# Interpreting CFD Surrogates through Sparse Autoencoders

arXiv: https://arxiv.org/abs/2507.16069 · HTML: https://mlsanity.com/paper/2507.16069/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Sparse autoencoder training and evaluation, one of 13 directions in Mechanistic interpretability.
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 21 Jul 2025.

## Placed in

- Mechanistic interpretability / [Sparse autoencoder training and evaluation](https://mlsanity.com/mechinterp/sparse-autoencoder-training-and-evaluation/)

## Builds on (most cited first, 12 of 12)

- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Gemma Scope: Open Sparse Autoencoders Everywhere All At Once on Gemma 2](https://mlsanity.com/paper/2408.05147/) (2024)
- [Jumping Ahead: Improving Reconstruction Fidelity with JumpReLU Sparse Autoencoders](https://mlsanity.com/paper/2407.14435/) (2024)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Improving Dictionary Learning with Gated Sparse Autoencoders](https://mlsanity.com/paper/2404.16014/) (2024)
- [Universal Sparse Autoencoders: Interpretable Cross-Model Concept Alignment](https://mlsanity.com/paper/2502.03714/) (2025)
- [Efficient Dictionary Learning with Switch Sparse Autoencoders](https://mlsanity.com/paper/2410.08201/) (2024)
- [Enhancing Neural Network Interpretability with Feature-Aligned Sparse Autoencoders](https://mlsanity.com/paper/2411.01220/) (2024)
- [Interpretable and Testable Vision Features via Sparse Autoencoders](https://mlsanity.com/paper/2502.06755/) (2025)
- [Decoding Dark Matter: Specialized Sparse Autoencoders for Interpreting Rare Concepts in Foundation Models](https://mlsanity.com/paper/2411.00743/) (2024)

## Built on by (most cited first, 3 of 3)

- [Sparse Autoencoders as a Steering Basis for Phase Synchronization in Graph-Based CFD Surrogates](https://mlsanity.com/paper/2604.04946/) (2026)
- [Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition](https://mlsanity.com/paper/2605.25115/) (2026)
- [PhysSAE: Mechanistic Interpretability of PINNs with Sparse Autoencoders](https://mlsanity.com/paper/2609.07061/) (2026)

## Abstract (arXiv)

Learning-based surrogate models have become a practical alternative to high-fidelity CFD solvers, but their latent representations remain opaque and hinder adoption in safety-critical or regulation-bound settings. This work introduces a posthoc interpretability framework for graph-based surrogate models used in computational fluid dynamics (CFD) by leveraging sparse autoencoders (SAEs). By obtaining an overcomplete basis in the node embedding space of a pretrained surrogate, the method extracts a dictionary of interpretable latent features. The approach enables the identification of monosemantic concepts aligned with physical phenomena such as vorticity or flow structures, offering a model-agnostic pathway to enhance explainability and trustworthiness in CFD applications.