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Structure-preserving neural networks
- Source :
- Journal of Computational Physics, Journal of Computational Physics, Elsevier, 2020, pp.1-16. ⟨10.1016/j.jcp.2020.109950⟩, Zaguán. Repositorio Digital de la Universidad de Zaragoza, instname
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
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.<br />Comment: 19 pages, 11 figures
- Subjects :
- FOS: Computer and information sciences
Computer Science - Machine Learning
Matériaux [Sciences de l'ingénieur]
Physics and Astronomy (miscellaneous)
Computer science
Physical system
FOS: Physical sciences
Machine Learning (stat.ML)
010103 numerical & computational mathematics
01 natural sciences
Machine Learning (cs.LG)
[SPI.MAT]Engineering Sciences [physics]/Materials
Hamiltonian system
Statistics - Machine Learning
GENERIC
Applied mathematics
Entropy (information theory)
0101 mathematics
Scientific machine learning
Numerical Analysis
Artificial neural network
Applied Mathematics
Computational Physics (physics.comp-ph)
Dissipation
Computer Science Applications
Structure preservation
010101 applied mathematics
Computational Mathematics
Modeling and Simulation
Dissipative system
Balance equation
Feedforward neural network
Physics - Computational Physics
Neural networks
Subjects
Details
- ISSN :
- 00219991 and 10902716
- Volume :
- 426
- Database :
- OpenAIRE
- Journal :
- Journal of Computational Physics
- Accession number :
- edsair.doi.dedup.....dec0c99cd9560831c8321dc6e19d50b9
- Full Text :
- https://doi.org/10.1016/j.jcp.2020.109950