# Sparse Autoencoders as a Steering Basis for Phase Synchronization in Graph-Based CFD Surrogates

arXiv: https://arxiv.org/abs/2604.04946 · HTML: https://mlsanity.com/paper/2604.04946/

## Key facts

- Cited by 1 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 29 of its 49 references that are in the map.
- First posted on arXiv 28 Mar 2026.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Representation Engineering: A Top-Down Approach to AI Transparency](https://mlsanity.com/paper/2310.01405/) (2023)
- [Inference-Time Intervention: Eliciting Truthful Answers from a Language Model](https://mlsanity.com/paper/2306.03341/) (2023)
- [Steering Llama 2 via Contrastive Activation Addition](https://mlsanity.com/paper/2312.06681/) (2023)
- [Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations](https://mlsanity.com/paper/1811.12359/) (2018)
- [Steering Language Models With Activation Engineering](https://mlsanity.com/paper/2308.10248/) (2023)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Interpreting the Latent Space of GANs for Semantic Face Editing](https://mlsanity.com/paper/1907.10786/) (2019)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [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)
- [Extracting Latent Steering Vectors from Pretrained Language Models](https://mlsanity.com/paper/2205.05124/) (2022)
- [k-Sparse Autoencoders](https://mlsanity.com/paper/1312.5663/) (2013)
- [Improving Dictionary Learning with Gated Sparse Autoencoders](https://mlsanity.com/paper/2404.16014/) (2024)
- [Isolating Sources of Disentanglement in Variational Autoencoders](https://mlsanity.com/paper/1802.04942/) (2018)
- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [MultiScale MeshGraphNets](https://mlsanity.com/paper/2210.00612/) (2022)
- [Steering Language Model Refusal with Sparse Autoencoders](https://mlsanity.com/paper/2411.11296/) (2024)
- [Predicting Physics in Mesh-reduced Space with Temporal Attention](https://mlsanity.com/paper/2201.09113/) (2022)
- [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)
- [Decoding Dark Matter: Specialized Sparse Autoencoders for Interpreting Rare Concepts in Foundation Models](https://mlsanity.com/paper/2411.00743/) (2024)
- [Interpretable and Steerable Concept Bottleneck Sparse Autoencoders](https://mlsanity.com/paper/2512.10805/) (2025)
- [Interpreting CFD Surrogates through Sparse Autoencoders](https://mlsanity.com/paper/2507.16069/) (2025)
- [M4GN: Mesh-based Multi-segment Hierarchical Graph Network for Dynamic Simulations](https://mlsanity.com/paper/2509.10659/) (2025)
- [Visual Exploration of Feature Relationships in Sparse Autoencoders with Curated Concepts](https://mlsanity.com/paper/2511.06048/) (2025)

## Built on by (most cited first, 1 of 1)

- [A survey detection channel overrides the pixels in an astronomical foundation model, and biases tomographic mean redshifts](https://mlsanity.com/paper/2608.23626/) (2026)

## Abstract (arXiv)

Graph-based surrogate models provide fast alternatives to high-fidelity CFD solvers, but their opaque latent spaces and limited controllability restrict use in safety-critical settings. A key failure mode in oscillatory flows is phase drift, where predictions remain qualitatively correct but gradually lose temporal alignment with observations, limiting use in digital twins and closed-loop control. Correcting this through retraining is expensive and impractical during deployment. We ask whether phase drift can instead be corrected post hoc by manipulating the latent space of a frozen surrogate. We propose a phase-steering framework for pretrained graph-based CFD models that combines the right representation with the right intervention mechanism. To obtain disentangled representation for effective steering, we use sparse autoencoders (SAEs) on frozen MeshGraphNet embeddings. To steer dynamics, we move beyond static per-feature interventions such as scaling or clamping, and introduce a temporally coherent, phase-aware method. Specifically, we identify oscillatory feature pairs with Hilbert analysis, project spatial fields into low-rank temporal coefficients via SVD, and apply smooth time-varying rotations to advance or delay periodic modes while preserving amplitude-phase structure. Using a representation-agnostic setup, we compare SAE-based steering with PCA and raw embedding spaces under the same intervention pipeline. Results show that sparse, disentangled representations outperform dense or entangled ones, while static interventions fail in this dynamical setting. Overall, this work shows that latent-space steering can be extended from semantic domains to time-dependent physical systems when interventions respect the underlying dynamics, and that the same sparse features used for interpretability can also serve as physically meaningful control axes.