Automated Discovery of Operable Dynamics from Videos

• URL: http://arxiv.org/abs/2410.11894v2
• Date: Wed, 23 Apr 2025 19:17:09 GMT
• Title: Automated Discovery of Operable Dynamics from Videos
• Authors: Kuang Huang, Dong Heon Cho, Boyuan Chen,
• Abstract summary: We introduce a framework that automatically discovers a low-dimensional and operable representation of system dynamics.<n>Results highlight the potential of our data-driven approach to advance automated scientific discovery.
• Score: 4.690264156292023
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Dynamical systems form the foundation of scientific discovery, traditionally modeled with predefined state variables such as the angle and angular velocity, and differential equations such as the equation of motion for a single pendulum. We introduce a framework that automatically discovers a low-dimensional and operable representation of system dynamics, including a set of compact state variables that preserve the smoothness of the system dynamics and a differentiable vector field, directly from video without requiring prior domain-specific knowledge. The prominence and effectiveness of the proposed approach are demonstrated through both quantitative and qualitative analyses of a range of dynamical systems, including the identification of stable equilibria, the prediction of natural frequencies, and the detection of of chaotic and limit cycle behaviors. The results highlight the potential of our data-driven approach to advance automated scientific discovery.

Related papers

• Identifiable Representation and Model Learning for Latent Dynamic Systems [0.0]
  We study the problem of identifiable representation and model learning for latent dynamic systems. We prove that, for linear and affine nonlinear latent dynamic systems with sparse input matrices, it is possible to identify the latent variables up to scaling.
  arXiv  Detail & Related papers  (2024-10-23T13:55:42Z)
• Integrating Physics-Informed Deep Learning and Numerical Methods for Robust Dynamics Discovery and Parameter Estimation [0.0]
  In this work, we combine deep learning techniques and classic numerical methods for differential equations to solve two challenging problems in dynamical systems theory. Results demonstrate the effectiveness of the proposed approaches on a suite of test problems exhibiting chaotic dynamics.
  arXiv  Detail & Related papers  (2024-10-05T22:40:02Z)
• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement [42.896772730859645]
  We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations. We apply this approach to the classic logistic and Lorenz systems in both integrable and chaotic regimes.
  arXiv  Detail & Related papers  (2024-10-04T18:06:12Z)
• Probabilistic Decomposed Linear Dynamical Systems for Robust Discovery of Latent Neural Dynamics [5.841659874892801]
  Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. Existing methods for latent variable estimation are not robust to dynamical noise and system nonlinearity. We propose a probabilistic approach to latent variable estimation in decomposed models that improves robustness against dynamical noise.
  arXiv  Detail & Related papers  (2024-08-29T18:58:39Z)
• Physics-informed Discovery of State Variables in Second-Order and Hamiltonian Systems [1.7406327893433848]
  This research proposes a method that leverages the physical characteristics of second-order Hamiltonian systems to constrain the baseline model. The proposed model outperforms the baseline model in identifying a minimal set of non-redundant and interpretable state variables.
  arXiv  Detail & Related papers  (2024-08-21T15:10:50Z)
• Learning System Dynamics without Forgetting [60.08612207170659]
  Predicting trajectories of systems with unknown dynamics is crucial in various research fields, including physics and biology. We present a novel framework of Mode-switching Graph ODE (MS-GODE), which can continually learn varying dynamics. We construct a novel benchmark of biological dynamic systems, featuring diverse systems with disparate dynamics.
  arXiv  Detail & Related papers  (2024-06-30T14:55:18Z)
• 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)
• An information field theory approach to Bayesian state and parameter estimation in dynamical systems [0.0]
  This paper develops a scalable Bayesian approach to state and parameter estimation suitable for continuous-time, deterministic dynamical systems. We construct a physics-informed prior probability measure on the function space of system responses so that functions that satisfy the physics are more likely.
  arXiv  Detail & Related papers  (2023-06-03T16:36:43Z)
• Newton-Cotes Graph Neural Networks: On the Time Evolution of Dynamic Systems [49.50674348130157]
  We propose a new approach to predict the integration based on several velocity estimations with Newton-Cotes formulas. Experiments on several benchmarks empirically demonstrate consistent and significant improvement compared with the state-of-the-art methods.
  arXiv  Detail & Related papers  (2023-05-24T02:23:00Z)
• 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)
• Physics-Inspired Temporal Learning of Quadrotor Dynamics for Accurate Model Predictive Trajectory Tracking [76.27433308688592]
  Accurately modeling quadrotor's system dynamics is critical for guaranteeing agile, safe, and stable navigation. We present a novel Physics-Inspired Temporal Convolutional Network (PI-TCN) approach to learning quadrotor's system dynamics purely from robot experience. Our approach combines the expressive power of sparse temporal convolutions and dense feed-forward connections to make accurate system predictions.
  arXiv  Detail & Related papers  (2022-06-07T13:51:35Z)
• 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)
• 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)
• 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)
• Learning Continuous System Dynamics from Irregularly-Sampled Partial Observations [33.63818978256567]
  We present LG-ODE, a latent ordinary differential equation generative model for modeling multi-agent dynamic system with known graph structure. It can simultaneously learn the embedding of high dimensional trajectories and infer continuous latent system dynamics. Our model employs a novel encoder parameterized by a graph neural network that can infer initial states in an unsupervised way.
  arXiv  Detail & Related papers  (2020-11-08T01:02:22Z)
• Euclideanizing Flows: Diffeomorphic Reduction for Learning Stable Dynamical Systems [74.80320120264459]
  We present an approach to learn such motions from a limited number of human demonstrations. The complex motions are encoded as rollouts of a stable dynamical system. The efficacy of this approach is demonstrated through validation on an established benchmark as well demonstrations collected on a real-world robotic system.
  arXiv  Detail & Related papers  (2020-05-27T03:51:57Z)

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.