NeuralROMs.jl

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.

Smooth neural field ROM

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

Offline stage

Online stage

Setup and run

Download the code by cloning this Git repo.

```bash $ git clone git@github.com:vpuri3/NeuralROMs.jl.git

$ cd NeuralROMs.jl ```

Start Julia and activate the environment.

bash $ julia

```julia julia> import Pkg

julia> Pkg.activate(".") # switch environment

julia> Pkg.instantiate() # download environment ```

We 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 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 julia> include("experiments_SNFROM/advect_fourier1D/snf.jl")

Code Structure

```bash $ 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)

```

bash $ 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

bash $ 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

Citing

bib @article{puri2025snf, title={SNF-ROM: Projection-based nonlinear reduced order modeling with smooth neural fields}, author={Puri, Vedant and Prakash, Aviral and Kara, Levent Burak and Zhang, Yongjie Jessica}, journal={Journal of Computational Physics}, pages={113957}, year={2025}, publisher={Elsevier} }