Inverse Thermal Process Design for Interlayer Temperature Control in Wire-Directed Energy Deposition Using Physics-Informed Neural Networks

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.