用少量噪声数据零样本推断微分方程，像大模型一样即插即用。
Towards Foundation Inference Models that Learn ODEs In-Context
- 基于预训练神经算子，直接从稀疏观测中推断微分方程
- 在合成数据上表现接近顶尖方法，抗噪能力强
- 适合需要快速建模动态系统的科研与工程人员
常微分方程（ODE）描述了连续时间下确定性演化动力系统。在自然科学中，基于数据准确建模系统为ODE仍是核心挑战，尤其当数据稀疏或含噪声时。我们提出FIM-ODE（面向ODE的基石推理模型），一种预训练神经模型，可零样本（即上下文）从稀疏和噪声观测中估计ODE。该模型在合成数据上训练，利用灵活的神经算子实现鲁棒的ODE推断，即使在数据被污染时仍有效。我们实证验证了FIM-ODE能提供高精度估计，性能与当前先进的神经方法相当，并定性比较了其估计向量场的结构。
原文摘要 · Abstract (English)
Ordinary differential equations (ODEs) describe dynamical systems evolving deterministically in continuous time. Accurate data-driven modeling of systems as ODEs, a central problem across the natural sciences, remains challenging, especially if the data is sparse or noisy. We introduce FIM-ODE (Foundation Inference Model for ODEs), a pretrained neural model designed to estimate ODEs zero-shot (i.e., in context) from sparse and noisy observations. Trained on synthetic data, the model utilizes a flexible neural operator for robust ODE inference, even from corrupted data. We empirically verify that FIM-ODE provides accurate estimates, on par with a neural state-of-the-art method, and qualitatively compare the structure of their estimated vector fields.
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