Differentiable Thermo-Mechanical Simulation of Laser Powder Bed Fusion for Uncertainty Quantification and Digital Twins
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Additive manufacturing methods such as laser powder bed fusion (LPBF) offer unprecedented design freedom compared to conventional counterparts; however, industrial certification and process control remain significant hurdles. The localized nature of selective laser melting can induce defects across multiple spatial and temporal scales, rendering associated uncertainty quantification and optimal control problems acutely high-dimensional. In these settings, derivative-free methods often suffer from slow convergence and require an intractable number of evaluations. To enable scalable derivative-based approaches, we present a macroscale differentiable simulator that leverages thermodynamic arguments and algorithmic innovations to efficiently compute sensitivities of the thermo-mechanical material response during LPBF. Our model is derived from thermodynamic principles to provide a rigorous physical foundation while simultaneously justifying the regularizations necessary to smooth the underlying dynamics for differentiability. A non-isothermal Ginzburg-Landau functional first establishes coupled thermal-phase dynamics, which are then reduced to a smooth enthalpy formulation via scaling arguments. From the remaining dissipation inequality, the framework of generalized standard materials yields differentiable viscoplasticity with nonlinear kinematic hardening and recovery. We employ symbolic differentiation via the Unified Form Language within the FEniCSx library. This supports novel matrix- and tensor-free methods for computing higher-order derivative actions, significantly reducing the memory overhead typically associated with computing sensitivities. Crucially, derivative actions are evaluated by a lattice of linear solves with the same operator which may be factorized or effectively preconditioned. Hence, the cumulative cost of these linear solves is marginal compared to the expensive coupled nonlinear iterations required for the primary thermo-mechanical solve. We show that the simulator facilitates efficient derivative-informed forward uncertainty quantification approaches, specifically regarding the influence of material parameter and powder bed packing priors on defect-characterizing quantities of interest. These initial results indicate a scalable pathway for predictive digital twins in LPBF process control.
