Helix-FNO：谱域算子学习与高保真机理模型耦合的快速代理仿真

中文摘要 AI 辅助

全规模处理过程的机理仿真模型仍然是底层物理化学动力学唯一可信且可外推的描述，但其运行时间过慢，无法支持现代决策引擎在5分钟决策节奏下所需的数千次前向评估。标准的补救措施——代理建模——通常会产生一个针对单一配置学习单一解的网络，因此对新进水水质概况、控制设置或工厂布局的泛化能力较差。本文提出了Helix-FNO，一种师生架构，将三十二状态机理教师模型与傅里叶神经算子（FNO）学生模型耦合。教师模型提供由拉丁超立方体和基于不确定性的主动学习精心策划的输入场到解对的高保真数据集，以覆盖实践中重要的边界和过载工况；学生模型在谱域中学习解算子本身，而非任何单一解，从而从学习单个实例转变为学习整个方程族。我们给出了算子公式、谱卷积定义、加权蒸馏损失和主动学习准则，并分析了截断傅里叶展开相对于参数化解流形光滑性的逼近误差。一项示例性研究将Helix-FNO与物理信息网络和数据驱动的循环代理模型在准确性、数据集效率和推理延迟方面进行比较，并将这些方法置于速度-准确性帕累托前沿上。所得算子比机理教师模型快三个数量级，推理时间为毫秒级，这正是大规模候选筛选和在线决策支持所需的能力。

英文摘要

Mechanistic simulation models of full-scale treatment processes remain the only trustworthy, extrapolative description of the underlying physico-chemical dynamics, yet their runtime is far too slow to support the thousands of forward evaluations that a modern decision engine requires at a 5-minute decision cadence. The standard remedy-surrogate modelling-often produces a network that learns a single solution for a single configuration, so it generalises poorly to new influent profiles, control settings or plant layouts. This paper presents Helix-FNO, a teacher-student architecture that couples a thirty-two-state mechanistic teacher with a Fourier neural operator (FNO) student. The teacher supplies a high-fidelity dataset of input-field-to-solution pairs, curated by Latin-hypercube and uncertainty-based active learning to cover the boundary and overload regimes that matter in practice; the student learns, in the spectral domain, the solution operator itself rather than any single solution, thereby moving from learning one instance to learning an entire family of equations. We give the operator formulation, the spectral convolution definition, the weighted distillation loss and the active-learning criterion, and we analyse the approximation error of a truncated Fourier expansion with respect to the smoothness of the parametric solution manifold. An illustrative study compares Helix-FNO against a physics-informed network and a data-driven recurrent surrogate on accuracy, dataset efficiency and inference latency, and places the methods on a speed-accuracy Pareto front. The resulting operator is three orders of magnitude faster than the mechanistic teacher at millisecond inference, which is precisely the capability required for massive candidate screening and online decision support.

发表机构

• University of Science and Technology Liaoning（辽宁科技大学）
• Wuhan University（武汉大学）

机构由 AI 辅助整理，请以论文原文为准。