# A Pretraining-Finetuning Computational Framework for Material Homogenization

arXiv: https://arxiv.org/abs/2404.07943 · HTML: https://mlsanity.com/paper/2404.07943/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 107 references that are in the map.
- First posted on arXiv 18 Mar 2024.

## Builds on (most cited first, 17 of 17)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [One pixel attack for fooling deep neural networks](https://mlsanity.com/paper/1710.08864/) (2017)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow](https://mlsanity.com/paper/2109.03697/) (2021)
- [A physics-informed variational DeepONet for predicting the crack path in brittle materials](https://mlsanity.com/paper/2108.06905/) (2021)
- [Generic bounds on the approximation error for physics-informed (and) operator learning](https://mlsanity.com/paper/2205.11393/) (2022)
- [Blending Neural Operators and Relaxation Methods in PDE Numerical Solvers](https://mlsanity.com/paper/2208.13273/) (2022)
- [Three-dimensional convolutional neural network (3D-CNN) for heterogeneous material homogenization](https://mlsanity.com/paper/2002.07600/) (2020)
- [An Introduction to Kernel and Operator Learning Methods for Homogenization by Self-consistent Clustering Analysis](https://mlsanity.com/paper/2212.00802/) (2022)
- [Learning Homogenization for Elliptic Operators](https://mlsanity.com/paper/2306.12006/) (2023)
- [Deep learning for size-agnostic inverse design of random-network 3D printed mechanical metamaterials](https://mlsanity.com/paper/2212.12047/) (2022)

## Built on by (most cited first, 7 of 7)

- [Energy-based physics-informed neural network for frictionless contact problems under large deformation](https://mlsanity.com/paper/2411.03671/) (2024)
- [Universal Fourier Neural Operators for periodic homogenization problems in linear elasticity](https://mlsanity.com/paper/2507.12233/) (2025)
- [WINO: A Weak-Form Physics Informed Neural Operator for Hyperelasticity on Variable Domains](https://mlsanity.com/paper/2605.24651/) (2026)
- [Spectrally Safe Neural Operator Warm-Starts for Large-Scale Newton Solvers](https://mlsanity.com/paper/2606.21828/) (2026)
- [Replay-Based Continual Learning for Physics-Informed Neural Operators](https://mlsanity.com/paper/2605.04832/) (2026)
- [GA-VINO: A Geometry-Aware Variational Physics-informed Neural Operator for Mindlin-Reissner Plates](https://mlsanity.com/paper/2606.16624/) (2026)
- [PIKFNO: An Interpretable Neural Operator Based on Physics Informed Kernel Function](https://mlsanity.com/paper/2608.14619/) (2026)

## Abstract (arXiv)

Homogenization is a fundamental tool for studying multiscale physical phenomena. Traditional numerical homogenization methods, heavily reliant on finite element analysis, demand significant computational resources, especially for complex geometries, materials, and high-resolution problems. To address these challenges, we propose PreFine-Homo, a novel numerical homogenization framework comprising two phases: pretraining and fine-tuning. In the pretraining phase, a Fourier Neural Operator (FNO) is trained on large datasets to learn the mapping from input geometries and material properties to displacement fields. In the fine-tuning phase, the pretrained predictions serve as initial solutions for iterative algorithms, drastically reducing the number of iterations needed for convergence. The pretraining phase of PreFine-Homo delivers homogenization results up to 1000 times faster than conventional methods, while the fine-tuning phase further enhances accuracy. Moreover, the fine-tuning phase grants PreFine-Homo unlimited generalization capabilities, enabling continuous learning and improvement as data availability increases. We validate PreFine-Homo by predicting the effective elastic tensor for 3D periodic materials, specifically Triply Periodic Minimal Surfaces (TPMS). The results demonstrate that PreFine-Homo achieves high precision, exceptional efficiency, robust learning capabilities, and strong extrapolation ability, establishing it as a powerful tool for multiscale homogenization tasks.