pyALDIC: A Python Implementation of Augmented Lagrangian Digital Image Correlation with a GUI, Adaptive Meshing, and Mask-Aware Subset Splitting

Digital volume correlation (DVC) provides three-dimensional full-field displacement measurements from volumetric images, but how the internal resolution of a machine-learning-based DVC model affects accuracy and operating range remains poorly understood. Here, we present RAFT-DVC, a resolution-aware family of recurrent all-pairs field transforms (RAFT)-based DVC solvers with encoder downsampling factors s = 2, 4, and 8. Using a matched design, we find that the three solvers localize displacement to approximately 0.017 feature-grid voxel, giving an empirical raw-volume error scaling of approximately 0.017s voxel. The solvers exhibit complementary operating regimes governed jointly by displacement reach and volumetric-texture compatibility. Synthetic benchmarks show that RAFT-DVC achieves errors of the same order as tuned classical DVC under fine-texture, small-to-moderate-displacement conditions and becomes competitive or advantageous under coarse-texture, large-displacement conditions. Frequency-swept tests quantify deformation spatial resolution, while tiled inference enables dense estimation on large volumes. Evaluation on confocal volumetric images acquired during indentation illustrates the importance of matching solver operating regime to deformation magnitude and image texture. Tests on micro-CT images of elastomeric foam, despite training only on particle-labeled synthetic data, provide evidence of cross-texture transfer. We also identify coordinate-order inconsistencies in three-dimensional RAFT correlation sampling and introduce a non-cubic impulse test to verify sampler geometry independently of network training. Correcting the sampler improves native-input accuracy and generalization to unseen volume dimensions. Together, these results establish RAFT-DVC as a fast, resolution-aware framework for dense DVC with characterized accuracy and operating regimes.

This work aims to develop a fast and physically consistent surrogate model for real-time structural health monitoring of fractured elastic domains. We propose a physics-informed DeepONet framework that predicts displacement fields from both boundary conditions and fracture geometry, using a dedicated encoding strategy for the latter and without relying on finite-element-generated training data. The traction-free condition on the fracture boundary is imposed weakly through a localized penalty term. The presented numerical example focuses on one representative fracture geometry, demonstrating the feasibility of the formulation and laying the groundwork for extensions to surrogate modeling across diverse fracture geometries.

Recently, partial differential equations (PDEs) have been used to directly model the measurement process in signal processing, although their evaluation is costly. In this paper, we propose a novel alternating direction method of multipliers (ADMM)-based algorithm called physics-aware linearized ADMM (PA-LADMM) for inverse problems from PDE-based measurement processes. The key idea is the linearization of the subproblem with PDEs, leading to a cost-efficient update rule that calls only a PDE solver and its gradient evaluation per iteration. The algorithm has a theoretical convergence guarantee under certain conditions. In addition, we combine it with deep unfolding to unroll the PA-LADMM and train its internal parameters using supervised data. Two distinct experiments, compressed sensing with optical fiber communication and image restoration from noisy anisotropic diffusion, demonstrated the effectiveness of the proposed algorithms.