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Found 5 papers, 5 papers with code
Volume-Preserving Transformers for Learning Time Series Data with Structure
Two of the many trends in neural network research of the past few years have been (i) the learning of dynamical systems, especially with recurrent neural networks such as long short-term memory networks (LSTMs) and (ii) the introduction of transformer neural networks for natural language processing (NLP) tasks.
Symplectic Autoencoders for Model Reduction of Hamiltonian Systems
In order to train the network, a non-standard gradient descent approach is applied that leverages the differential-geometric structure emerging from the network design.
Multi-Objective Loss Balancing for Physics-Informed Deep Learning
Physics-Informed Neural Networks (PINN) are algorithms from deep learning leveraging physical laws by including partial differential equations together with a respective set of boundary and initial conditions as penalty terms into their loss function.
Variational Integrators for Reduced Magnetohydrodynamics
Reduced magnetohydrodynamics is a simplified set of magnetohydrodynamics equations with applications to both fusion and astrophysical plasmas, possessing a noncanonical Hamiltonian structure and consequently a number of conserved functionals.
Computational Physics Numerical Analysis Plasma Physics
Variational Integrators for Nonvariational Partial Differential Equations
Variational integrators for Lagrangian dynamical systems provide a systematic way to derive geometric numerical methods.
Numerical Analysis Mathematical Physics Mathematical Physics 35A15, 65M06, 70S05, 70S10
