Learning of discrete models of variational PDEs from data
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Publication:6543708
DOI10.1063/5.0172287zbMATH Open1540.70001MaRDI QIDQ6543708
Sina Ober-Blöbaum, Christian Offen
Publication date: 25 May 2024
Published in: Chaos (Search for Journal in Brave)
discrete field theorytraveling wavediscrete Euler-Lagrange equationsspace-time latticediscrete Lagrangian densityneural network modenumerical regularizer
Artificial neural networks and deep learning (68T07) Learning and adaptive systems in artificial intelligence (68T05) Variational methods for problems in mechanics (70G75) Computational methods for problems pertaining to mechanics of particles and systems (70-08) Classical field theories (70S99)
Cites Work
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- On singular Lagrangian underlying the Schrödinger equation
- The principle of symmetric criticality
- Equations of motion, commutation relations and ambiguities in the Lagrangian formalism
- On the inverse problem with symmetries, and the appearance of cohomologies in classical Lagrangian dynamics
- Sympnets: intrinsic structure-preserving symplectic networks for identifying Hamiltonian systems
- Learning dynamical systems from data: a simple cross-validation perspective. I: Parametric kernel flows
- Variational learning of Euler-Lagrange dynamics from data
- Backward error analysis for variational discretisations of PDEs
- PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network
- Hamiltonian operator inference: physics-preserving learning of reduced-order models for canonical Hamiltonian systems
- Discretized Dynamical Low-Rank Approximation in the Presence of Small Singular Values
- Symmetric Criticality in Classical Field Theory
- Discrete mechanics and variational integrators
- Time Integration of Rank-Constrained Tucker Tensors
- Data-Driven Science and Engineering
- Learning partial differential equations via data discovery and sparse optimization
- Performance of the Low-Rank TT-SVD for Large Dense Tensors on Modern MultiCore CPUs
- Uniformly accurate machine learning-based hydrodynamic models for kinetic equations
- Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics
- Geometric Numerical Integration
- Symplectic Model Reduction of Hamiltonian Systems on Nonlinear Manifolds and Approximation with Weakly Symplectic Autoencoder
- Lectures on Quantum Mechanics
- Variational methods, multisymplectic geometry and continuum mechanics
- Travelling waves for adaptive grid discretizations of reaction diffusion systems. III: Nonlinear theory
- Backward error analysis for conjugate symplectic methods
- Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves
- Hamiltonian Neural Networks with Automatic Symmetry Detection
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