Discovering equations from data: symbolic regression in dynamical systems

• URL: http://arxiv.org/abs/2508.20257v1
• Date: Wed, 27 Aug 2025 20:30:09 GMT
• Title: Discovering equations from data: symbolic regression in dynamical systems
• Authors: Beatriz R. Brum, Luiza Lober, Isolde Previdelli, Francisco A. Rodrigues,
• Abstract summary: In this paper, five symbolic regression methods were used for recovering equations from nine dynamical processes, including chaotic dynamics and epidemic models.<n> Benchmark results demonstrate its high predictive power and accuracy, with some estimates being indistinguishable from the original analytical forms.<n>These results highlight the potential of symbolic regression as a robust tool for inferring and modelling real-world phenomena.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: The process of discovering equations from data lies at the heart of physics and in many other areas of research, including mathematical ecology and epidemiology. Recently, machine learning methods known as symbolic regression have automated this process. As several methods are available in the literature, it is important to compare them, particularly for dynamic systems that describe complex phenomena. In this paper, five symbolic regression methods were used for recovering equations from nine dynamical processes, including chaotic dynamics and epidemic models, with the PySR method proving to be the most suitable for inferring equations. Benchmark results demonstrate its high predictive power and accuracy, with some estimates being indistinguishable from the original analytical forms. These results highlight the potential of symbolic regression as a robust tool for inferring and modelling real-world phenomena.

Related papers

• Symbolic regression for defect interactions in 2D materials [0.2721477719641864]
  Symbolic regression is a powerful technique for discovering analytical equations that describe data.<n>In this work, we examined the application of the deep symbolic regression algorithm SEGVAE to determine the properties of two-dimensional materials with defects.
  arXiv  Detail & Related papers  (2025-12-23T21:33:11Z)
• Deep Generative Symbolic Regression [83.04219479605801]
  Symbolic regression aims to discover concise closed-form mathematical equations from data. Existing methods, ranging from search to reinforcement learning, fail to scale with the number of input variables. We propose an instantiation of our framework, Deep Generative Symbolic Regression.
  arXiv  Detail & Related papers  (2023-12-30T17:05:31Z)
• AI-Lorenz: A physics-data-driven framework for black-box and gray-box identification of chaotic systems with symbolic regression [2.07180164747172]
  We develop a framework that learns mathematical expressions modeling complex dynamical behaviors. We train a small neural network to learn the dynamics of a system, its rate of change in time, and missing model terms. This, in turn, enables us to predict the future evolution of the dynamical behavior.
  arXiv  Detail & Related papers  (2023-12-21T18:58:41Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• 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)
• Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regression [2.7071541526963805]
  This paper proposes a novel neural network-based symbolic regression method. It constructs physically plausible models based on even very small training data sets and prior knowledge about the system. We experimentally evaluate the approach on four test systems: the TurtleBot 2 mobile robot, the magnetic manipulation system, the equivalent resistance of two resistors in parallel, and the longitudinal force of the anti-lock braking system.
  arXiv  Detail & Related papers  (2023-02-01T22:05:04Z)
• 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)
• Constructing Neural Network-Based Models for Simulating Dynamical Systems [59.0861954179401]
  Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome.
  arXiv  Detail & Related papers  (2021-11-02T10:51:42Z)
• Contemporary Symbolic Regression Methods and their Relative Performance [5.285811942108162]
  We assess 14 symbolic regression methods and 7 machine learning methods on a set of 252 diverse regression problems. For the real-world datasets, we benchmark the ability of each method to learn models with low error and low complexity. For the synthetic problems, we assess each method's ability to find exact solutions in the presence of varying levels of noise.
  arXiv  Detail & Related papers  (2021-07-29T22:12:59Z)
• Inferring the Structure of Ordinary Differential Equations [12.202646598683888]
  We extend the approach by (Udrescu et al., 2020) called AIFeynman to the dynamic setting to perform symbolic regression on ODE systems. We compare this extension to state-of-the-art approaches for symbolic regression empirically on several dynamical systems for which the ground truth equations of increasing complexity are available.
  arXiv  Detail & Related papers  (2021-07-05T07:55:05Z)
• Neural Symbolic Regression that Scales [58.45115548924735]
  We introduce the first symbolic regression method that leverages large scale pre-training. We procedurally generate an unbounded set of equations, and simultaneously pre-train a Transformer to predict the symbolic equation from a corresponding set of input-output-pairs.
  arXiv  Detail & Related papers  (2021-06-11T14:35:22Z)
• Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach [9.36739413306697]
  We blend machine learning and dictionary-based learning with numerical analysis tools to discover governing differential equations. We obtain interpretable and parsimonious models which are prone to generalize better beyond the sampling regime. We discuss its extension to governing equations, containing rational nonlinearities that typically appear in biological networks.
  arXiv  Detail & Related papers  (2021-05-11T08:46:51Z)

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.