Constructing Neural Network-Based Models for Simulating Dynamical Systems

Overview

Constructing Neural Network-Based Models for Simulating Dynamical Systems

Note this repo is work in progress prior to reviewing

This is a companion repo for the review paper Constructing Neural Network-Based Models for Simulating Dynamical Systems. The goal is to provide PyTorch implementations that can be used as a starting point for implementation for other applications.

If you use the work please cite it using:

{
    TODO add bibtex key
}

Installing dependencies

python3 -m pip install -r requirements.txt

Where are the models located?

The table below contains the commands necessary to train and evaluate the models described in the review paper. Each experiment can be run using default parameters by executing the script in the python interpreter as follows:

python3 experiments/
   
    .py ...

   
Name Section Command
Vanilla Direct-Solution 3.2 python3 experiments/direct_solution.py --model vanilla
Automatic Differentiation in Direct-Solution 3.3 python3 experiments/direct_solution.py --model autodiff
Physics Informed Neural Networks 3.4 python3 experiments/direct_solution.py --model pinn
Hidden Physics Networks 3.5 python3 experiments/direct_solution.py --model hnn
Direct Time-Stepper 4.2.1 python3 experiments/time_stepper.py --solver direct
Residual Time-Stepper 4.2.2 python3 experiments/time_stepper.py --solver resnet
Euler Time-Stepper 4.2.3 python3 experiments/time_stepper.py --solver euler
Neural ODEs Time-Stepper 4.2.4 python3 experiments/time_stepper.py --solver {rk4,dopri5,tsit5}
Neural State-Space Model 4.3.1 ...
Neural ODEs with input 4.3.2-3 ...
Lagrangian Time-Stepper 4.4.1 ...
Hamiltonian Time-Stepper 4.4.1 ...
Deep Potential Time-Stepper 4.4.2 ...
Deep Markov-Model 4.5.1 ...
Latent Neural ODEs 4.5.2 python3 experiments/latent_neural_odes.py
Bayesian Neural ODEs 4.5.3 ...
Neural SDEs 4.5.4 ...

Docker Image

In an effort to ensure that the code can be executed in the future, we provide a docker image. The Docker image allows the code to be run in a Linux based virtual machine on any platform supported by Docker.

To use the docker image, invoke the build command in the root of this repository:

docker build . -t python_dynamical_systems

Following this "containers" containing the code and all dependencies can be instantiated via the "run" command:

docker run -ti python_dynamical_systems bash

The command will establish an interactive connection to the container. Following this you can execute the code as if it was running on your host machine:

python3 experiments/time_stepper.py ...
Owner
Christian Møldrup Legaard
Christian Møldrup Legaard
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