Wire-directed energy deposition (W-DED) produces steep thermal gradients and rapid heating-cooling cycles due to the moving heat source, where modest variations in process parameters significantly alter heat input per unit length and therefore the full thermal history. This sensitivity makes process tuning by trial-and-error or repeated FE sweeps expensive, motivating inverse analysis. This work proposes an inverse thermal process design framework that couples single-track experiments, a calibrated finite element (FE) thermal model, and a parametric physics-informed neural network (PINN) surrogate. By using experimentally calibrated heat-loss physics to define the training constraints, the PINN learns a parameterized thermal response from physics alone (no temperature data in the PINN loss), enabling inverse design without repeated FE runs. Thermocouple measurements are used to calibrate the convection film coefficient and emissivity in the FE model, and those parameters are used to train a parametric PINN over continuous ranges of arc power (1.5–3.0 kW) and travel speed (0.005–0.015 m/s) without using temperature data in the loss function. The trained PINN model was validated against the calibrated FE model at 3 probe locations with different power and travel speed combinations. Across these benchmark conditions, the mean absolute errors are between 6.5–17.4 °C, with cooling-tail errors ranging from 1.8–12.1 °C. The trained surrogate is then embedded in a sampling-based inverse optimization loop to identify power-speed combinations that achieve prescribed interlayer temperatures at a fixed dwell time. For target interlayer temperatures of 100, 130, and 160 °C with a 10 s dwell time, the optimized solutions remain within 3.3–5.6 °C of the target according to the PINN, while FE verification is within 4.0–6.6 °C. The results demonstrate that a physics-only parametric PINN surrogate enables inverse thermal process design without repeated FE runs while establishing a single-track baseline for extension to multi-track and multi-layer builds.

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.