# FRC-TOuNN: Topology Optimization of Continuous Fiber Reinforced Composites using Neural Network

arXiv: https://arxiv.org/abs/2205.03737 · HTML: https://mlsanity.com/paper/2205.03737/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 83 references that are in the map.
- First posted on arXiv 7 May 2022.

## Builds on (most cited first, 19 of 19)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Texture Fields: Learning Texture Representations in Function Space](https://mlsanity.com/paper/1905.07259/) (2019)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [Deep Generative Modeling for Mechanistic-based Learning and Design of Metamaterial Systems](https://mlsanity.com/paper/2006.15274/) (2020)
- [Neural reparameterization improves structural optimization](https://mlsanity.com/paper/1909.04240/) (2019)
- [Deep learning for determining a near-optimal topological design without any iteration](https://mlsanity.com/paper/1801.05463/) (2018)
- [Neural networks for topology optimization](https://mlsanity.com/paper/1709.09578/) (2017)
- [3D Topology Optimization using Convolutional Neural Networks](https://mlsanity.com/paper/1808.07440/) (2018)
- [AuTO: A Framework for Automatic differentiation in Topology Optimization](https://mlsanity.com/paper/2104.01965/) (2021)
- [De-homogenization using Convolutional Neural Networks](https://mlsanity.com/paper/2105.04232/) (2021)
- [Exploring Feasible Design Spaces for Heterogeneous Constraints](https://mlsanity.com/paper/1907.01117/) (2019)
- [Topology Optimization with Accessibility Constraint for Multi-Axis Machining](https://mlsanity.com/paper/2002.07627/) (2020)
- [Algorithmically-Consistent Deep Learning Frameworks for Structural Topology Optimization](https://mlsanity.com/paper/2012.05359/) (2020)
- [Speeding up Computational Morphogenesis with Online Neural Synthetic Gradients](https://mlsanity.com/paper/2104.12282/) (2021)
- [Topology Optimization for Manufacturing with Accessible Support Structures](https://mlsanity.com/paper/2108.02829/) (2021)

## Abstract (arXiv)

In this paper, we present a topology optimization (TO) framework to simultaneously optimize the matrix topology and fiber distribution of functionally graded continuous fiber-reinforced composites (FRC). Current approaches in density-based TO for FRC use the underlying finite element mesh both for analysis and design representation. This poses several limitations while enforcing sub-element fiber spacing and generating high-resolution continuous fibers. In contrast, we propose a mesh-independent representation based on a neural network (NN) both to capture the matrix topology and fiber distribution. The implicit NN-based representation enables geometric and material queries at a higher resolution than a mesh discretization. This leads to the accurate extraction of functionally-graded continuous fibers. Further, by integrating the finite element simulations into the NN computational framework, we can leverage automatic differentiation for end-to-end automated sensitivity analysis, i.e., we no longer need to manually derive cumbersome sensitivity expressions. We demonstrate the effectiveness and computational efficiency of the proposed method through several numerical examples involving various objective functions. We also show that the optimized continuous fiber reinforced composites can be directly fabricated at high resolution using additive manufacturing.