Learning of discrete Lagrangian densities from data

Accompanying source code for the conference paper

Christian Offen, Sina Ober-Blöbaum
Learning discrete Lagrangians for variational PDEs from data and detection of travelling waves
In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2023. Lecture Notes in Computer Science, vol 14071. Springer, Cham.
DOI: 10.1007/978-3-031-38271-0_57

DOI SpringerLink
arXiv:2302.08232
ArXiv author page

Also see the follow-up project: arXiv.org:2302.08232, GitHub:Christian-Offen/DLNN_pde

Main files

FitDensity.jl

The script creates training data of a discrete field theory (discrete wave equation). Based on the training data it learns a model of discrete Lagrangian density.

Evaluation_Trained_Model.ipynb

Jupyter notebook containing numerical experiments with a machine learned discrete density on data of the discrete wave equation. Prediction accuracy is assessed and travelling waves are detected and compared to a reference.

Supporting files

7ptStencilFun.jl

Variational integrator for 1st order discrete field theories (2 dimensional space-time) and tools for preformance evaluation.

SpectralTools.jl

Tools for spectral interpolation and computation of spectral derivatives on periodic spatial domains.

TrainingData.jl

Creation of training data to be used in FitDensity.jl

2023-01-31_08-53-14run_data.json

Learned model of a Lagrangian density. Created by FitDensity.jl

2023-02-14_11-21-06run_dataTW05pert.json

Learned Fourier coefficients of travelling wave. Created by Evaluation_Trained_Model.ipynb