dynoGP: Deep Gaussian Processes for dynamic system identification
- URL: http://arxiv.org/abs/2502.05620v1
- Date: Sat, 08 Feb 2025 15:57:59 GMT
- Title: dynoGP: Deep Gaussian Processes for dynamic system identification
- Authors: Alessio Benavoli, Dario Piga, Marco Forgione, Marco Zaffalon,
- Abstract summary: We present a novel approach to system identification for dynamical systems based on a specific class of Gaussian Deep Processes (Deep GPs)
Our approach combines the strengths of data-driven methods, such as those based on neural network architectures, with the ability to output a probability distribution.
Using both simulated and real-world data, we demonstrate the effectiveness of the proposed approach.
- Score: 0.7692572272935511
- License:
- Abstract: In this work, we present a novel approach to system identification for dynamical systems, based on a specific class of Deep Gaussian Processes (Deep GPs). These models are constructed by interconnecting linear dynamic GPs (equivalent to stochastic linear time-invariant dynamical systems) and static GPs (to model static nonlinearities). Our approach combines the strengths of data-driven methods, such as those based on neural network architectures, with the ability to output a probability distribution. This offers a more comprehensive framework for system identification that includes uncertainty quantification. Using both simulated and real-world data, we demonstrate the effectiveness of the proposed approach.
Related papers
- Koopman-Equivariant Gaussian Processes [39.34668284375732]
We propose a family of Gaussian processes (GP) for dynamical systems with linear time-invariant responses.
This linearity allows us to tractably quantify forecasting and representational uncertainty.
Experiments demonstrate on-par and often better forecasting performance compared to kernel-based methods for learning dynamical systems.
arXiv Detail & Related papers (2025-02-10T16:35:08Z) - LeARN: Learnable and Adaptive Representations for Nonlinear Dynamics in System Identification [0.0]
We introduce a nonlinear system identification framework called LeARN.
It transcends the need for prior domain knowledge by learning the library of basis functions directly from data.
We validate our framework on the Neural Fly dataset, showcasing its robust adaptation and capabilities.
arXiv Detail & Related papers (2024-12-16T18:03:23Z) - Learning Controlled Stochastic Differential Equations [61.82896036131116]
This work proposes a novel method for estimating both drift and diffusion coefficients of continuous, multidimensional, nonlinear controlled differential equations with non-uniform diffusion.
We provide strong theoretical guarantees, including finite-sample bounds for (L2), (Linfty), and risk metrics, with learning rates adaptive to coefficients' regularity.
Our method is available as an open-source Python library.
arXiv Detail & Related papers (2024-11-04T11:09:58Z) - SINDyG: Sparse Identification of Nonlinear Dynamical Systems from Graph-Structured Data [0.27624021966289597]
We develop a new method called Sparse Identification of Dynamical Systems from Graph-structured data (SINDyG)
SINDyG incorporates the network structure into sparse regression to identify model parameters that explain the underlying network dynamics.
Our experiments validate the improved accuracy and simplicity of discovered network dynamics.
arXiv Detail & Related papers (2024-09-02T17:51:37Z) - Modeling Latent Neural Dynamics with Gaussian Process Switching Linear Dynamical Systems [2.170477444239546]
We develop an approach that balances these two objectives: the Gaussian Process Switching Linear Dynamical System (gpSLDS)
Our method builds on previous work modeling the latent state evolution via a differential equation whose nonlinear dynamics are described by a Gaussian process (GP-SDEs)
Our approach resolves key limitations of the rSLDS such as artifactual oscillations in dynamics near discrete state boundaries, while also providing posterior uncertainty estimates of the dynamics.
arXiv Detail & Related papers (2024-07-19T15:32:15Z) - Capturing dynamical correlations using implicit neural representations [85.66456606776552]
We develop an artificial intelligence framework which combines a neural network trained to mimic simulated data from a model Hamiltonian with automatic differentiation to recover unknown parameters from experimental data.
In doing so, we illustrate the ability to build and train a differentiable model only once, which then can be applied in real-time to multi-dimensional scattering data.
arXiv Detail & Related papers (2023-04-08T07:55:36Z) - Capturing Actionable Dynamics with Structured Latent Ordinary
Differential Equations [68.62843292346813]
We propose a structured latent ODE model that captures system input variations within its latent representation.
Building on a static variable specification, our model learns factors of variation for each input to the system, thus separating the effects of the system inputs in the latent space.
arXiv Detail & Related papers (2022-02-25T20:00:56Z) - 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) - Supervised DKRC with Images for Offline System Identification [77.34726150561087]
Modern dynamical systems are becoming increasingly non-linear and complex.
There is a need for a framework to model these systems in a compact and comprehensive representation for prediction and control.
Our approach learns these basis functions using a supervised learning approach.
arXiv Detail & Related papers (2021-09-06T04:39:06Z) - 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) - Active Learning for Nonlinear System Identification with Guarantees [102.43355665393067]
We study a class of nonlinear dynamical systems whose state transitions depend linearly on a known feature embedding of state-action pairs.
We propose an active learning approach that achieves this by repeating three steps: trajectory planning, trajectory tracking, and re-estimation of the system from all available data.
We show that our method estimates nonlinear dynamical systems at a parametric rate, similar to the statistical rate of standard linear regression.
arXiv Detail & Related papers (2020-06-18T04:54:11Z)
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.