通过傅里叶空间适配，让模型轻松泛化到新物理系统。
Generalizing to New Dynamical Systems via Frequency Domain Adaptation
- 在傅里叶频域中划分共享与特定动态，实现高效参数化适配。
- 在4类动力系统上测试，性能优于或媲美现有方法，参数量大幅降低。
- 适合需要快速适应新环境的物理模拟场景，如机器人控制、气候建模。
从数据中学习底层动力学的深度神经网络在建模各类复杂物理系统方面展现出巨大潜力。然而，现有方法在特定领域预测可靠性不足，且难以泛化到由相同基本动力学但环境特征不同的新系统。本文提出一种参数高效的通用方法——傅里叶神经模拟器用于动力学适配（FNSDA），通过在傅里叶空间进行自适应调整，实现对新系统的快速泛化。FNSDA基于已知环境自动划分傅里叶模式，识别共享动力学，并通过低维潜在系统参数条件化，学习每种新环境特有的模式以实现高效泛化。我们在四类代表性动力系统上评估该方法，结果表明，相比现有方法，FNSDA在保持显著更低参数成本的同时，实现了更优或相当的泛化性能。代码已公开于https://github.com/WonderSeven/FNSDA。
原文摘要 · Abstract (English)
Learning the underlying dynamics from data with deep neural networks has shown remarkable potential in modeling various complex physical dynamics. However, current approaches are constrained in their ability to make reliable predictions in a specific domain and struggle with generalizing to unseen systems that are governed by the same general dynamics but differ in environmental characteristics. In this work, we formulate a parameter-efficient method, Fourier Neural Simulator for Dynamical Adaptation (FNSDA), that can readily generalize to new dynamics via adaptation in the Fourier space. Specifically, FNSDA identifies the shareable dynamics based on the known environments using an automatic partition in Fourier modes and learns to adjust the modes specific for each new environment by conditioning on low-dimensional latent systematic parameters for efficient generalization. We evaluate our approach on four representative families of dynamic systems, and the results show that FNSDA can achieve superior or competitive generalization performance compared to existing methods with a significantly reduced parameter cost. Our code is available at https://github.com/WonderSeven/FNSDA.
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