Aug 2026· Journal of turbomachinery· pp. 1-45· 0 citations
Abstract
Non-intrusive optical measurement techniques are widely used to obtain high-resolution pressure, temperature, and velocity fields, but they often suffer from random data loss caused by geometric obstruction, surface reflection, or illumination non-uniformity. Conventional reconstruction methods usually depend on high-fidelity CFD priors or large paired datasets, which limits their flexibility for arbitrary missing patterns and scarce experimental samples. This study proposes a Physics-Informed Multi-Scale Resampled Denoising Diffusion Probabilistic Model (MSR-DDPM) for missing-data reconstruction in optical flow measurements. The method shifts the reconstruction paradigm from deterministic mapping to probabilistic distribution modeling. Three features are introduced: a multi-scale hierarchical reconstruction strategy that reduces computational cost by 56% and improves stability; embedded physics-informed constraints, including divergence and gradient-continuity terms, to enhance physical consistency and reduce dependence on large training datasets; and an optional conditional diffusion module that incorporates auxiliary low-fidelity data for extreme missing-data scenarios. The framework is validated for incompressible velocity-field imputation using turbine cascade passage data, demonstrating its ability to recover complex unsteady flow structures. For missing ratios of 10%-45%, MSR-DDPM achieves high-accuracy reconstruction with Symmetric Mean Absolute Percentage Error (SMAPE) below 6% without auxiliary data. Under more severe missing ratios of 45%-65%, auxiliary guidance substantially recovers flow details and reduces reconstruction errors by approximately 60%. These results indicate that MSR-DDPM offers a flexible, data-efficient, and physically consistent solution for missing-data imputation in complex experimental flow measurements.
Estimating spatially heterogeneous elastic properties from low-resolution displacement measurements is a severely ill-posed inverse elasticity problem because low resolution obscures spatial details needed to distinguish heterogeneous property variations, and small measurement perturbations or fitting errors are amplified through inverse estimation. Existing inverse methods often rely on high-fidelity observations and manually prespecified loss weights, limiting their adaptability and making them sensitive to noise and resolution degradation. We propose a Probabilistic Inverse Elasticity Physics-Informed Neural Network (PIE-PINN) framework for robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data. PIE-PINN models displacement observation, strain-discrepancy, and equilibrium residuals using Laplace distributions within a unified probabilistic model. To improve robustness, the framework combines a B-spline-guided displacement network with a hierarchical half-Cauchy model for displacement residual scales. The B-spline provides a smooth global representation of the displacement field, while the neural network correction captures local variations. The hierarchical scale model adaptively downweights severe displacement fitting errors, enabling more robust recovery of the latent mean displacement field. An alternating maximum-likelihood training strategy updates the mean through weighted residual minimization and updates the scales to adjust the loss weights. Systematic case studies across varying noise levels and observation resolutions demonstrate the robustness of PIE-PINN.
Multidimensional NMR spectroscopy provides rich molecular-level information on species and structures, with broad significance across chemistry, biology, and materials science. However, its widespread application is generally limited by prolonged acquisition times. Combining non-uniform sampling techniques with spectra reconstruction methods offers a promising solution to this acquisition bottleneck. Traditional reconstruction methods are robust but constrained by algorithmic assumptions and approximations, whereas deep learning approaches can potentially overcome these limitations and achieve higher reconstruction fidelity, though generalization to unseen data remains challenging. Here, we present an accelerated conditional diffusion model for multidimensional NMR spectra reconstruction, formulating the task as a probabilistic iterative denoising process that progressively refines undersampled spectra under physical constraints. Experiments demonstrate that this method outperforms both traditional and end-to-end deep learning algorithms in peak recovery, artifact suppression, and robustness across multiple sampling conditions and experimental datasets.
Bo Chen, Xun Guan, Zhuoran Rong et al.· National Science Review· 0 citations
Diffusion models can be used to generate spatiotemporal signals of physical phenomena, such as time-series images of fluid dynamics. However, a major limitation of standard diffusion models is that they do not incorporate constraints derived from the underlying physical laws. Consequently, generated samples may appear visually plausible while deviating substantially from the true dynamics. In this study, we propose a simple yet effective physics-informed approach based on diffusion guidance with self-generated data augmentation. The proposed method learns the data distribution conditioned on the degree of deviation from the physically correct dynamics and generates samples by explicitly setting the deviation condition to be zero. The method decouples the evaluation of the governing equations from the diffusion model training and sampling processes, avoiding the need to solve the governing equations at every iteration of the denoising process. This design makes the method applicable to problems requiring computationally expensive numerical simulations and enables faster sample generation. Experimental results demonstrate that the proposed model not only significantly reduces the deviations compared with standard diffusion models but also achieves further reductions when combined with existing physics-constrained diffusion methods.
Akira Osaka, Naoya Takeishi, T. Yairi· 0 citations
Reconstructing multidimensional vector fields from path-integrated projection data is a fundamental challenge in high-energy-density physics, particularly when experimental sources exhibit spectral broadening and shot-to-shot jitter. We present a physics-guided deep-learning framework that addresses this ill-posed inverse problem by formulating global reconstruction as an aggregation of local inference tasks. By training a neural network on single-particle trajectories in randomized uniform magnetic fields, we develop a “local solver” that demonstrates strong zero-shot transfer to previously unseen magnetohydrodynamic topologies. Central to addressing non-ideal laser-driven proton sources, we introduce a spectral out-of-distribution filter that rejects inputs outside the training energy envelope. By preventing extrapolation, the filter enables accurate reconstruction within the represented training domain while maintaining stable populated-cell reconstruction metrics across diverse spectral conditions. Furthermore, we introduce an a priori reconstruction-reliability indicator based on the in-distribution fraction of the source spectrum, which provides a practical estimate of reconstruction coverage before inference. This approach can be integrated with energy-resolved detector systems, such as stacked nuclear track detectors, establishing a practical and highly parallelizable framework for quantitative plasma diagnostics.
Catherine Jao, Chiung-Yin Chang, Kun-Han Lee et al.· APL Machine Learning· 0 citations
The results demonstrate that PINN achieves more accurate and stable full-field vibration reconstructions than conventional PINNs, particularly under conditions involving high-frequency modes, and highlights the potential of hybrid data-physics neural frameworks as an efficient and reliable approach for solving complex PDE-governed dynamical systems.
Hailong Liu, S. Hedayatrasa, Yunpeng Zhu et al.· e-Journal of Nondestructive...· 0 citations
Monte Carlo simulation of calorimeter showers is a principal bottleneck for the High-Luminosity LHC, and diffusion models have emerged as fast, high-fidelity surrogates. Their denoising objective is purely statistical, however: a model can minimize it while placing the physics wrong. Existing physics-informed generative methods cannot close this gap, because they assume a closed-form law, a governing PDE residual or a hard per-sample constraint, that a shower does not supply: no per-sample PDE governs a stochastic cascade, and energy conservation fixes only one scalar per shower. Standard metrics ignore the correlation structure across calorimeter layers and voxels, comparing showers only in a physics feature space. We address both gaps. We introduce the Correlation Frobenius Distance (CFD), a single normalized score for correlation fidelity at layer-wise and voxel-wise scales. We then encode the soft per-sample structure available in a shower as two physics-aware auxiliary losses: a variance-stabilized voxel residual loss grounded in counting statistics, and a graph Laplacian loss over the detector geometry. We combine both with denoising through GradBlend, which anchors the step magnitude to the denoising gradient while letting the auxiliary steer its direction, yielding Lantern, a physics-guided diffusion surrogate. On CaloChallenge Dataset 2, injecting the physics losses through task-symmetric rules such as PCGrad, GradNorm, IMTL-G, and ConFIG inflates FPD by 2-100x relative to denoising alone, whereas GradBlend admits the same signal without regression and, with the Laplacian loss, Lantern improves both FPD and CFD. Our ablation on the auxiliary loss scheduler shows that the voxel residual loss, whose gradient conflicts with denoising, requires a terminal denoising-only phase to preserve shower fidelity, whereas the non-conflicting Laplacian loss is insensitive to the schedule.
Farzana Yasmin Ahmad, V. Venkataswamy, Geoffrey C. Fox· 0 citations