Deep Autoencoder with SVD Convergence

This repository contains implementations of learnable weighted dimensionality reduction frameworks for various fluid dynamics and turbulence datasets using deep autoencoders with SVD convergence.

Overview

The project implements hybrid autoencoder architectures that combine deep learning with singular value decomposition (SVD) for dimensionality reduction and surrogate modeling across multiple fluid dynamics problems.

Datasets

1D Kuramoto-Sivashinsky (KS) Dimensionality Reduction

• Data Files: ks_512_extended.mat, ks_1024_extended.mat, ks_2048_extended.mat
• Description: Extended Kuramoto-Sivashinsky equation data for dimensionality reduction analysis

3D Homogeneous Isotropic Turbulence (HIT)

• Data Source: Johns Hopkins University (JHU) Turbulence Database
• Configuration: See manuscript for specific configuration details
• Download: Available from JHU turbulence database based on manuscript specifications

1D Wave Koopman

• Data Generation: Generated within the training file
• Description: Synthetic data for Koopman operator analysis of traveling waves

2D Cylinder Koopman

• Data File: VORTALL.mat
• Description: Vorticity data for flow over cylinder analysis

1D Viscous Burgers' Surrogate

• Data Generation: Part of training script (uploaded as ESM)
• Description: Synthetic data for surrogate modeling using LSTM

2D Shallow Water

• Data Source: Generated using codes from CAE_LSTM_ROMS
• Repository: https://github.com/Romit-Maulik/CAE_LSTM_ROMS.git

3D Viscous Burgers' Surrogate

• Data Source: Generated using Apebench
• Configuration: See manuscript for specific configuration details
• Repository: https://github.com/tum-pbs/apebench.git

Code Files

Dimensionality Reduction Frameworks

hybrid_ae_ks.py

• Description: Learnable weighted dimensionality reduction framework for 1D KS data
• Features: Hybrid autoencoder with SVD convergence for Kuramoto-Sivashinsky equation

hybrid_ae_3d.py

• Description: Learnable weighted dimensionality reduction framework for 3D Turbulence data
• Features: 3D autoencoder implementation for homogeneous isotropic turbulence

Surrogate Modeling with LSTM

lstm_training_1d_vb.py

• Description: Surrogate modeling using LSTM with learnable weighted dimensionality reduction for 1D Viscous Burgers' data
• Features: LSTM-based surrogate model with autoencoder preprocessing

lstm_training_shallow_water.py

• Description: Surrogate modeling with learnable weighted dimensionality reduction for 2D Shallow Water data
• Features: 2D LSTM surrogate model for shallow water equations

lstm_training_3d_vb.py

• Description: Surrogate modeling with learnable weighted dimensionality reduction for 3D Viscous Burgers'
• Features: 3D LSTM surrogate model for viscous Burgers' equation

Data Generation

generate_data.py

• Description: Generate 1D Viscous Burgers' data for surrogate modeling using LSTM
• Features: Synthetic data generation for training and testing

Koopman Forecasting

wave.py

• Description: Koopman forecast with learnable weighted dimensionality reduction for 1D traveling wave
• Features: Koopman operator analysis for wave dynamics

cylinder_vortall.py

• Description: Koopman forecast with learnable weighted dimensionality reduction for 2D flow over cylinder
• Features: Koopman operator analysis for cylinder wake dynamics

Installation and Setup

1. Clone this repository:

git clone <repository-url>
cd deep-ae-with-svd-convergence

2. Install required dependencies:

pip install -r requirements.txt

3. Download or generate the required datasets as specified above.

Usage

Running Dimensionality Reduction

# For 1D KS data
python hybrid_ae_ks.py

# For 3D turbulence data
python hybrid_ae_3d.py

Running Surrogate Models

# For 1D Viscous Burgers'
python lstm_training_1d_vb.py

# For 2D Shallow Water
python lstm_training_shallow_water.py

# For 3D Viscous Burgers'
python lstm_training_3d_vb.py

Running Koopman Forecasting

# For 1D traveling wave
python wave.py

# For 2D cylinder flow
python cylinder_vortall.py

Data Generation

# Generate 1D Viscous Burgers' data
python generate_data.py

Data Sources

• JHU Turbulence Database: For 3D HIT data
• CAE_LSTM_ROMS Repository: For 2D Shallow Water data generation
• Apebench Repository: For 3D Viscous Burgers' data generation

Citation

If you use this code in your research, please cite the associated manuscript.

@misc{somasekharan2025kolmogorovbarrierlearnableweighted, title={Beyond the Kolmogorov Barrier: A Learnable Weighted Hybrid Autoencoder for Model Order Reduction}, author={Nithin Somasekharan and Shaowu Pan}, year={2025}, eprint={2410.18148}, archivePrefix={arXiv}, primaryClass={cs.LG}, url={https://arxiv.org/abs/2410.18148}, }