A Fast and Generalizable Fourier Neural Operator-Based Surrogate for Melt-Pool Prediction in Laser Processing

High-fidelity simulations of laser welding capture complex thermo-fluid phenomena, including phase change, free-surface deformation, and keyhole dynamics, however their computational cost limits large-scale process exploration and real-time use. In this work we present the Laser Processing Fourier Neural Operator (LP-FNO), a Fourier Neural Operator (FNO) based surrogate model that learns the parametric solution operator of various laser processes from multiphysics simulations generated with FLOW-3D WELD (registered trademark). Through a novel approach of reformulating the transient problem in the moving laser frame and applying temporal averaging, the system results in a quasi-steady state setting suitable for operator learning, even in the keyhole welding regime. The proposed LP-FNO maps process parameters to three-dimensional temperature fields and melt-pool boundaries across a broad process window spanning conduction and keyhole regimes using the non-dimensional normalized enthalpy formulation. The model achieves temperature prediction errors on the order of 1% and intersection-over-union scores for melt-pool segmentation over 0.9. We demonstrate that a LP-FNO model trained on coarse-resolution data can be evaluated on finer grids, yielding accurate super-resolved predictions in mesh-converged conduction regimes, whereas discrepancies in keyhole regimes reflect unresolved dynamics in the coarse-mesh training data. These results indicate that the LP-FNO provides an efficient surrogate modeling framework for laser welding, enabling prediction of full three-dimensional fields and phase interfaces over wide parameter ranges in just tens of milliseconds, up to a hundred thousand times faster than traditional Finite Volume multi-physics software.

💡 Research Summary

This paper introduces a novel surrogate model, the Laser Processing Fourier Neural Operator (LP‑FNO), designed to predict three‑dimensional temperature fields and melt‑pool geometries in laser welding with unprecedented speed and accuracy. High‑fidelity multiphysics simulations of single‑track laser scans on Ti‑6Al‑4V were generated using the commercial software FLOW‑3D WELD®. The simulations capture the full Navier‑Stokes equations with free‑surface tracking, recoil pressure, Marangoni convection, phase change, and ray‑traced laser absorption, covering a wide process window that includes conduction, partial melting, and stable keyhole regimes.

To make the problem amenable to operator learning, the authors reformulate the transient physics in a reference frame moving with the laser beam. In this moving frame the governing equations become quasi‑steady; the remaining temporal fluctuations are removed by averaging over a short time window. Consequently, each simulation instance can be represented as a static mapping from the process parameters (laser power P and scan speed Vₛₐₙ) to the full solution fields (temperature T, volume fraction α, and a temperature‑dependent fluid fraction fₗ).

The core of the surrogate is a Fourier Neural Operator (FNO). The input parameters are lifted into a high‑dimensional channel space, processed through several Fourier layers that perform global convolutions in spectral space, and finally projected back to the physical fields. Only a limited set of low‑frequency Fourier modes is retained, exploiting the empirical observation that PDE solution operators are dominated by low‑frequency content while high‑frequency components are often noisy or discretization artifacts. The architecture uses four Fourier layers, 64 channels per layer, and GELU non‑linearity, resulting in O(N log N) computational complexity for a three‑dimensional grid of size N.

Training data were sampled on an evenly spaced grid in normalized enthalpy H* (a non‑dimensional quantity proportional to P √Vₛₐₙ) and laser power, ensuring uniform coverage of all welding regimes. A total of 120 simulation cases were generated, each saved at 5 µs intervals; after moving‑frame transformation and temporal averaging, each case provides a single input‑output pair for the operator learning task. The loss function combines L₂ errors on temperature and volume fraction, with weighting that balances conduction and keyhole regions.

The trained LP‑FNO achieves mean absolute temperature errors below 1 % and Intersection‑over‑Union (IoU) scores above 0.90 for melt‑pool segmentation across the entire process window. Inference on an NVIDIA RTX 3090 GPU takes 8–12 ms per prediction, representing a speed‑up of roughly 10⁵‑fold compared with the original finite‑volume simulations, which require tens of minutes to hours.

A notable capability demonstrated is super‑resolution: the model trained on coarse 10 µm meshes can be evaluated on finer 2 µm grids. In the conduction regime, the super‑resolved predictions retain the same accuracy (≈1 % temperature error) and faithfully reproduce melt‑pool shapes. In the keyhole regime, discrepancies appear because the coarse training data do not resolve the rapid pressure and temperature gradients inside the keyhole; nevertheless, the overall melt‑pool morphology and average temperature remain physically consistent.

The authors discuss the implications for digital twins, real‑time process control, rapid design space exploration, and uncertainty quantification in laser manufacturing. By providing near‑instantaneous, physics‑consistent full‑field predictions over a broad parameter space, LP‑FNO opens the door to closed‑loop control strategies that were previously infeasible due to computational constraints. Moreover, the use of normalized enthalpy as a sampling metric suggests that the approach can be generalized to other alloys, laser wavelengths, or pulsed laser processes with minimal retraining.

In summary, this work presents the first surrogate modeling framework that simultaneously spans conduction and keyhole welding regimes, treats keyhole dynamics within a quasi‑steady operator‑learning formulation, and leverages Fourier Neural Operators to achieve both high fidelity and extreme computational efficiency. The results constitute a significant step toward real‑time, physics‑based digital twins for laser‑based additive manufacturing and welding applications.