arXiv:2510.12618cs.LG2025-10被引 2

用预训练模型加速复杂系统降维与方程发现,无需重训练。

Towards Fast Coarse-graining and Equation Discovery with Foundation Inference Models

  • 分离降维与方程求解任务,用冻结的奠基推理模型直接推断动力学
  • 在含半圆扩散的随机双阱系统上实现快速、稳定的低维表征学习
  • 适合需要高效复用降维流程的科研人员,尤其物理建模与数据驱动研究

高维动态过程通常由少量有效变量描述,其演化位于低维流形上。识别这些隐含动力学需同时解决两个耦合问题:发现合适的粗粒化变量并拟合控制方程。现有机器学习方法多通过联合训练自编码器与动态一致性模型来处理。本文提出解耦策略:利用近期提出的奠基推理模型(Foundation Inference Models, FIMs),该模型可零样本估计动态系统的无穷小生成元(如随机微分方程的漂移与扩散项)。通过固定FIM权重,仅训练编码器-解码器映射,并基于此定义一个简单且模拟一致的损失函数,显著稳定了表示学习。在嵌入合成视频数据的随机双阱系统(含半圆扩散)上的概念验证实验表明,该方法具备构建快速、可复用的粗粒化流水线的潜力。

原文摘要 · Abstract (English)

High-dimensional recordings of dynamical processes are often characterized by a much smaller set of effective variables, evolving on low-dimensional manifolds. Identifying these latent dynamics requires solving two intertwined problems: discovering appropriate coarse-grained variables and simultaneously fitting the governing equations. Most machine learning approaches tackle these tasks jointly by training autoencoders together with models that enforce dynamical consistency. We propose to decouple the two problems by leveraging the recently introduced Foundation Inference Models (FIMs). FIMs are pretrained models that estimate the infinitesimal generators of dynamical systems (e.g., the drift and diffusion of a stochastic differential equation) in zero-shot mode. By amortizing the inference of the dynamics through a FIM with frozen weights, and training only the encoder-decoder map, we define a simple, simulation-consistent loss that stabilizes representation learning. A proof of concept on a stochastic double-well system with semicircle diffusion, embedded into synthetic video data, illustrates the potential of this approach for fast and reusable coarse-graining pipelines.

降维动力系统基础模型方程发现

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