arXiv:2606.22969cs.LGmath.DS2026-06被引 1

提出新方法实现动力系统零样本外域预测,突破传统模型在临界点外的局限。

Topological Out-of-Domain Generalization in Dynamical Systems Reconstruction

论文配图:Topological Out-of-Domain Generalization in Dynamical Systems Reconstruction
图 1 · 摘自论文原文
  • 通过特征拆分与结构修正,解决模型对物理系统性质的误匹配问题。
  • 推导出可靠外推范围的闭式边界,首次量化外推能力上限。
  • 可在不微调情况下准确预测跨临界点的新动态行为,适合科学建模研究者。

预测动力系统(DS)在训练中未覆盖的动力学与参数范围之外的行为,是科学机器学习中的核心难题。现有基于层次化与超网络的方法虽可同时训练多个系统,发现潜在特征常关联关键控制参数,但其真正外域预测能力仍有限,尤其在跨越临界点时需重新微调甚至全量重训。本文数学分析了旧模型的根本缺陷,识别出三类源于模型结构假设与物理系统典型特性不匹配的不足。提出改进方案,核心为特征拆分,并推导出可靠外推范围的闭式上界。实验证明,所提方法可在无需微调情况下实现对新动力学区域的精确零样本预测,如跨临界点场景。

原文摘要 · Abstract (English)

Predicting the behavior of dynamical systems (DS) beyond the dynamical and parameter regimes observed in training is a pivotal and essentially unresolved problem in scientific ML. It is central to any good scientific theory, which we expect to be able to make predictions about regimes not covered by currently available data. Recent hierarchical and hyper-network guided approaches for DS reconstruction (DSR) enable training on many DS simultaneously, and revealed that extracted latent features are often related to crucial control parameters of the underlying DS that varied across the training corpus. However, true out-of-domain forecasting abilities of these models, e.g., across tipping points, remain limited, and fine-tuning, or even full model retraining, on time series from the new dynamical regime is usually required. Here, we mathematically analyze the root of these limitations in previous model formulations and identify three core shortcomings rooted in a mismatch between structural assumptions of the reconstruction model and typical properties of physical systems. We propose a combination of remedies for these shortcomings, most importantly feature splitting, and furthermore derive a closed-form bound on the reliable extrapolation range. We demonstrate empirically that our techniques allow for accurate zero-shot prediction into new dynamical regimes, outside the observed training regime, as, e.g., encountered across tipping points.

动力系统外域泛化零样本预测科学机器学习

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