Structure-preserving neural networks

Abstract

We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing the metriplectic structure of dissipative Hamiltonian systems in the form of the so-called General Equation for the Non-Equilibrium Reversible-Irreversible Coupling, GENERIC [M. Grmela and H.C Oettinger (1997). Dynamics and thermodynamics of complex fluids. I. Development of a general formalism. Phys. Rev. E. 56 (6): 6620-6632]. The method does not need to enforce any kind of balance equation, and thus no previous knowledge on the nature of the system is needed. Conservation of energy and dissipation of entropy in the prediction of previously unseen situations arise as a natural by-product of the structure of the method. Examples of the performance of the method are shown that include conservative as well as dissipative systems, discrete as well as continuous ones.

19 pages, 11 figures

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• Thermodynamics-informed graph neural networks
• Parameterized Neural Ordinary Differential Equations: Applications to Computational Physics Problems
• Symplectic Neural Networks in Taylor Series Form for Hamiltonian Systems
• OnsagerNet: Learning Stable and Interpretable Dynamics using a Generalized Onsager Principle
• Thermodynamics-informed neural networks for physically realistic mixed reality
• Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems
• PGD-based advanced nonlinear multiparametric regressions for constructing metamodels at the scarce-data limit
• Exact conservation laws for neural network integrators of dynamical systems
• Thermodynamics-informed super-resolution of scarce temporal dynamics data
• Experimental Learning of a Hyperelastic Behavior with a Physics-Augmented Neural Network
• Structure-preserving Sparse Identification of Nonlinear Dynamics for Data-driven Modeling
• Optimal Dirichlet Boundary Control by Fourier Neural Operators Applied to Nonlinear Optics
• Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling
• Neural Vortex Method: from Finite Lagrangian Particles to Infinite Dimensional Eulerian Dynamics
• Hammering at the entropy: A GENERIC-guided approach to learning polymeric rheological constitutive equations using PINNs
• Learning the GENERIC evolution
• Reversible and irreversible bracket-based dynamics for deep graph neural networks
• Enhancing material behavior discovery using embedding-oriented Physically-Guided Neural Networks with Internal Variables
• Nonseparable Symplectic Neural Networks