This work presents a physics-guided parameter estimation framework for cold spray additive manufacturing (CSAM), focusing on simulating and validating deposit profiles across diverse process conditions. The proposed model employs a two-zone flow representation: quasi-constant velocity near the nozzle exit followed by an exponentially decaying free jet to capture particle acceleration and impact dynamics. The framework employs a comprehensive approach by numerically integrating drag-dominated particle trajectories to predict deposit formation with high accuracy. This physics-based framework incorporates both operational and geometric parameters to ensure robust prediction capabilities. Operational parameters include spray angle, standoff distance, traverse speed, and powder feed rate, while geometric factors encompass nozzle design characteristics such as exit diameter and divergence angle. Validation is performed using 36 experimentally measured profiles of commercially pure titanium powder. The simulator shows excellent agreement with the experimental data, achieving a global root mean square error (RMSE) of 0.048 mm and a coefficient of determination $R^2=0.991$, improving the mean absolute error by more than 40% relative to a neural network-based approach. Sensitivity analyses reveal that nozzle geometry, feed rate, and critical velocity strongly modulate the amplitude and shape of the deposit. Notably, decreasing the nozzle exit diameter or divergence angle significantly increases local deposition rates, while increasing the standoff distance dampens particle velocities, thereby reducing deposit height. Although the partial differential equation (PDE)-based framework entails a moderate increase in computational time—about 50 s per run, roughly 2.5 times longer than simpler empirical models—this remains practical for most process design and optimization tasks. Beyond its accuracy, the PDE-based simulation framework’s principal advantage lies in its minimal reliance on sampling data. It can readily be adapted to new materials or untested process parameters, making it a powerful predictive tool in cold spray process design. This study underscores the simulator’s potential for guiding parameter selection, improving process reliability and offering deeper physical insights into cold spray deposit formation.

Reliable in-line estimation of slurry rheology could improve the safety and control of pipeline-transfer operations, particularly in radioactive-waste processing where frequent manual sampling is undesirable. This study presents SW-RheoPINN, a physics-informed inverse pipe-rheometry framework for estimating pipe-effective yield stress and plastic viscosity from short windows of pressure-drop, mass-flow-rate, density, and pipe-geometry measurements. The framework combines a permutation-invariant sensor-window encoder with an analytical Bingham pipe-flow backbone, radial momentum balance, a regularized constitutive relation, cross-sectional mass conservation, and a tightly bounded velocity-profile correction for limited model discrepancy. SW-RheoPINN was evaluated using 20 two-state kaolin–water flow-loop experiments comprising 40 hydraulic states. In matched-physics synthetic tests with 2% multiplicative mass-flow noise, yield-stress recovery improved from $R^2=0.787$ for two-state windows to $R^2=0.923$ and $R^2=0.955$ for three- and four-state windows, respectively; plastic-viscosity recovery improved from $R^2=0.937$ to $R^2=0.967$ and $R^2=0.961$. For the experimental data, complete sensor-window reconstruction achieved a MAPE of 0.80% and $R^2=0.990$. Because measured mass flow is an encoder input in this reconstruction, these metrics characterize inverse self-consistency rather than prospective prediction. A separate target-flow-withheld evaluation, in which the withheld mass flow was not supplied to the inverse model, achieved an RMSE of $0.108$ kg.s-1, $R^2=0.790$, and a median absolute percentage error of 3.55%. Prediction was strongest for compositions with repeatable hydraulic behavior and degraded when nominally similar experiments occupied distinct response states. Ablation and sensitivity analyses showed that strongly resolved high-yield conditions were largely insensitive to composition-related regularization, Papanastasiou sharpness, and correction capacity, whereas low-yield estimates were more model dependent. Misspecified-physics tests further showed that small hydraulic residuals do not necessarily imply unbiased rheological parameters. The inferred pipe-effective yield stresses retained the broad composition-dependent trend observed by offline rheometry, although absolute cross-scale agreement was limited. These results support SW-RheoPINN as a physics-constrained inference and diagnostic framework for identifying both well-supported and weakly resolved rheological states from standard process measurements.