算力的增长变革了计算科学，提升了对复杂系统的预测能力，但许多现象仍超出当前模拟能力，或需要快速评估以支持快速设计迭代。闭合模型（closure model）通过逼近「被约简或不完整动力系统」中未解析的效应来应对这一挑战。数据驱动的闭合模型为提升精度与适用性提供了灵活机制，但将闭合嵌入到计算模型中、在建构与训练阶段联合处理的方法，可能计算昂贵并在训练期间引发数值不稳定。为避免嵌入式的挑战，研究者发展出分阶段（staged）的闭合模型学习方法：第一阶段用数据同化从观测中推断状态与闭合轨迹；第二阶段用同化数据离线训练机器学习闭合模型，避免训练期间反复调用模拟器。本文以带非线性状态依赖隔离闭合的合成的流行病学 SIQR 模型为例，研究嵌入式与分阶段数据驱动闭合建模之间的成本-精度权衡。结果展示了一种实际的精度-效率权衡：在该示例中，嵌入式训练提供最强的平均精度，而分阶段方法以适度增加的误差换取了显著更少的模型评估与更优的优化鲁棒性，定性行为相当。

原文摘要

Increased computing power has transformed computational science and improved predictive capabilities for complex systems, but many phenomena still exceed current simulation capabilities or require rapid evaluations for fast design iterations. Closure models address this challenge by approximating unresolved effects in reduced or incomplete dynamical systems. Data-driven closures offer a flexible mechanism for improving model accuracy and applicability, but approaches that embed the closure within a computational model for construction and training phases can be computationally expensive and cause numerical instabilities in the computational model during training. To avoid the challenges posed by embedded approaches, staged approaches to closure-model learning have been developed. The first...

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