mlsanityData to 14 Oct 2026

MAGI-X: Manifold-Constrained Gaussian Process Inference for Unknown System Dynamics

arXiv 2105.12894 ↗First posted 27 May 2021stat.ML cs.LG stat.COcited by 0

Not on the map. Why?

Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 18 of its 44 references that are in the map. First posted on arXiv 27 May 2021.

Builds on

18 of 44 references.

References · 18

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2017The Expressive Power of Neural Networks: A View from the Widthcited by 320
  3. 2016Benefits of depth in neural networkscited by 250
  4. 2015The Power of Depth for Feedforward Neural Networkscited by 183
  5. 2015A Complete Recipe for Stochastic Gradient MCMCcited by 146
  6. 2016Why does deep and cheap learning work so well?cited by 100
  7. 2020Minimum Width for Universal Approximationcited by 94
  8. 2018Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systemscited by 89
  9. 2017Numerical Gaussian Processes for Time-dependent and Non-linear Partial Differential Equationscited by 72
  10. 2018Learning unknown ODE models with Gaussian processescited by 54
  11. 2017The power of deeper networks for expressing natural functionscited by 35
  12. 2020Interpretable Sequence Learning for COVID-19 Forecastingcited by 22
6 more
  1. 2020Inference of dynamic systems from noisy and sparse data via manifold-constrained Gaussian processescited by 18
  2. 2018Fast Gaussian Process Based Gradient Matching for Parameter Identification in Systems of Nonlinear ODEscited by 17
  3. 2019ODIN: ODE-Informed Regression for Parameter and State Inference in Time-Continuous Dynamical Systemscited by 17
  4. 2020Learning ODE Models with Qualitative Structure Using Gaussian Processescited by 9
  5. 2013Reproducing kernel Hilbert space based estimation of systems of ordinary differential equationscited by 5
  6. 2014Learning nonparametric differential equations with operator-valued kernels and gradient matchingcited by 4

Built on by

Not cited yet.