Inference of dynamic systems from noisy and sparse data via manifold-constrained Gaussian processes

Significance Ordinary differential equations are a ubiquitous tool for modeling behaviors in science, such as gene regulation, biological rhythms, epidemics, and ecology. An important problem is to infer and characterize the uncertainty of parameters that govern equations. We present an accurate and fast inference method using manifold-constrained Gaussian processes, such that derivatives of the Gaussian process must satisfy the dynamics of the differential equations. Our method completely avoids the use of numerical integration and is thus fast to compute. Our construction is embedded in a principled statistical framework and is demonstrated to yield fast and reliable inference in a variety of practical problems. Our method works even when some system components are unobserved, which is a significant challenge for previous methods.