arXiv:2506.19609cs.LGnlin.CD2025-06

用可变网络生成器,让模型一次学会多种动态系统的行为。

Beyond Static Models: Hypernetworks for Adaptive and Generalizable Forecasting in Complex Parametric Dynamical Systems

  • 通过参数空间映射生成隐变量,动态调节预测网络权重。
  • 在未见参数组合下仍能准确预测长期轨迹和吸引子特征。
  • 适合需要跨参数泛化的复杂系统建模任务。

动力系统在科学多个领域中广泛用于建模、预测与决策。然而,系统参数的变化会引发截然不同的行为模式,给跨参数泛化建模带来挑战。本文提出参数化超网络学习插值网络(PHLieNet),同时学习:(a) 从参数空间到非线性嵌入的全局映射;(b) 从该嵌入到动态传播网络权重的映射。所学嵌入作为潜在表示,调控一个基础网络(即超网络),使其生成目标网络的权重,用于根据历史状态预测系统演化。通过在模型空间而非观测空间进行插值,PHLieNet实现不同参数系统行为间的平滑过渡,构建统一模型以覆盖广泛的参数配置。实验验证其在时间外推、参数空间内插与外推(即训练未见的动力学)方面的泛化能力。相比现有最优基线,该方法在短期预测精度及长期动力学特征(如吸引子统计)捕捉上表现更优。

原文摘要 · Abstract (English)

Dynamical systems play a key role in modeling, forecasting, and decision-making across a wide range of scientific domains. However, variations in system parameters, also referred to as parametric variability, can lead to drastically different model behavior and output, posing challenges for constructing models that generalize across parameter regimes. In this work, we introduce the Parametric Hypernetwork for Learning Interpolated Networks (PHLieNet), a framework that simultaneously learns: (a) a global mapping from the parameter space to a nonlinear embedding and (b) a mapping from the inferred embedding to the weights of a dynamics propagation network. The learned embedding serves as a latent representation that modulates a base network, termed the hypernetwork, enabling it to generate the weights of a target network responsible for forecasting the system's state evolution conditioned on the previous time history. By interpolating in the space of models rather than observations, PHLieNet facilitates smooth transitions across parameterized system behaviors, enabling a unified model that captures the dynamic behavior across a broad range of system parameterizations. The performance of the proposed technique is validated in a series of dynamical systems with respect to its ability to extrapolate in time and interpolate and extrapolate in the parameter space, i.e., generalize to dynamics that were unseen during training. Our approach outperforms state-of-the-art baselines in both short-term forecast accuracy and in capturing long-term dynamical features such as attractor statistics.

动态系统超网络参数泛化

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