Table of contents

• General info
• Methods-pipeline
• Examples
• Contents
• Getting started
• Demonstration

General info

This Git repository contains python codes for implementing the Latent DeepONet model proposed here: https://arxiv.org/abs/2304.07599. Latent DeepONet employs auroencoder models with the operator regressor DeepONet, to learn operators in latent spaces by leveraging the intrinsic dimensionality of physics-based data.

The code has the following capabilities:

• Perform operator regression for PDE problems of very high dimensionality (e.g., high-dimensional time-dependent PDEs)
• Compare the performance of latent DeepONet for different autoencoder models. The current version includes the following models:
  1. Autoencoder (vanilla-AE)
  2. Multi-Layer Autoencoder (MLAE)
  3. Convolutional Autoencoder (CAE) and
  4. Wasserstein Autoencoder (WAE)
• Train latent DeepONet for different values of the latent dimension (d) and compare results with the standard DeepONet trained on the full-dimensional data.

Methods-pipeline

Details of the methdology can be found in the published paper here.

Below, a graphical summary of the method is provided:

Contents

Each folder contains the following codes adjusted for each application:

• AE.py - Contains all AE classes and code to train Autoencoders

• DON.py - Containts all DON classes and code to train latent DeepONet

• plot.py - Generates plots with comparative results for all methods and latent dimensions

• main.py - Demonstrates how to generate results for multiple methods and latent dimensions

generate-data.py - Code to generate the shallow-water equation data using the Dedalus Project v2.

Getting started

1. Create an Anaconda Python 3.8 virtual environment:

conda create -n latent_don python==3.8.13  
conda activate latent_don

2. Clone our repo:

git clone https://github.com/katiana22/latent-deeponet.git

3. Install dependencies via pip with the following commands:

cd latent-deeponet 
pip install -r requirements.txt

or

Install the entire conda environment:

conda env create -f environment.yml

Demonstration

To train an autoencoder model following by the training of L-DeepONet with the reduced data run the following on the terminal:

python AE.py --method MLAE --latent_dim 16 --n_samples 800 --n_epochs 1000  --ood 1 --noise 1   
python DON.py --method MLAE --latent_dim 16 --n_samples 800 --n_epochs 1000 --ood 1 --noise 1

In the example above, we chose to run L-DeepONet with a MLAE, a latent dimensionality of 16, 800 in total train/test sampels and choose 1 for ood and noise which will generate results for out-of-distribution and noisy data.

One can also use the script main.py to generate results for multiple methods (e.g., vanilla-AE, MLAE, CAE), latent dimensions (e.g., 16,25,81) and random seed numbers via the reps variable (e.g., run 5 times each with a loop) and generate comparative violin plots via the plot.py.

Citation

Mainteners

Katiana Kontolati

📧 : kontolati@jhu.edu