从非规则观测中无模拟学习GP-SDE
Simulation-Free Learning of GP-SDEs from Irregular Observations
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中文总结 AI 辅助
提出GP-SDE匹配框架，通过解析边缘化稀疏GP后验实现无模拟贝叶斯漂移学习，并引入非规则时间感知变分后验，在Lorenz-63及五个基准上显著提升漂移恢复、状态重建与预测稳健性。
中文摘要 AI 辅助
高斯过程随机微分方程（GP-SDE）为具有不确定性量化的未知连续时间状态动力学提供了一种灵活的贝叶斯模型，但从噪声和非规则观测中进行学习和推断在计算上仍具挑战性。为解决此问题，我们提出了GP-SDE匹配，一种用于贝叶斯GP漂移学习和连续时间状态平滑的无模拟变分框架。我们通过解析边缘化稀疏GP后验，推导出一个可处理的漂移匹配目标，该目标同时考虑了未知漂移的后验均值和不确定性。为处理非规则观测，我们进一步引入了一种非规则时间感知的变分状态后验，在编码和连续时间边际查询期间均纳入实际观测时间。在随机Lorenz-63系统上的实验表明，在非规则观测下，漂移恢复和状态重建显著改善，而五个系统辨识基准在观测稀疏性增加时显示出稳健的预测性能，并与现有潜SDE和状态空间方法相比具有竞争力。
英文摘要
Gaussian process stochastic differential equations (GP-SDEs) provide a flexible Bayesian model for unknown continuous-time state dynamics with uncertainty quantification, but learning and inference from noisy and irregular observations remain computationally challenging. To address this issue, we propose GP-SDE Matching, a simulation-free variational framework for Bayesian GP drift learning and continuous-time state smoothing. We analytically marginalize the sparse GP posterior to derive a tractable drift-matching objective that accounts for both the posterior mean and uncertainty of the unknown drift. To handle irregular observations, we further introduce an irregular-time-aware variational state posterior that incorporates the actual observation times during both encoding and continuous-time marginal querying. Experiments on the stochastic Lorenz--63 system demonstrate substantially improved drift recovery and state reconstruction under irregular observations, while five system identification benchmarks show robust forecasting under increasing observation sparsity and competitive performance against existing latent-SDE and state-space methods.
