Fast Gaussian Process Based Gradient Matching for Parameter Identification in Systems of Nonlinear ODEs
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Abstract (arXiv)
Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a dynamical system without explicitly solving it. While the benefits in computational cost are well established, a rigorous mathematical framework has been missing. We offer a novel interpretation which leads to a better understanding and improvements in state-of-the-art performance in terms of accuracy for nonlinear dynamical systems.
Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 12 Apr 2018.
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Citing papers per year: 2021: 5; 2022: 2; 2023: 7; 2024: 1; 2025: 1; 2026: 1.
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- 2024Marrying Causal Representation Learning with Dynamical Systems for Sciencecited by 22
- 2022AutoIP: A United Framework to Integrate Physics into Gaussian Processescited by 20
- 2023Causal Deep Learningcited by 20
- 2021Gaussian processes meet NeuralODEs: A Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy datacited by 13
- 2022Fenrir: Physics-Enhanced Regression for Initial Value Problemscited by 11
- 2021Structure-preserving Gaussian Process Dynamicscited by 9
- 2023Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernelscited by 5
- 2023Data-Adaptive Probabilistic Likelihood Approximation for Ordinary Differential Equationscited by 3
- 2023Exact Inference for Continuous-Time Gaussian Process Dynamicscited by 3
- 2023Scalable Bayesian optimization with high-dimensional outputs using randomized prior networkscited by 2
- 2021Distributional Gradient Matching for Learning Uncertain Neural Dynamics Modelscited by 1
- 2021Approximate Latent Force Model Inferencecited by 1
5 more
- 2021MAGI-X: Manifold-Constrained Gaussian Process Inference for Unknown System Dynamicscited by 0
- 2023Using Intermediate Forward Iterates for Intermediate Generator Optimizationcited by 0
- 2023Uncertainty Informed Optimal Resource Allocation with Gaussian Process based Bayesian Inferencecited by 0
- 2025Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Modelcited by 0
- 2026Gaussian process learning with flow map refinement for parameter estimation in dynamical systemscited by 0
- 2026Gaussian process learning with flow map refinement for parameter estimation in dynamical systems23 Aug 2026
- 2025Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Model15 Jul 2025
- 2024Marrying Causal Representation Learning with Dynamical Systems for Science22 May 2024
- 2023Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels9 Oct 2023
- 2023Exact Inference for Continuous-Time Gaussian Process Dynamics5 Sep 2023
- 2023Uncertainty Informed Optimal Resource Allocation with Gaussian Process based Bayesian Inference30 Jun 2023
- 2023Data-Adaptive Probabilistic Likelihood Approximation for Ordinary Differential Equations8 Jun 2023
- 2023Causal Deep Learning3 Mar 2023
- 2023Scalable Bayesian optimization with high-dimensional outputs using randomized prior networks14 Feb 2023
- 2023Using Intermediate Forward Iterates for Intermediate Generator Optimization5 Feb 2023
- 2022AutoIP: A United Framework to Integrate Physics into Gaussian Processes24 Feb 2022
- 2022Fenrir: Physics-Enhanced Regression for Initial Value Problems2 Feb 2022
5 more
- 2021Approximate Latent Force Model Inference24 Sep 2021
- 2021Distributional Gradient Matching for Learning Uncertain Neural Dynamics Models22 Jun 2021
- 2021MAGI-X: Manifold-Constrained Gaussian Process Inference for Unknown System Dynamics27 May 2021
- 2021Gaussian processes meet NeuralODEs: A Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data4 Mar 2021
- 2021Structure-preserving Gaussian Process Dynamics2 Feb 2021
- 2024Marrying Causal Representation Learning with Dynamical Systems for Sciencecited by 22
- 2022AutoIP: A United Framework to Integrate Physics into Gaussian Processescited by 20
- 2023Causal Deep Learningcited by 20
- 2021Gaussian processes meet NeuralODEs: A Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy datacited by 13
- 2022Fenrir: Physics-Enhanced Regression for Initial Value Problemscited by 11
- 2021Structure-preserving Gaussian Process Dynamicscited by 9
- 2023Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernelscited by 5
- 2023Data-Adaptive Probabilistic Likelihood Approximation for Ordinary Differential Equationscited by 3
- 2023Exact Inference for Continuous-Time Gaussian Process Dynamicscited by 3
- 2023Scalable Bayesian optimization with high-dimensional outputs using randomized prior networkscited by 2
- 2021Distributional Gradient Matching for Learning Uncertain Neural Dynamics Modelscited by 1
- 2021Approximate Latent Force Model Inferencecited by 1
12 most cited of 16 All 16 (JSON)
- 2026Gaussian process learning with flow map refinement for parameter estimation in dynamical systems23 Aug 2026
- 2025Learning from Imperfect Data: Robust Inference of Dynamic Systems using Simulation-based Generative Model15 Jul 2025
- 2024Marrying Causal Representation Learning with Dynamical Systems for Science22 May 2024
- 2023Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels9 Oct 2023
- 2023Exact Inference for Continuous-Time Gaussian Process Dynamics5 Sep 2023
- 2023Uncertainty Informed Optimal Resource Allocation with Gaussian Process based Bayesian Inference30 Jun 2023
- 2023Data-Adaptive Probabilistic Likelihood Approximation for Ordinary Differential Equations8 Jun 2023
- 2023Causal Deep Learning3 Mar 2023
- 2023Scalable Bayesian optimization with high-dimensional outputs using randomized prior networks14 Feb 2023
- 2022AutoIP: A United Framework to Integrate Physics into Gaussian Processes24 Feb 2022
- 2022Fenrir: Physics-Enhanced Regression for Initial Value Problems2 Feb 2022
- 2021Approximate Latent Force Model Inference24 Sep 2021
12 newest of 16 All 16 (JSON)