LagrangianNeuralNetworks.jl

LagrangianNeuralNetworks learns a scalar Lagrangian $L(q, \dot{q})$ with a neural network, and takes the dynamics from that Lagrangian through the Euler–Lagrange equations.

It exports the architecture LagrangianNeuralNetwork and two losses: LNNLoss, which compares the acceleration that the learned Lagrangian predicts against accelerations in the data, and VariationalMidpointLoss, which needs positions only. The training itself — the data loader, the batches, the optimiser and train! — is GeometricMachineLearning's.

using LagrangianNeuralNetworks
using GeometricMachineLearning: NeuralNetwork

arch = LagrangianNeuralNetwork(2; width = 4, nhidden = 1)
nn = NeuralNetwork(arch)
loss = LNNLoss(arch)

The page Lagrangian Neural Network derives the loss and documents the functions.