pdPINN

Files

The code for the individual experiments is provided in the following directories:

FokkerPlacnk
HeatEquation
MassConservation

Each experiment uses a different conda environment, which is provided in form of '.yml' files in the respective directories.

Mass Conservation Experiments

Setup

The environment information is given in env.yml. We propose to the package manager mamba for creating the environment with: mamba env create -f env.yml

Alternatively, conda should also work (by simply replacing mamba with conda), but it was only tested using mamba.

Experiments

experiment_2d.py Includes the code for the 2D mass conservation experiment, i.e. the projection to the xy-plane.
experiment_3d.py Includes the code for the 3D mass conservation experiment.

Via command-line arguments the settings of the training procedure can be set for each experiment. E.g.: python experiment_3d.py --n-samples 2048 --sampling-method mh_pdpinn --pde-weight 400

Note, that --sampling-method mh_pdpinn refers to the proposed pdPINN, --sampling-method uniform to the uniform sampler. Adaptive Refinement can be included via the flags --rar and --ot-rar.

Data

create_data.py simulates the particles and creates the necessary data for all the experiments. Note that this may require a lot of RAM. This is NOT required to run, as the used data is already made available within the data/ folder.
pdPINN/util/data_gen.py and pdPINN/util/vecfield_util.py contain the details of the data generation.

Implementation

pdPINN/model/ contains the implementations of the PINN, including the architecture.
The specific models for the 2d and 3d experiment are in
- pdPINN/model/siren_2d.py
- pdPINN/model/siren_3d.py.
The Metropolis Hastings implementation is in lib/model/sampler.py
The SIREN specific implementations (i.e. intializations and custom layers) can be found in lib/model/modules

Videos

Here we can see a comparison between MH-pdPINN and OT-RAR for 2000 collocation points in the 3D experiment. The noteworthy difference is the vanishing and reappearing of density, which is more pronounced in the first two columns.

More videos can be found in the Videos/ directory.

Experiment 3D Baseline	Experiment 3D, OT-RAR, ~2000 samples	Experiment 3D, MH-pdPINN, ~2000 samples	Groundtruth