论文标题
通过歧管受限的高斯过程从嘈杂和稀疏数据中推断动态系统
Inference of dynamic systems from noisy and sparse data via manifold-constrained Gaussian processes
论文作者
论文摘要
在许多领域中，使用嘈杂和稀疏数据以普通微分方程（ODE）表示的非线性动态系统模型的参数估计是一项至关重要的任务。我们为此任务提出了一种快速准确的方法，即Magi（流动构成的高斯过程推断）。 Magi使用高斯过程模型在时间序列数据上使用，明确条件是在多种限制下进行的，即高斯过程的衍生物必须满足ODE系统。通过这样做，我们完全绕过了对数值集成的需求，并在计算时间内实现了大量节省。 MAGI也适用于使用未观察到的系统组件的推断，这些组件通常在实际实验中发生。 MAGI与现有方法不同，因为我们在贝叶斯框架下提供了原则上的统计结构，该框架通过歧管约束结合了ODE系统。我们使用基于物理实验的现实示例来证明MAGI的准确性和速度。
Parameter estimation for nonlinear dynamic system models, represented by ordinary differential equations (ODEs), using noisy and sparse data is a vital task in many fields. We propose a fast and accurate method, MAGI (MAnifold-constrained Gaussian process Inference), for this task. MAGI uses a Gaussian process model over time-series data, explicitly conditioned on the manifold constraint that derivatives of the Gaussian process must satisfy the ODE system. By doing so, we completely bypass the need for numerical integration and achieve substantial savings in computational time. MAGI is also suitable for inference with unobserved system components, which often occur in real experiments. MAGI is distinct from existing approaches as we provide a principled statistical construction under a Bayesian framework, which incorporates the ODE system through the manifold constraint. We demonstrate the accuracy and speed of MAGI using realistic examples based on physical experiments.
