Additive friction stir deposition (AFSD) involves coupled thermal and material-flow fields governed by frictional heating, plastic deformation, and tool-imposed boundary conditions. High-fidelity finite-volume methods (FVMs) can resolve these fields but are computationally expensive, while constant-property approximations can distort the predicted thermo-mechanical response. This work develops a steady-state multi-task coupled physics-informed neural network (MCoPINN) to predict three-dimensional temperature and material-flow fields while reconstructing temperature-dependent thermal conductivity, density, and specific heat from sparse property measurements. A theoretical analysis decomposes prediction error into property reconstruction and neural field-solver contributions and characterizes the discrepancy associated with constant-property models. A controlled one-dimensional nonlinear-conduction study evaluates property reconstruction under sparse measurements. The framework is then evaluated for AFSD against a temperature-dependent FVM benchmark and experimental thermocouple measurements. MCoPINN reproduces the reference thermal and material-flow fields and reduces average temperature root-mean-square error from 50.13 K for the constant-property CoPINN to 30.28 K across four traverse speeds. MCoPINN requires approximately 8.5 hours of training per condition, compared with 52 hours for the FVM benchmark. These results demonstrate computationally efficient, physics-coupled prediction with temperature-dependent material properties.

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