Structure-preserving neural networks
- URL: http://arxiv.org/abs/2004.04653v2
- Date: Fri, 16 Oct 2020 15:07:50 GMT
- Title: Structure-preserving neural networks
- Authors: Quercus Hern\'andez, Alberto Badias, David Gonzalez, Francisco
Chinesta, and Elias Cueto
- Abstract summary: We develop a method to learn physical systems from data that employs feedforward neural networks.
The method employs a minimum amount of data by enforcing the metriplectic structure of dissipative Hamiltonian systems.
- Score: 0.08209843760716957
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
Related papers
- Thermodynamics-Consistent Graph Neural Networks [50.0791489606211]
We propose excess Gibbs free energy graph neural networks (GE-GNNs) for predicting composition-dependent activity coefficients of binary mixtures.
The GE-GNN architecture ensures thermodynamic consistency by predicting the molar excess Gibbs free energy.
We demonstrate high accuracy and thermodynamic consistency of the activity coefficient predictions.
arXiv Detail & Related papers (2024-07-08T06:58:56Z) - TANGO: Time-Reversal Latent GraphODE for Multi-Agent Dynamical Systems [43.39754726042369]
We propose a simple-yet-effective self-supervised regularization term as a soft constraint that aligns the forward and backward trajectories predicted by a continuous graph neural network-based ordinary differential equation (GraphODE)
It effectively imposes time-reversal symmetry to enable more accurate model predictions across a wider range of dynamical systems under classical mechanics.
Experimental results on a variety of physical systems demonstrate the effectiveness of our proposed method.
arXiv Detail & Related papers (2023-10-10T08:52:16Z) - Learning Neural Constitutive Laws From Motion Observations for
Generalizable PDE Dynamics [97.38308257547186]
Many NN approaches learn an end-to-end model that implicitly models both the governing PDE and material models.
We argue that the governing PDEs are often well-known and should be explicitly enforced rather than learned.
We introduce a new framework termed "Neural Constitutive Laws" (NCLaw) which utilizes a network architecture that strictly guarantees standard priors.
arXiv Detail & Related papers (2023-04-27T17:42:24Z) - Thermodynamics-informed graph neural networks [0.09332987715848712]
We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting integration scheme.
The first is achieved with Graph Neural Networks, which induces a non-Euclidean geometrical prior and permutation invariant node and edge update functions.
The second bias is forced by learning the GENERIC structure of the problem, an extension of the Hamiltonian formalism, to model more general non-conservative dynamics.
arXiv Detail & Related papers (2022-03-03T17:30:44Z) - Decimation technique for open quantum systems: a case study with
driven-dissipative bosonic chains [62.997667081978825]
Unavoidable coupling of quantum systems to external degrees of freedom leads to dissipative (non-unitary) dynamics.
We introduce a method to deal with these systems based on the calculation of (dissipative) lattice Green's function.
We illustrate the power of this method with several examples of driven-dissipative bosonic chains of increasing complexity.
arXiv Detail & Related papers (2022-02-15T19:00:09Z) - 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) - Open-system approach to nonequilibrium quantum thermodynamics at
arbitrary coupling [77.34726150561087]
We develop a general theory describing the thermodynamical behavior of open quantum systems coupled to thermal baths.
Our approach is based on the exact time-local quantum master equation for the reduced open system states.
arXiv Detail & Related papers (2021-09-24T11:19:22Z) - Machine learning structure preserving brackets for forecasting
irreversible processes [0.0]
We present a novel parameterization of dissipative brackets from metriplectic dynamical systems.
The process learns generalized Casimirs for energy and entropy guaranteed to be conserved and nondecreasing.
We provide benchmarks for dissipative systems demonstrating learned dynamics are more robust and generalize better than either "black-box" or penalty-based approaches.
arXiv Detail & Related papers (2021-06-23T18:27:59Z) - Assessing the role of initial correlations in the entropy production
rate for non-equilibrium harmonic dynamics [0.0]
We shed light on the relation between correlations, initial preparation of the system and non-Markovianity.
We show that the global purity of the initial state of the system influences the behaviour of the entropy production rate.
arXiv Detail & Related papers (2020-04-22T17:29:43Z) - On dissipative symplectic integration with applications to
gradient-based optimization [77.34726150561087]
We propose a geometric framework in which discretizations can be realized systematically.
We show that a generalization of symplectic to nonconservative and in particular dissipative Hamiltonian systems is able to preserve rates of convergence up to a controlled error.
arXiv Detail & Related papers (2020-04-15T00:36:49Z)
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.