无需训练即可预测新动态系统长期行为，且速度与参数量远超现有模型。
True Zero-Shot Inference of Dynamical Systems Preserving Long-Term Statistics
- 基于ALRNN的混合专家架构，预训练实现零样本泛化。
- 仅用0.1%参数量，推理速度提升数个数量级，长期统计误差更小。
- 适合需要快速部署、跨领域预测的科学建模场景。
复杂的时间演化现象（如气候、脑活动）由动力系统（DS）支配。动力系统重建（DSR）旨在从观测数据中推断生成性代理模型，复现其长期行为。现有方法需为每个新系统单独训练，缺乏类似大语言模型的零样本与上下文推理能力。本文提出DynaMix，首个通过预训练实现零样本泛化的多变量ALRNN混合专家架构。仅凭给定上下文信号，无需重训练，即可准确预测全新动力系统的长期演化；而现有时间序列基础模型（如Chronos）在此类任务中失败。DynaMix参数量仅为0.1%，推理速度提升数个数量级，在真实世界数据（如交通、天气）上长期统计性能超越主流模型，甚至短时预测也表现更优。我们揭示了时间序列模型在DSR任务中的失效模式，表明基于动力系统原理的模型对时间序列预测领域具有巨大潜力。
原文摘要 · Abstract (English)
Complex, temporally evolving phenomena, from climate to brain activity, are governed by dynamical systems (DS). DS reconstruction (DSR) seeks to infer generative surrogate models of these from observed data, reproducing their long-term behavior. Existing DSR approaches require purpose-training for any new system observed, lacking the zero-shot and in-context inference capabilities known from LLMs. Here we introduce DynaMix, a novel multivariate ALRNN-based mixture-of-experts architecture pre-trained for DSR, the first DSR model able to generalize zero-shot to out-of-domain DS. Just from a provided context signal, without any re-training, DynaMix faithfully forecasts the long-term evolution of novel DS where existing time series (TS) foundation models, like Chronos, fail -- at a fraction of the number of parameters (0.1%) and orders of magnitude faster inference times. DynaMix outperforms TS foundation models in terms of long-term statistics, and often also short-term forecasts, even on real-world time series, like traffic or weather data, typically used for training and evaluating TS models, but not at all part of DynaMix' training corpus. We illustrate some of the failure modes of TS models for DSR problems, and conclude that models built on DS principles may bear a huge potential also for advancing the TS prediction field.
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