# Residual fourier neural operator for thermochemical curing of composites

arXiv: https://arxiv.org/abs/2111.10262 · HTML: https://mlsanity.com/paper/2111.10262/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 23 references that are in the map.
- First posted on arXiv 15 Nov 2021.

## Builds on (most cited first, 7 of 7)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [A Physics-Informed Machine Learning Approach for Solving Heat Transfer Equation in Advanced Manufacturing and Engineering Applications](https://mlsanity.com/paper/2010.02011/) (2020)
- [Physics-Informed Neural Network for Modelling the Thermochemical Curing Process of Composite-Tool Systems During Manufacture](https://mlsanity.com/paper/2011.13511/) (2020)
- [A Machine Learning Framework for Real-time Inverse Modeling and Multi-objective Process Optimization of Composites for Active Manufacturing Control](https://mlsanity.com/paper/2104.11342/) (2021)
- [Theory-Guided Machine Learning for Process Simulation of Advanced Composites](https://mlsanity.com/paper/2103.16010/) (2021)

## Built on by (most cited first, 5 of 5)

- [Towards Multi-spatiotemporal-scale Generalized PDE Modeling](https://mlsanity.com/paper/2209.15616/) (2022)
- [Clifford Neural Layers for PDE Modeling](https://mlsanity.com/paper/2209.04934/) (2022)
- [Neural Operator: Is data all you need to model the world? An insight into the paradigm of data-driven scientific ML](https://mlsanity.com/paper/2301.13331/) (2023)
- [An Advanced Physics-Informed Neural Operator for Comprehensive Design Optimization of Highly-Nonlinear Systems: An Aerospace Composites Processing Case Study](https://mlsanity.com/paper/2406.14715/) (2024)
- [A Bregman Proximal Viewpoint on Neural Operators](https://mlsanity.com/paper/2610.20120/) (2026)

## Abstract (arXiv)

During the curing process of composites, the temperature history heavily determines the evolutions of the field of degree of cure as well as the residual stress, which will further influence the mechanical properties of composite, thus it is important to simulate the real temperature history to optimize the curing process of composites. Since thermochemical analysis using Finite Element (FE) simulations requires heavy computational loads and data-driven approaches suffer from the complexity of highdimensional mapping. This paper proposes a Residual Fourier Neural Operator (ResFNO) to establish the direct high-dimensional mapping from any given cure cycle to the corresponding temperature histories. By integrating domain knowledge into a time-resolution independent parameterized neural network, the mapping between cure cycles to temperature histories can be learned using limited number of labelled data. Besides, a novel Fourier residual mapping is designed based on mode decomposition to accelerate the training and boost the performance significantly. Several cases are carried out to evaluate the superior performance and generalizability of the proposed method comprehensively.