LocSympNets

PyTorch code for training locally-symplectic neural networks LocSympNets, and symmetric version SymLocSympNets, for learning phase volume-preserving linear and nonlinear dynamics. Using the code, please cite Jānis Bajārs, Locally-symplectic neural networks for learning volume-preserving dynamics, Journal of Computational Physics 476:111911, 2023 (DOI: 10.1016/j.jcp.2023.111911).

File LocSympNets_PureCode_WithoutData.zip contains pure code without precomputed training data, images, and examples of pre-trained neural networks.

Numerical code has been built on Anaconda's open-source Python distribution platform using Spyder IDE. Code contains script files for training and predicting phase volume-preserving dynamics with LocSympNets and SymLocSympNets, considering three examples: learning linear traveling wave solutions to the semi-discretized advection equation, periodic trajectories of the Euler equations of the motion of a free rigid body, and quasi-periodic solutions of the charged particle motion in an electromagnetic field. The rigid body example contains two cases: learning a single periodic trajectory and the whole dynamics from randomly sampled training data.

Instructions to run the code

• Volume-preserving differential equations are defined in file DynamicalSystems/VolumePreservingODEs.py.
• Training and testing data for four example cases are computed in the following files: DynamicalSystems/TrainingData_AdvectionEq.py, DynamicalSystems/TrainingData_RigidBody_Single.py, DynamicalSystems/TrainingData_RigidBody_Whole.py, and DynamicalSystems/TrainingData_ChargedParticle.py, respectively.
• All training and testing data is saved in associated problem folders DynamicalSystems/SavedTrainingData/.
• All neural network functionas are defined in folder NeuralNetworkFnc.
• File NeuralNetworkFnc/module-class.py contains LocSympNets and SymLocSympNets modules.
• File NeuralNetworkFnc/training-class.py contains neural network training functions.
• Additional neural network supporting functions are defined in files NeuralNetworkFnc/mySequential.py and NeuralNetworkFnc/custom_dataset.py.
• LocSympNets training script files for four example cases are: training_AdvectionEq_script.py, training_RigidBody_Single_script.py, training_RigidBody_Whole_script.py, and training_ChargedParticle_script.py, respectively.
• SymLocSympNets training script files for four example cases are: training_AdvectionEq_sym_script.py, training_RigidBody_Single_sym_script.py, training_RigidBody_Whole_sym_script.py, and training_ChargedParticle_sym_script.py, respectively.
• All trained neural networks are saved in associated problem folders SavedNeuralNets/.
• LocSympNets prediction and testing script files for four example cases are: predictions_AdvectionEq_script.py, predictions_RigidBody_Single_script.py, predictions_RigidBody_Whole_script.py, and predictions_ChargedParticle_script.py, respectively.
• SymLocSympNets training and testing script files for four example cases are: predictions_AdvectionEq_sym_script.py, predictions_RigidBody_Single_sym_script.py, predictions_RigidBody_Whole_sym_script.py, and predictions_ChargedParticle_sym_script.py, respectively.
• Produced images are saved in associated problem folders Figures/.