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PhysSAE: Mechanistic Interpretability of PINNs with Sparse Autoencoders

arXiv · AI, language, vision and robotics · article · Sep 7, 2026 · UTC

Physics-Informed Neural Networks (PINNs) embed PDE residuals into neural network training, but their internal representations remain opaque: it is unknown what physical features their hidden layers encode or whether those features have a localized causal role. We present PhysSAE, a mechanistic interpretability framework that trains overcomplete sparse autoencoders (SAEs) on PINN penultimate-layer activations and evaluates dictionary atoms through direct causal intervention in the original frozen hidden state: $h_{\mathrm{cf}} = h - αz_k d_k$, bypassing the SAE decoder entirely. Across six PDE

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