Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs

  title={Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs},
  author={Shenglin Huang and Zequn He and Bryan Chem and Celia Reina},
  journal={Journal of the Mechanics and Physics of Solids},

Variational methods and deep Ritz method for active elastic solids.

Variational methods have been widely used in soft matter physics for both static and dynamic problems. These methods are mostly based on two variational principles: the variational principle of

Automated identification of linear viscoelastic constitutive laws with EUCLID

EUCLID, a computational strategy for automated material model discovery and identification, is extended to linear viscoelasticity and shown to accurately identify a linear visCOelastic model out of a library with several hundreds of terms spanning relaxation times across seven orders of magnitude.

Physics-informed Reinforcement Learning for Perception and Reasoning about Fluids

Learning and reasoning about physical phenomena is still a challenge in robotics development, and computational sciences play a capital role in the search for accurate methods able to provide

Modular machine learning-based elastoplasticity: generalization in the context of limited data

from limited data was the main reason for the early and continued success of phenomenological models and the main shortcoming in machine learning-enabled constitutive modeling approaches. Training

Thermodynamics of learning physical phenomena

description for the learning

Automated discovery of generalized standard material models with EUCLID



Deep learning of thermodynamics-aware reduced-order models from data

Coarse-scale PDEs from fine-scale observations via machine learning

A data-driven framework for the identification of unavailable coarse-scale PDEs from microscopic observations via machine-learning algorithms using Gaussian processes, artificial neural networks, and/or diffusion maps is introduced.

Onsager's variational principle in active soft matter.

By incorporating the activity of biological systems into OVP, this work develops a general approach to construct thermodynamically consistent models for better understanding the emergent behaviors of individual animal cells and cell aggregates or tissues.

Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations

  • M. Raissi
  • Computer Science
    J. Mach. Learn. Res.
  • 2018
This work puts forth a deep learning approach for discovering nonlinear partial differential equations from scattered and potentially noisy observations in space and time by approximate the unknown solution as well as the nonlinear dynamics by two deep neural networks.

Harnessing fluctuation theorems to discover free energy and dissipation potentials from non-equilibrium data.

GFINNs: GENERIC formalism informed neural networks for deterministic and stochastic dynamical systems

It is proved theoretically that GFINNs are sufficiently expressive to learn the underlying equations, hence establishing the universal approximation theorem.

Machine learning materials physics: Integrable deep neural networks enable scale bridging by learning free energy functions