MAGI-X: Manifold-Constrained Gaussian Process Inference for Unknown System Dynamics
This provides a practical solution for inferring partially observed systems in scientific applications, addressing a bottleneck where existing methods fail.
The paper tackles the problem of learning unknown dynamic systems from observational data without requiring domain knowledge or costly numerical integration, proposing MAGI-X which achieves competitive accuracy in fitting and forecasting while significantly reducing computational time compared to state-of-the-art methods.
Ordinary differential equations (ODEs), commonly used to characterize the dynamic systems, are difficult to propose in closed-form for many complicated scientific applications, even with the help of domain expert. We propose a fast and accurate data-driven method, MAGI-X, to learn the unknown dynamic from the observation data in a non-parametric fashion, without the need of any domain knowledge. Unlike the existing methods that mainly rely on the costly numerical integration, MAGI-X utilizes the powerful functional approximator of neural network to learn the unknown nonlinear dynamic within the MAnifold-constrained Gaussian process Inference (MAGI) framework that completely circumvents the numerical integration. Comparing against the state-of-the-art methods on three realistic examples, MAGI-X achieves competitive accuracy in both fitting and forecasting while only taking a fraction of computational time. Moreover, MAGI-X provides practical solution for the inference of partial observed systems, which no previous method is able to handle.