Inferring the Structure of Ordinary Differential Equations

• URL: http://arxiv.org/abs/2107.07345v1
• Date: Mon, 5 Jul 2021 07:55:05 GMT
• Title: Inferring the Structure of Ordinary Differential Equations
• Authors: Juliane Weilbach, Sebastian Gerwinn, Christian Weilbach and Melih Kandemir
• Abstract summary: 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.
• Score: 12.202646598683888
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Understanding physical phenomena oftentimes means understanding the underlying dynamical system that governs observational measurements. While accurate prediction can be achieved with black box systems, they often lack interpretability and are less amenable for further expert investigation. Alternatively, the dynamics can be analysed via symbolic regression. In this paper, we extend the approach by (Udrescu et al., 2020) called AIFeynman to the dynamic setting to perform symbolic regression on ODE systems based on observations from the resulting trajectories. 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. Although the proposed approach performs best on this benchmark, we observed difficulties of all the compared symbolic regression approaches on more complex systems, such as Cart-Pole.

Related papers

• Response Theory via Generative Score Modeling [0.0]
  We introduce an approach for analyzing the responses of dynamical systems to external perturbations that combines score-based generative modeling with the Generalized Fluctuation-Dissipation Theorem (GFDT) The methodology enables accurate estimation of system responses, including those with non-Gaussian statistics.
  arXiv  Detail & Related papers  (2024-02-01T21:38:10Z)
• 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)
• Exploring Complex Dynamical Systems via Nonconvex Optimization [0.0]
  We present an alternative, optimization-driven approach using tools from machine learning. We apply this approach to a novel, fully-optimizable, reaction-diffusion model which incorporates complex chemical reaction networks. This allows us to systematically identify new states and behaviors, including pattern formation, dissipation-maximizing nonequilibrium states, and replication-like dynamical structures.
  arXiv  Detail & Related papers  (2023-01-03T01:35:39Z)
• 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)
• DySMHO: Data-Driven Discovery of Governing Equations for Dynamical Systems via Moving Horizon Optimization [77.34726150561087]
  We introduce Discovery of Dynamical Systems via Moving Horizon Optimization (DySMHO), a scalable machine learning framework. DySMHO sequentially learns the underlying governing equations from a large dictionary of basis functions. Canonical nonlinear dynamical system examples are used to demonstrate that DySMHO can accurately recover the governing laws.
  arXiv  Detail & Related papers  (2021-07-30T20:35:03Z)
• Discovering Sparse Interpretable Dynamics from Partial Observations [0.0]
  We propose a machine learning framework for discovering these governing equations using only partial observations. Our tests show that this method can successfully reconstruct the full system state.
  arXiv  Detail & Related papers  (2021-07-22T18:23:23Z)
• Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems [65.44033635330604]
  We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system. We show that its use of intrinsic linear dynamics offers a number of desirable properties in terms of interpretability and parsimony. Results are presented for a test case using load data from an electrical grid.
  arXiv  Detail & Related papers  (2020-10-08T20:25:52Z)
• Variational Deep Learning for the Identification and Reconstruction of Chaotic and Stochastic Dynamical Systems from Noisy and Partial Observations [15.82296284460491]
  The identification of governing equations remains challenging when dealing with noisy and partial observations. Within the proposed framework, we learn an inference model to reconstruct the true states of the system. This framework bridges classical data assimilation and state-of-the-art machine learning techniques.
  arXiv  Detail & Related papers  (2020-09-04T16:48:00Z)

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.