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

Alix Benoit, Toni Ivas, Mateusz Papierz, Asel Sagingalieva, Alexey Melnikov, Elia Iseli

TL;DR

The paper tackles the cost of high-fidelity laser-welding simulations by introducing LP-FNO, a Fourier Neural Operator surrogate trained on FLOW-3D WELD data to predict 3D temperature fields and melt-pool boundaries across conduction to keyhole regimes. By reformulating the problem in a moving laser frame and applying temporal averaging, the authors cast the transient dynamics into a quasi-steady operator-learning task and use normalized enthalpy $H^*$ to sample the parameter space. LP-FNO achieves temperature predictions with ~1% error and melt-pool segmentation IoU above 0.9, while providing mesh-independent, rapid inferences (tens of milliseconds) and enabling effective super-resolution from coarse training data. The work demonstrates strong generalization without retraining over a broad process window and highlights limitations tied to training data fidelity, suggesting future directions in efficient spectral mixing and possible quantum-inspired extensions to improve scalability and accuracy for more complex physics.

Abstract

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.

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

TL;DR

The paper tackles the cost of high-fidelity laser-welding simulations by introducing LP-FNO, a Fourier Neural Operator surrogate trained on FLOW-3D WELD data to predict 3D temperature fields and melt-pool boundaries across conduction to keyhole regimes. By reformulating the problem in a moving laser frame and applying temporal averaging, the authors cast the transient dynamics into a quasi-steady operator-learning task and use normalized enthalpy to sample the parameter space. LP-FNO achieves temperature predictions with ~1% error and melt-pool segmentation IoU above 0.9, while providing mesh-independent, rapid inferences (tens of milliseconds) and enabling effective super-resolution from coarse training data. The work demonstrates strong generalization without retraining over a broad process window and highlights limitations tied to training data fidelity, suggesting future directions in efficient spectral mixing and possible quantum-inspired extensions to improve scalability and accuracy for more complex physics.

Abstract

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.
Paper Structure (31 sections, 22 equations, 12 figures, 6 tables)

This paper contains 31 sections, 22 equations, 12 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Physical Model and Data Generation
  4. Simulation Software.
  5. Process Parameter Variations.
  6. The Fourier Neural Operator
  7. Mathematical Setting.
  8. Solution Operator.
  9. For our case.
  10. Discretized operator learning problem.
  11. Architecture overview.
  12. Fourier layer as global convolution.
  13. Mode truncation and learnable spectral weights.
  14. Input/output maps and physical fields.
  15. Training objective.
  16. ...and 16 more sections

Figures (12)

  • Figure 1: Process-space coverage of high-fidelity simulation data generated with FLOW-3D WELD. The dataset spans laser power $P$ and scan speed $V_{\mathrm{scan}} \in [0.1m\per s, 1.0m\per s]$, and is constructed on a grid uniform in normalized enthalpy $H^*$ and power. Markers denote the training, validation, and super-resolution test sets used for neural operator learning
  • Figure 2: Architecture of LP-FNO forward pass
  • Figure 3: Conduction regime ($P=70$, $V_{scan}=0.298$, $H^*=4.75$). Temporal evolution of the mean absolute temperature difference in the laser reference frame. Quasi-static behavior appears around $t=30$ for non-averaged data, and in averaged data from $t_{avg}=50$. Time averaging is defined in \ref{['eq:window_avg']}
  • Figure 4: Keyhole regime ($P=150$, $V_{scan}=0.542$, $H^*=7.54$). Temporal evolution of the mean absolute temperature difference in the laser reference frame. Temporal averaging suppresses high-frequency interface fluctuations, revealing quasi-static behavior once the laser has traveled a sufficient distance. Time averaging is defined in \ref{['eq:window_avg']}
  • Figure 5: LP-FNO 3D inference result for keyhole regime simulation with $P=150W$ and $V_{\mathrm{scan}}=0.54m/s$. Domain cut in half for visual clarity. Visualized using ParaView ahrens_paraview_2005
  • ...and 7 more figures