Autonomous Algorithm Discovery for Ptychography via Evolutionary LLM Reasoning

Xiangyu Yin; Ming Du; Junjing Deng; Zhi Yang; Yimo Han; Yi Jiang

cs.CEMar 5, 2026

Autonomous Algorithm Discovery for Ptychography via Evolutionary LLM Reasoning

Authors: Xiangyu Yin, Ming Du, Junjing Deng, Zhi Yang, Yimo Han, Yi Jiang

Organizations: Advanced Photon Source, Argonne National Laboratory, Lemont, IL, USA · Department of Materials Science and NanoEngineering, Rice University, Houston, TX, USA

Abstract

Ptychography is a computational imaging technique widely used for high-resolution materials characterization, but high-quality reconstructions often require the use of regularization functions that largely remain manually designed. We introduce Ptychi-Evolve, an autonomous framework that uses large language models (LLMs) to discover and evolve novel regularization algorithms. The framework combines LLM-driven code generation with evolutionary mechanisms, including semantically-guided crossover and mutation. Experiments on three challenging datasets (X-ray integrated circuits, low-dose electron microscopy of apoferritin, and multislice imaging with crosstalk artifacts) demonstrate that discovered regularizers outperform conventional reconstructions, achieving up to +0.26 SSIM and +8.3~dB PSNR improvements. Besides, Ptychi-Evolve records algorithm lineage and evolution metadata, enabling interpretable and reproducible analysis of discovered regularizers.

Figures & tables

Figure 1: System architecture of Ptychi-Evolve showing the discovery loop. The LLM Engine generates regularizer code, which is executed by the Pty-Chi reconstruction library. The Evaluator assesses reconstruction quality and records metrics to the History Manager. Context from the history informs both the Evolution Controller (for selecting parent algorithms and actions) and the LLM Engine (for code generation). The Evolution Controller triggers actions (generate, tune, crossover, or mutate) that prompt the LLM to produce new regularizer variants.

Dataset	Algorithms	Success	Best	$\Delta$ SSIM	$\Delta$ PSNR	Duration
X-ray IC	100	83%	0.785	+0.26	+8.3 dB	16.5 hrs
Apoferritin	147	97%	0.836	+0.12	+3.2 dB	29.5 hrs
Multislice	97	94%	0.871	+0.18	+8.0 dB	10.5 hrs

Table 1: Discovery Statistics and Performance. Best reports the discovery-evaluation SSIM at the fixed discovery horizon (IC: 3000 iterations; apoferritin and multislice: 1000).

\Delta

SSIM and

\Delta

PSNR report improvement of the best discovered regularizer over the baseline at the representative comparison iteration in Figure 3 (IC: 3000 iterations; apoferritin: 1000; multislice: 1000) using the same evaluation references as in Figure 2 . For multislice,

\Delta

values are computed on the mean across layers.

Figure 2: Visual comparison of reconstructed phase images at representative iterations. Columns show a reference image, baseline reconstruction, and best discovered regularizer. For multislice and apoferritin, the reference is the simulated ground-truth phase; for X-ray IC, the reference is a long-iteration (i.e., 10,000) reconstruction used as an evaluation reference in the absence of ground truth. SSIM values overlaid on baseline/best are computed against the corresponding reference, and all images within each row share a unified color scale (shown by the colorbar on the right). X-ray IC is shown at 3000 iterations; apoferritin and multislice are shown at 1000 iterations.

Panel of Figure 3 — Figure 3: Convergence comparison showing SSIM, PSNR, RMSE, and MAE versus reconstruction iterations for baseline (grey) and best discovered regularizer (green), computed against the same evaluation references as in Figure 2 . IC is swept up to 10,000 iterations; apoferritin and multislice are swept up to 1,000 iterations. Multislice results are shown per layer (top row: layer 1; bottom row: layer 2).

Dataset	Technique	Description
X-ray IC	Adaptive notch filtering	FFT-based grid artifact suppression
X-ray IC	Structure-tensor TV	Edge-aware anisotropic smoothing
X-ray IC	Barzilai-Borwein	Adaptive step size acceleration
Apoferritin	Variance-gated	Preserves features under noise
Apoferritin	Soft-Huber	Noise-adaptive shrinkage
Apoferritin	Perona-Malik	Anisotropic diffusion

Table 2: Key Techniques Discovered by Dataset

Panel of Figure 4 — Figure 4: Discovery trajectory over generation number from the merged history. Grey points show successfully evaluated algorithms; the green curve shows the best discovery-evaluation SSIM found so far (computed at the fixed discovery horizon: IC 3000 iterations; apoferritin and multislice 1000).

Panel of Figure 5 — Figure 5: Technique adoption timeline from the merged history, showing the generations in which successfully evaluated algorithms include each technique. Lines span first-to-last appearance and markers indicate that a technique appears in at least one algorithm in that generation (techniques shown have $\geq$ 5 occurrences; technique names are normalized to merge spelling variants).

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Iterative ptychographic reconstruction algorithms are widely used for coherent diffractive imaging but can exhibit slow convergence under realistic experimental conditions. We propose a machine learning-augmented approach that accelerates iterative ptychographic reconstruction by introducing a learned fast-forward operator applied during reconstruction. Following an initial warm-up using standard iterations, the fast-forward operator advances the reconstruction toward a more converged state, after which conventional iterative updates are resumed. This strategy preserves the physical consistency and flexibility of established ptychographic solvers while reducing the number of iterations required for convergence. The model is trained on diverse ptychographic datasets and evaluated on experimental data acquired in a different year, demonstrating robustness and temporal generalization. Compared with conventional iterative solvers, the machine learning-augmented method achieves comparable reconstruction quality while converging faster in terms of Poisson negative log-likelihood, yielding over a two-fold reduction in wall-clock time. The approach has been integrated into an existing reconstruction pipeline and deployed in production at a synchrotron beamline, demonstrating practicality for real-time experimental operation.

Abstract

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