Gaussian process learning of nonlinear dynamics

• URL: http://arxiv.org/abs/2312.12193v2
• Date: Tue, 16 Apr 2024 17:06:37 GMT
• Title: Gaussian process learning of nonlinear dynamics
• Authors: Dongwei Ye, Mengwu Guo,
• Abstract summary: We propose a new method that learns nonlinear dynamics through a Bayesian inference of characterizing model parameters. We will discuss the applicability of the proposed method to several typical scenarios for dynamical systems.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly available and can be approximated conventionally by finite differences. However, the discrete approximations of time derivatives may result in poor estimations when state data are scarce and/or corrupted by noise, thus compromising the predictiveness of the learned dynamical models. To overcome this technical hurdle, we propose a new method that learns nonlinear dynamics through a Bayesian inference of characterizing model parameters. This method leverages a Gaussian process representation of states, and constructs a likelihood function using the correlation between state data and their derivatives, yet prevents explicit evaluations of time derivatives. Through a Bayesian scheme, a probabilistic estimate of the model parameters is given by the posterior distribution, and thus a quantification is facilitated for uncertainties from noisy state data and the learning process. Specifically, we will discuss the applicability of the proposed method to several typical scenarios for dynamical systems: identification and estimation with an affine parametrization, nonlinear parametric approximation without prior knowledge, and general parameter estimation for a given dynamical system.

Related papers

• Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertainty [8.815974147041048]
  We develop a novel framework to identify parsimonious governing equations of nonlinear (spatiotemporal) dynamics from sparse, noisy data with quantified uncertainty. The proposed algorithm is evaluated on multiple nonlinear dynamical systems governed by canonical ordinary and partial differential equations.
  arXiv  Detail & Related papers  (2022-10-14T20:37:36Z)
• A Causality-Based Learning Approach for Discovering the Underlying Dynamics of Complex Systems from Partial Observations with Stochastic Parameterization [1.2882319878552302]
  This paper develops a new iterative learning algorithm for complex turbulent systems with partial observations. It alternates between identifying model structures, recovering unobserved variables, and estimating parameters. Numerical experiments show that the new algorithm succeeds in identifying the model structure and providing suitable parameterizations for many complex nonlinear systems.
  arXiv  Detail & Related papers  (2022-08-19T00:35:03Z)
• A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study [68.8204255655161]
  We investigate and compare the performance of several local and global smoothing techniques to a priori denoise the state measurements. We show that, in general, global methods, which use the entire measurement data set, outperform local methods, which employ a neighboring data subset around a local point.
  arXiv  Detail & Related papers  (2022-01-29T23:31:25Z)
• Time varying regression with hidden linear dynamics [74.9914602730208]
  We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system. Counterintuitively, we show that when the underlying dynamics are stable the parameters of this model can be estimated from data by combining just two ordinary least squares estimates.
  arXiv  Detail & Related papers  (2021-12-29T23:37:06Z)
• Structure-Preserving Learning Using Gaussian Processes and Variational Integrators [62.31425348954686]
  We propose the combination of a variational integrator for the nominal dynamics of a mechanical system and learning residual dynamics with Gaussian process regression. We extend our approach to systems with known kinematic constraints and provide formal bounds on the prediction uncertainty.
  arXiv  Detail & Related papers  (2021-12-10T11:09:29Z)
• MINIMALIST: Mutual INformatIon Maximization for Amortized Likelihood Inference from Sampled Trajectories [61.3299263929289]
  Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer an amortized estimator for the likelihood-to-evidence ratio. We show that this approach can be formulated in terms of mutual information between model parameters and simulated data.
  arXiv  Detail & Related papers  (2021-06-03T12:59:16Z)
• Gaussian processes meet NeuralODEs: A Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data [0.0]
  This paper presents a machine learning framework (GP-NODE) for Bayesian systems identification from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers. A series of numerical studies is presented to demonstrate the effectiveness of the proposed GP-NODE method including predator-prey systems, systems biology, and a 50-dimensional human motion dynamical system.
  arXiv  Detail & Related papers  (2021-03-04T23:42:14Z)
• Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components [52.77024349608834]
  We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is noisy partial measurements. We show that by using partial measurements of the state of the dynamical system, we can train a machine learning model to improve predictions made by an imperfect knowledge-based model.
  arXiv  Detail & Related papers  (2021-02-15T19:56:48Z)
• Neural Dynamic Mode Decomposition for End-to-End Modeling of Nonlinear Dynamics [49.41640137945938]
  We propose a neural dynamic mode decomposition for estimating a lift function based on neural networks. With our proposed method, the forecast error is backpropagated through the neural networks and the spectral decomposition. Our experiments demonstrate the effectiveness of our proposed method in terms of eigenvalue estimation and forecast performance.
  arXiv  Detail & Related papers  (2020-12-11T08:34:26Z)
• Data Assimilation Networks [1.5545257664210517]
  Data assimilation aims at forecasting the state of a dynamical system by combining a mathematical representation of the system with noisy observations. We propose a fully data driven deep learning architecture generalizing recurrent Elman networks and data assimilation algorithms. Our architecture achieves comparable performance to EnKF on both the analysis and the propagation of probability density functions of the system state at a given time without using any explicit regularization technique.
  arXiv  Detail & Related papers  (2020-10-19T17:35:36Z)
• Bayesian differential programming for robust systems identification under uncertainty [14.169588600819546]
  This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable programming to propagate gradient information through ordinary differential equation solvers. The use of sparsity-promoting priors enables the discovery of interpretable and parsimonious representations for the underlying latent dynamics.
  arXiv  Detail & Related papers  (2020-04-15T00:51:14Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.