Additive friction stir deposition (AFSD) involves strongly coupled thermal and material-flow fields generated by frictional heating, severe plastic deformation, and tool-imposed boundary conditions. High-fidelity finite-volume methods (FVMs) can resolve these coupled fields accurately, but their computational cost limits repeated evaluation across process conditions. A separate modeling challenge arises from the strong temperature dependence of thermophysical properties. Treating thermal conductivity, density, and specific heat as constants can introduce substantial error in the predicted thermo-mechanical response. This work develops a steady-state multi-task coupled physics-informed neural network (MCoPINN) that predicts the three-dimensional velocity and temperature fields while reconstructing temperature-dependent thermophysical properties from sparse material data. A theoretical analysis formally decomposes the MCoPINN prediction error into contributions from property reconstruction and the neural field solver. A controlled one-dimensional nonlinear heat-conduction problem is first used to demonstrate this error decomposition and evaluate property reconstruction under sparse data. The framework is then applied to AFSD and evaluated against an FVM benchmark and experimental thermocouple measurements. MCoPINN reproduces the benchmark thermal and material-flow fields while improving the thermal prediction relative to the constant-property CoPINN. The benchmark FVM required approximately 52 hours per operating condition, whereas MCoPINN required about 8.5 hours of training. The results demonstrate that MCoPINN can account for temperature-dependent thermophysical properties in full-field AFSD prediction while requiring significantly less computation than the FVM benchmark.

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