Physics-informed multi-fidelity modeling of single-track geometry in laser directed energy deposition

Accurate prediction of single-track geometry in laser directed energy deposition remains challenging when only limited experimental data are available. This study proposes a physics-informed multi-fidelity framework, in which physics is embedded through response-specific low-fidelity priors rather than through direct physical constraints on the Gaussian-process surrogate. Specifically, the Eagar–Tsai heat-conduction model provides low-fidelity priors for clad width and penetration depth, while a semi-physical model based on mass conservation and cross-sectional geometric closure provides the prior for deposition height. These priors are fused with high-fidelity experimental measurements through a multi-fidelity Gaussian process to learn structured LF–HF discrepancies and quantify prediction uncertainty. Forty single-track experiments were conducted using laser power, scanning speed, and powder feed rate as input variables. On eight reserved independent test samples, the proposed model achieved R 2 values of 0.941, 0.918, and 0.969 for width, depth, and height, respectively, outperforming RSM, HF-only GP, and SVR models. The framework also provides guidance for balancing predictive accuracy, uncertainty, and experimental cost through HF/LF data-allocation analysis. These results demonstrate that response-specific low-fidelity priors combined with limited experimental data can provide accurate, interpretable, and uncertainty-aware geometry prediction for L-DED under small-sample conditions.