AutoMat: Physics-Guided Agentic Reasoning for Solving Ill-Posed Inverse Microscopy Problems

Reconstructing atomistic crystal structures from a single noisy STEM projection is an ill-posed inverse problem: multiple lattices can explain similar contrast, and purely feed-forward models cannot verify physical validity. We present AutoMat, a failure-aware agentic controller that performs inference-time hypothesis search with closed-loop verification to convert Scanning Transmission Electron Microscopy (STEM) images into simulation-ready crystal structures and downstream properties. AutoMat composes perception and physics modules—pattern-adaptive denoising, physics-guided template retrieval (as a fallback), symmetry-constrained atomic reconstruction, and MLIP-based relaxation/validation—and triggers rollback-and-retry when verification fails. For systematic evaluation, we introduce STEM2Mat-Bench, a benchmark dataset containing 450+ annotated samples. Performance is assessed using lattice root-mean-square deviation (RMSD), formation energy mean absolute error (MAE), and structure matching accuracy. Results demonstrate that AutoMat outperforms existing approaches including SOTA models, specialized domain tools, and closed-source multimodal large models. This work establishes a direct pathway from microscopic characterization to atomic-scale modeling, addressing a fundamental challenge in materials science.