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, manifold-constrained Gaussian process inference (MAGI), 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.

用常微分方程 (ODE) 表示的非线性动态系统模型的参数估计，使用噪声和稀疏数据，是许多领域的一项重要任务。我们为此任务提出了一种快速准确的方法，即流形约束高斯过程推理 (MAGI)。MAGI 在时间序列数据上使用高斯过程模型，明确地以高斯过程的导数必须满足 ODE 系统的流形约束为条件。通过这样做，我们完全绕过了数值积分的需要，并大大节省了计算时间。MAGI 也适用于未观察到的系统组件的推理，这在实际实验中经常发生。MAGI 与现有方法不同，因为我们在贝叶斯框架下提供有原则的统计结构，它通过流形约束合并了 ODE 系统。我们使用基于物理实验的真实示例来证明 MAGI 的准确性和速度。