ArticleProceedings of the National Academy of Sciences of the United States of America2021
Inference of dynamic systems from noisy and sparse data via manifold-constrained Gaussian processes.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2021. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 9 papers.
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Who cites it
9 citing papers in PubMed.
- Modeling with uncertainty quantification reveals the essentials of a non-canonical algal carbon-concentrating mechanism.Plant physiology · 2025Article
- Weak-form inference for hybrid dynamical systems in ecology.Journal of the Royal Society, Interface · 2024Article
- Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics.Bulletin of mathematical biology · 2023Article
- Nonlinear expression patterns and multiple shifts in gene network interactions underlie robust phenotypic change in Drosophila melanogaster selected for night sleep duration.PLoS computational biology · 2023Article
- Direct Estimation of Parameters in ODE Models Using WENDy: Weak-form Estimation of Nonlinear Dynamics.ArXiv · 2023Article
- Estimating and Assessing Differential Equation Models with Time-Course Data.The journal of physical chemistry. B · 2023Article
- Inferring potential landscapes from noisy trajectories of particles within an optical feedback trap.iScience · 2022Article
- Quantifying nanoscale forces using machine learning in dynamic atomic force microscopy.Nanoscale advances · 2022Article
- InfPolyn, a Nonparametric Bayesian Characterization for Composition-Dependent Interdiffusion Coefficients.Materials (Basel, Switzerland) · 2021Article
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Authors and funding
3 authors.
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Abstract
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.
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