Domain-informed Adaptive Sampling for Generalizable PINNs in Metal Additive Manufacturing via Conditional Flow Matching

Accurate thermal modeling in metal additive manufacturing (AM) is essential for understanding the process-structure-performance relationship. While prior studies have explored generalization across unseen process conditions, they often require extensive datasets, costly retraining, or pre-training. Generalization across different materials also remains relatively unexplored due to the challenges posed by distinct material-dependent thermal behaviors. This paper introduces a parametric physics-informed neural network (PINN) framework for zero-shot generalization across arbitrary materials without labeled data, retraining, or pre-training. The framework adopts a decoupled parametric PINN architecture that separately encodes material properties and spatiotemporal coordinates, fusing them through conditional modulation to better align with the multiplicative role of material parameters in the governing equation and boundary conditions. Physics-guided output scaling derived from Rosenthal's analytical solution and a hybrid optimization strategy are further incorporated to enhance physical consistency, training stability, and convergence. Experiments on bare plate laser powder bed fusion (LPBF) across diverse metal alloys, including both in-distribution and out-of-distribution cases, demonstrate effective zero-shot generalizability along with superior training efficiency. Specifically, the proposed framework achieved up to a 64.2% reduction in relative L2 error compared to the non-parametric baseline while surpassing its performance within only 4.4% of the baseline training epochs. Ablation studies confirm that the proposed framework's components are broadly applicable to other PINN-based approaches. Overall, the proposed framework provides an efficient and scalable material-agnostic solution for zero-shot thermal modeling, contributing to more flexible and practical deployment in metal AM.

Physics-informed neural network (PINN) training minimizes a weighted combination of partial differential equation (PDE), boundary-condition, and initial-condition losses. Because adaptive methods modify these weights during training, their weighted total losses are not always directly comparable. We compare fixed-weight PINN, gradient-normalized PINN (GNPINN), and a rule-based adaptive controller (AgenticPINN) under matched settings on a heat-equation benchmark and a simplified Czochralski-oriented thermal-fluid problem. In the crystal-growth MLP experiment, adaptive control reduced the PDE residual from the order of $10^{-5}$ to $10^{-6}$, while the boundary-condition loss increased from the order of $10^{-5}$ to $10^{-2}$. On the heat-equation benchmark, GNPINN achieved the lowest relative $L_2$ field error (0.054), whereas AgenticPINN obtained the smallest PDE residual but a relative $L_2$ error of 1.368. Gaussian-process surrogates were additionally evaluated using case-wise holdout tests on corrected Czochralski CFD parameter sweeps. The temperature-field error for the temperature sweep was approximately 6%, whereas the axial-velocity error for the crystal-rotation sweep was approximately 42%. These findings show that adaptive control can improve equation satisfaction while weakening other physical constraints. PINN training should therefore be evaluated using separate PDE, boundary-condition, and solution-error metrics rather than weighted total loss alone.

Time-dependent high-dimensional partial differential equations (PDEs) with spatially localised and dynamically evolving solutions pose a fundamental challenge for physics-informed neural networks (PINNs), as uniform collocation sampling becomes increasingly ineffective in high-dimensional spatiotemporal domains. In this work, a deep adaptive sampling framework for PINNs is extended to the time-dependent setting by treating space and time as a unified domain without any explicit time marching. A normalising flow neural network model effectively learns the distribution induced by the PDE residual and generates new collocation points concentrated in regions where the solution is most difficult to learn. Unlike conventional adaptive strategies that require explicit time stepping or moving meshes, high-residual regions are automatically identified and tracked across both space and time, driven purely by the PDE residual distribution. The effectiveness of the proposed strategy is assessed on a range of benchmark problems, from sharp and moving features in two spatial dimensions to localised structures in up to eight spatial dimensions.