[论文] HyCOP: Hybrid Composition Operators for Interpretable Learning of PDEs

论文概要

研究领域: ML 作者: Jinpai Zhao, Nishant Panda, Yen Ting Lin, Eirik Valseth, Diane Oyen, Clint Dawson 发布时间: 2026-05-01 arXiv: 2605.00820

中文摘要

本文提出HyCOP，一种模块化框架，通过组合简单模块（对流、扩散、学习闭包、边界处理）以查询条件化的方式学习参数化PDE解算子。与单块映射不同，HyCOP学习对短程序的策略——基于工况特征和状态统计决定应用哪个模块及持续多久。

模块可以是数值子求解器或学习组件，实现无需自回归展开即可在任意查询时间评估的混合代理。在多样化PDE基准上，HyCOP产生可解释的程序，在分布外(OOD)场景比单块神经算子提升一个数量级，并支持通过字典更新的模块化迁移（如边界交换、残差增强）。

理论刻画了表达能力，给出将组合误差与模块误差分离的误差分解，兼作过程级诊断工具。

原文摘要

We introduce HyCOP, a modular framework that learns parametric PDE solution operators by composing simple modules (advection, diffusion, learned closures, boundary handling) in a query-conditioned way. Rather than learning a monolithic map, HyCOP learns a policy over short programs - which module to apply and for how long - conditioned on regime features and state statistics. Modules may be numerical sub-solvers or learned components, enabling hybrid surrogates evaluated at arbitrary query times without autoregressive rollout. Across diverse PDE benchmarks, HyCOP produces interpretable programs, delivers order-of-magnitude OOD improvements over monolithic neural operators, and supports modular transfer through dictionary updates (e.g., boundary swaps, residual enrichment). Our theory characterizes expressivity and gives an error decomposition that separates composition error from module error and doubles as a process-level diagnostic.

自动采集于 2026-05-05

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