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

arXiv: https://arxiv.org/abs/2602.06241 · HTML: https://mlsanity.com/paper/2602.06241/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 46 references that are in the map.
- First posted on arXiv 5 Feb 2026.

## Builds on (most cited first, 15 of 15)

- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Symbolic Discovery of Optimization Algorithms](https://mlsanity.com/paper/2302.06675/) (2023)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [Multi-Objective Loss Balancing for Physics-Informed Deep Learning](https://mlsanity.com/paper/2110.09813/) (2021)
- [Hybrid quantum physics-informed neural networks for simulating computational fluid dynamics in complex shapes](https://mlsanity.com/paper/2304.11247/) (2023)
- [Deep Neural Operator Enabled Digital Twin Modeling for Additive Manufacturing](https://mlsanity.com/paper/2405.09572/) (2024)
- [Surrogate Modeling of Melt Pool Thermal Field using Deep Learning](https://mlsanity.com/paper/2207.12259/) (2022)
- [Adaptive Physics-informed Neural Networks: A Survey](https://mlsanity.com/paper/2503.18181/) (2025)
- [Fast and Accurate Reduced-Order Modeling of a MOOSE-based Additive Manufacturing Model with Operator Learning](https://mlsanity.com/paper/2308.02462/) (2023)
- [Partitioned Hybrid Quantum Fourier Neural Operators for Scientific Quantum Machine Learning](https://mlsanity.com/paper/2507.08746/) (2025)
- [Physics-Informed Surrogates for Temperature Prediction of Multi-Tracks in Laser Powder Bed Fusion](https://mlsanity.com/paper/2502.01820/) (2025)

## Built on by (most cited first, 2 of 2)

- [Hybrid Fourier Neural Operator for Surrogate Modeling of Laser Processing with a Quantum-Circuit Mixer](https://mlsanity.com/paper/2604.04828/) (2026)
- [Generative World Models Enable Predictive Control of Laser Melt Pool Dynamics](https://mlsanity.com/paper/2610.06250/) (2026)

## Abstract (arXiv)

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.