Model-free machine learning of conservation laws from data
- URL: http://arxiv.org/abs/2301.07503v1
- Date: Thu, 12 Jan 2023 19:18:07 GMT
- Title: Model-free machine learning of conservation laws from data
- Authors: Shivam Arora, Alex Bihlo, R\"udiger Brecht, Pavel Holba
- Abstract summary: We present a machine learning based method for learning first integrals of systems of ordinary differential equations from given trajectory data.
As a by-product, once the first integrals have been learned, also the system of differential equations will be known.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: We present a machine learning based method for learning first integrals of
systems of ordinary differential equations from given trajectory data. The
method is model-free in that it does not require explicit knowledge of the
underlying system of differential equations that generated the trajectories. As
a by-product, once the first integrals have been learned, also the system of
differential equations will be known. We illustrate our method by considering
several classical problems from the mathematical sciences.
Related papers
- Physics-informed nonlinear vector autoregressive models for the prediction of dynamical systems [0.36248657646376703]
We focus on one class of models called nonlinear vector autoregression (N VAR) to solve ordinary differential equations (ODEs)
Motivated by connections to numerical integration and physics-informed neural networks, we explicitly derive the physics-informed N VAR.
Because N VAR and piN VAR completely share their learned parameters, we propose an augmented procedure to jointly train the two models.
We evaluate the ability of the piN VAR model to predict solutions to various ODE systems, such as the undamped spring, a Lotka-Volterra predator-prey nonlinear model, and the chaotic Lorenz system.
arXiv Detail & Related papers (2024-07-25T14:10:42Z) - Towards true discovery of the differential equations [57.089645396998506]
Differential equation discovery is a machine learning subfield used to develop interpretable models.
This paper explores the prerequisites and tools for independent equation discovery without expert input.
arXiv Detail & Related papers (2023-08-09T12:03:12Z) - Symbolic Recovery of Differential Equations: The Identifiability Problem [52.158782751264205]
Symbolic recovery of differential equations is the ambitious attempt at automating the derivation of governing equations.
We provide both necessary and sufficient conditions for a function to uniquely determine the corresponding differential equation.
We then use our results to devise numerical algorithms aiming to determine whether a function solves a differential equation uniquely.
arXiv Detail & Related papers (2022-10-15T17:32:49Z) - D-CIPHER: Discovery of Closed-form Partial Differential Equations [80.46395274587098]
We propose D-CIPHER, which is robust to measurement artifacts and can uncover a new and very general class of differential equations.
We further design a novel optimization procedure, CoLLie, to help D-CIPHER search through this class efficiently.
arXiv Detail & Related papers (2022-06-21T17:59:20Z) - Neural Laplace: Learning diverse classes of differential equations in
the Laplace domain [86.52703093858631]
We propose a unified framework for learning diverse classes of differential equations (DEs) including all the aforementioned ones.
Instead of modelling the dynamics in the time domain, we model it in the Laplace domain, where the history-dependencies and discontinuities in time can be represented as summations of complex exponentials.
In the experiments, Neural Laplace shows superior performance in modelling and extrapolating the trajectories of diverse classes of DEs.
arXiv Detail & Related papers (2022-06-10T02:14:59Z) - 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) - Differential Equation Based Path Integral for System-Bath Dynamics [0.0]
We propose the differential equation based path integral (DEBPI) method to simulate the real-time evolution of open quantum systems.
New numerical schemes can be derived by discretizing these differential equations.
It is numerically verified that in certain cases, by selecting appropriate systems and applying suitable numerical schemes, the memory cost required in the i-QuAPI method can be significantly reduced.
arXiv Detail & Related papers (2021-07-22T15:06:22Z) - Learning Runge-Kutta Integration Schemes for ODE Simulation and
Identification [35.877707234293624]
We propose a novel framework to learn integration schemes that minimize an integration-related cost function.
We demonstrate the relevance of the proposed learning-based approach for non-linear equations.
arXiv Detail & Related papers (2021-05-11T13:02:20Z) - Multi-objective discovery of PDE systems using evolutionary approach [77.34726150561087]
In the paper, a multi-objective co-evolution algorithm is described.
The single equations within the system and the system itself are evolved simultaneously to obtain the system.
In contrast to the single vector equation, a component-wise system is more suitable for expert interpretation and, therefore, for applications.
arXiv Detail & Related papers (2021-03-11T15:37:52Z) - Knowledge-Based Learning of Nonlinear Dynamics and Chaos [3.673994921516517]
We present a universal learning framework for extracting predictive models from nonlinear systems based on observations.
Our framework can readily incorporate first principle knowledge because it naturally models nonlinear systems as continuous-time systems.
arXiv Detail & Related papers (2020-10-07T13:50:13Z)
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.