This repository implements machine learning (ML) based reduced order models (ROMs). Specifically, we introduce smooth neural field ROM (SNF-ROM) for solving advection dominated PDE problems.
SNF-ROM: Projection-based nonlinear reduced order modeling with smooth neural fields
Vedant Puri, Aviral Prakash, Levent Burak Kara, Yongjie Jessica Zhang
Project page / Paper / Code / Slides / Talk
Download the code by cloning this Git repo.
$ git clone [email protected]:vpuri3/NeuralROMs.jl.git
$ cd NeuralROMs.jlStart Julia and activate the environment.
$ juliajulia> import Pkg
julia> Pkg.activate(".") # switch environment
julia> Pkg.instantiate() # download environmentWe show how to run the 1D Advection test case corresponding to Section 6.1 of the paper.
Each test case in Section 6 of the paper has a corresponding directory in experiments_SNFROM/.
julia> include("experiments_SNFROM/advect_fourier1D/datagen_advect1D.jl")The script solves the 1D advection problem and stores the dataset as a JLD2 binary in
experiments_SNFROM/advect_fourier1D/data_advect/.
To train SNF-ROM, run
julia> include("experiments_SNFROM/advect_fourier1D/snf.jl")$ tree . -L 1 --filesfirst
.
├── CITATION.bib # arXiv paper
├── LICENSE # MIT License
├── Manifest.toml # environment metadata
├── Project.toml # environment spec
├── README.md # this file
├── benchmarks # internal benchmarking scripts
├── docs # documentation (incomplete)
├── examples # playground
├── experiments_SNFROM # experiments in SNF-ROM paper Section 6
├── figs # figures in SNF-ROM paper
├── src # source code
└── test # test scripts (incomplete)
$ tree src/ -L 2 --filesfirst
.
├── autodiff.jl # AD wrapper for 1-4th order derivatives
├── metrics.jl # Loss functions
├── neuralgridmodel.jl # Grid-dependent neural space discretization (e.g., CAE-ROM, POD-ROM)
├── neuralmodel.jl # Neural field spatial discretization (e.g., C-ROM, SNF-ROM)
├── NeuralROMs.jl # Main file: declares Julia module and imports relevant packages
├── nonlinleastsq.jl # Nonlinear least square solve for LSPG and for initializing auto-decode.
├── optimisers.jl # Modified weight decay optimisers based on Optimisers.jl
├── pdeproblems.jl # PDE problem definitions du/dt = f(x, u, t, u', ...)
├── train.jl # Training loop
├── utils.jl # Miscalleneous utility functions
├── vis.jl # 1D/2D visualizations
├── dynamics #
│ ├── evolve.jl # Logic for dynamics evaluation
│ └── timeintegrator.jl # Time integrator object definition
├── layers #
│ ├── basic.jl # Basic layer definitions (e.g., PermuteLayer, HyperNet)
│ ├── encoder_decoder.jl # Encoder-decoder network definitions (auto-decode, CAE, C-ROM, SNF-ROM)
│ └── sdf.jl # Layers for 3D shape encoding
└── operator #
├── oplayers.jl # Fourier neural operator kernel definitions
└── transform.jl # Spectral transforms for FNO$ tree experiments_SNFROM/ -L 1 --filesfirst
experiments_SNFROM/
├── autodecode.jl # Autodecode-ROM training and inference
├── cases.jl # Experiment setup
├── compare.jl # Comparison script
├── convAE.jl # CAE-ROM training and inference
├── convINR.jl # C-ROM training and inference
├── PCA.jl # POD-ROM training and inference
├── smoothNF.jl # SNF-ROM training and inference
├── advect_fourier1D # Section 6.1
├── advect_fourier2D # Section 6.2
├── burgers_fourier1D # Section 6.3
├── burgers_fourier2D # Section 6.4
└── ks_fourier1D # Section 6.5@misc{
puri2024snfrom,
title={{SNF-ROM}: {P}rojection-based nonlinear reduced order modeling with smooth neural fields},
author={Vedant Puri and Aviral Prakash and Levent Burak Kara and Yongjie Jessica Zhang},
year={2024},
eprint={2405.14890},
archivePrefix={arXiv},
primaryClass={physics.flu-dyn},
}