将物理约束融入变分状态空间高斯过程，实现高效时空建模。
Physics-Informed Variational State-Space Gaussian Processes
- 基于变分推断构建时空状态空间高斯过程，融合线性与非线性物理规律。
- 计算复杂度线性于时间，显著优于现有方法。
- 适合需要物理一致性与不确定性量化的真实世界科学建模任务。
微分方程是许多科学与工程应用中重要的机制模型。随着数据的丰富，数据驱动的物理信息模型日益受到关注。高斯过程（GPs）因其能建模复杂非线性现象、融入先验知识并量化不确定性，特别适用于此类任务。现有方法虽有一定成效，但受限于计算效率低或仅适用于时间序列场景。本文提出一种变分时空状态空间高斯过程，可在保持线性与非线性物理约束的同时，实现线性于时间的计算开销。我们在多种合成与真实世界场景中验证了该方法，其在预测性能和计算效率上均优于当前最优水平。
原文摘要 · Abstract (English)
Differential equations are important mechanistic models that are integral to many scientific and engineering applications. With the abundance of available data there has been a growing interest in data-driven physics-informed models. Gaussian processes (GPs) are particularly suited to this task as they can model complex, non-linear phenomena whilst incorporating prior knowledge and quantifying uncertainty. Current approaches have found some success but are limited as they either achieve poor computational scalings or focus only on the temporal setting. This work addresses these issues by introducing a variational spatio-temporal state-space GP that handles linear and non-linear physical constraints while achieving efficient linear-in-time computation costs. We demonstrate our methods in a range of synthetic and real-world settings and outperform the current state-of-the-art in both predictive and computational performance.
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