Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting

• URL: http://arxiv.org/abs/2010.04456v6
• Date: Tue, 10 May 2022 12:56:21 GMT
• Title: Augmenting Physical Models with Deep Networks for Complex Dynamics Forecasting
• Authors: Yuan Yin, Vincent Le Guen, J\'er\'emie Dona, Emmanuel de B\'ezenac, Ibrahim Ayed, Nicolas Thome, Patrick Gallinari
• Abstract summary: APHYNITY is a principled approach for augmenting incomplete physical dynamics described by differential equations with deep data-driven models. It consists in decomposing the dynamics into two components: a physical component accounting for the dynamics for which we have some prior knowledge, and a data-driven component accounting for errors of the physical model.
• Score: 34.61959169976758
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Forecasting complex dynamical phenomena in settings where only partial knowledge of their dynamics is available is a prevalent problem across various scientific fields. While purely data-driven approaches are arguably insufficient in this context, standard physical modeling based approaches tend to be over-simplistic, inducing non-negligible errors. In this work, we introduce the APHYNITY framework, a principled approach for augmenting incomplete physical dynamics described by differential equations with deep data-driven models. It consists in decomposing the dynamics into two components: a physical component accounting for the dynamics for which we have some prior knowledge, and a data-driven component accounting for errors of the physical model. The learning problem is carefully formulated such that the physical model explains as much of the data as possible, while the data-driven component only describes information that cannot be captured by the physical model, no more, no less. This not only provides the existence and uniqueness for this decomposition, but also ensures interpretability and benefits generalization. Experiments made on three important use cases, each representative of a different family of phenomena, i.e. reaction-diffusion equations, wave equations and the non-linear damped pendulum, show that APHYNITY can efficiently leverage approximate physical models to accurately forecast the evolution of the system and correctly identify relevant physical parameters. Code is available at https://github.com/yuan-yin/APHYNITY .

Related papers

• 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)
• Learning Physical Dynamics with Subequivariant Graph Neural Networks [99.41677381754678]
  Graph Neural Networks (GNNs) have become a prevailing tool for learning physical dynamics. Physical laws abide by symmetry, which is a vital inductive bias accounting for model generalization. Our model achieves on average over 3% enhancement in contact prediction accuracy across 8 scenarios on Physion and 2X lower rollout MSE on RigidFall.
  arXiv  Detail & Related papers  (2022-10-13T10:00:30Z)
• Scientific Machine Learning for Modeling and Simulating Complex Fluids [0.0]
  rheological equations relate internal stresses and deformations in complex fluids. Data-driven models provide accessible alternatives to expensive first-principles models. Development of similar models for complex fluids has lagged.
  arXiv  Detail & Related papers  (2022-10-10T04:35:31Z)
• Neural Implicit Representations for Physical Parameter Inference from a Single Video [49.766574469284485]
  We propose to combine neural implicit representations for appearance modeling with neural ordinary differential equations (ODEs) for modelling physical phenomena. Our proposed model combines several unique advantages: (i) Contrary to existing approaches that require large training datasets, we are able to identify physical parameters from only a single video. The use of neural implicit representations enables the processing of high-resolution videos and the synthesis of photo-realistic images.
  arXiv  Detail & Related papers  (2022-04-29T11:55:35Z)
• Multi-Objective Physics-Guided Recurrent Neural Networks for Identifying Non-Autonomous Dynamical Systems [0.0]
  We propose a physics-guided hybrid approach for modeling non-autonomous systems under control. This is extended by a recurrent neural network and trained using a sophisticated multi-objective strategy. Experiments conducted on real data reveal substantial accuracy improvements by our approach compared to a physics-based model.
  arXiv  Detail & Related papers  (2022-04-27T14:33:02Z)
• 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)
• Hard Encoding of Physics for Learning Spatiotemporal Dynamics [8.546520029145853]
  We propose a deep learning architecture that forcibly encodes known physics knowledge to facilitate learning in a data-driven manner. The coercive encoding mechanism of physics, which is fundamentally different from the penalty-based physics-informed learning, ensures the network to rigorously obey given physics.
  arXiv  Detail & Related papers  (2021-05-02T21:40:39Z)
• Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modeling [86.9726984929758]
  We focus on the integration of incomplete physics models into deep generative models. We propose a VAE architecture in which a part of the latent space is grounded by physics. We demonstrate generative performance improvements over a set of synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2021-02-25T20:28:52Z)
• Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanics [3.214927790437842]
  Two main modeling approaches often fail to meet requirements: first principles methods suffer from high bias, whereas data-driven modeling tends to have high variance. We present physics-informed neural ordinary differential equations (PINODE), a hybrid model that combines the two modeling techniques to overcome the aforementioned problems. Our findings are of interest for model-based control and system identification of mechanical systems.
  arXiv  Detail & Related papers  (2020-05-29T15:10:43Z)

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.