Physics-Informed Synthetic Dataset and Denoising TIE-Reconstructed Phase Maps in Transient Flows Using Deep Learning

Reconstructing high-fidelity flow fields from low-fidelity observations is a central problem in scientific machine learning, yet recent diffusion and flow-matching models typically rely on iterative sampling, making them costly for latency-sensitive workflows such as ensemble forecasting, real-time visualization, and simulation-in-the-loop inference. We study whether a high-fidelity flow-matching generative model can be compressed into a compact one-step model for fast scientific flow reconstruction. Our approach distills an optimal-transport flow-matching teacher into a one-step consistency model. Low-fidelity observations are incorporated at inference by initializing the generative trajectory from a noised observation along the transport path, allowing an unconditional high-fidelity flow model to perform conditional reconstruction without retraining the teacher. We evaluate this distillation strategy on three fluid benchmarks, Smoke Buoyancy, Turbulent Channel Flow, and Kolmogorov Flow, using coarse-to-fine reconstruction as a controlled testbed at field sizes up to $256 \times 256$. Across these settings, the distilled student retains similar performance of the teacher's model on spectrum metrics, while using roughly half as many parameters and achieving a $12\times$ inference speedup over the flow-matching teacher. Under the same training budget, the distilled student also outperforms a one-step consistency model trained directly from scratch by $23.1\%$ in SSIM, showing that teacher distillation improves training efficiency rather than merely accelerating sampling. These results suggest a promising route for turning future high-capacity scientific generative models into compact reconstruction models that are faster to train, cheaper to run, and easier to deploy.

Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty quantification. Generative models, by learning distributions over spatiotemporal fields, can better handle sparsity and uncertainty. However, existing generative approaches enforce data consistency and PDE constraints simultaneously via sampling-time gradient guidance, resulting in slow and unstable inference. To this end, we propose PerFlow, a Physics-embedded rectified Flow for efficient sparse reconstruction and uncertainty quantification of spatiotemporal dynamics. PerFlow decouples observation conditioning from physics enforcement, performing guidance-free conditioning by feeding observations into rectified-flow dynamics while embedding hard physics via a constraint-preserving projection (e.g., incompressibility or conservation). Theoretically, we establish invariance guarantees to ensure that trajectories remain on the physics-consistent manifold throughout sampling. Experiments on various PDE systems demonstrate competitive reconstruction accuracy with sound physics consistency, while enabling efficient conditional sampling (e.g., 50 steps) and up to 320x faster inference than 2000-step guided diffusion baselines.

Ptychographic phase reconstruction is commonly formulated as an iterative inverse problem, requiring repeated object-probe updates and resulting in substantial computational cost for large-scale 4D-STEM data. We present a direct local-to-global learning framework that reconstructs full-field phase maps from diffraction measurements without iterative refinement during inference. The proposed network predicts local wrapped-phase patches from individual diffraction patterns using a sine-cosine representation, and the predictions are assembled into a full-field reconstruction using calibrated scan positions and Gaussian-weighted stitching. To evaluate generalization beyond the training domain, the model is trained on one material and directly applied to another in a zero-shot setting without target-domain fine-tuning. Experiments on AuPd and MoS$_2$ demonstrate consistent cross-material transfer in both directions, with the proposed method achieving the best full-field MSE, PSNR, and MS-SSIM among the evaluated learning-based methods. Compared with the iterative ePIE approach, the proposed direct local-to-global pipeline reduces end-to-end reconstruction time by approximately 10x, demonstrating its potential for efficient and transferable ptychographic reconstruction.