# NITO: Neural Implicit Fields for Resolution-free Topology Optimization

arXiv: https://arxiv.org/abs/2402.05073 · HTML: https://mlsanity.com/paper/2402.05073/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 85 references that are in the map.
- First posted on arXiv 7 Feb 2024.

## Builds on (most cited first, 30 of 47)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [Hierarchical Text-Conditional Image Generation with CLIP Latents](https://mlsanity.com/paper/2204.06125/) (2022)
- [Zero-Shot Text-to-Image Generation](https://mlsanity.com/paper/2102.12092/) (2021)
- [GLIDE: Towards Photorealistic Image Generation and Editing with Text-Guided Diffusion Models](https://mlsanity.com/paper/2112.10741/) (2021)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [FiLM: Visual Reasoning with a General Conditioning Layer](https://mlsanity.com/paper/1709.07871/) (2017)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Arbitrary Style Transfer in Real-time with Adaptive Instance Normalization](https://mlsanity.com/paper/1703.06868/) (2017)
- [Rethinking Network Design and Local Geometry in Point Cloud: A Simple Residual MLP Framework](https://mlsanity.com/paper/2202.07123/) (2022)
- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [Very Deep VAEs Generalize Autoregressive Models and Can Outperform Them on Images](https://mlsanity.com/paper/2011.10650/) (2020)
- [Generating Videos with Dynamics-aware Implicit Generative Adversarial Networks](https://mlsanity.com/paper/2202.10571/) (2022)
- [Adversarial Generation of Continuous Images](https://mlsanity.com/paper/2011.12026/) (2020)
- [BEGAN: Boundary Equilibrium Generative Adversarial Networks](https://mlsanity.com/paper/1703.10717/) (2017)
- [NeRF-VAE: A Geometry Aware 3D Scene Generative Model](https://mlsanity.com/paper/2104.00587/) (2021)
- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [Diffusion Models Beat GANs on Topology Optimization](https://mlsanity.com/paper/2208.09591/) (2022)
- [TopologyGAN: Topology Optimization Using Generative Adversarial Networks Based on Physical Fields Over the Initial Domain](https://mlsanity.com/paper/2003.04685/) (2020)
- [Aligning Optimization Trajectories with Diffusion Models for Constrained Design Generation](https://mlsanity.com/paper/2305.18470/) (2023)
- [Deep neural networks for the evaluation and design of photonic devices](https://mlsanity.com/paper/2007.00084/) (2020)
- [Learning Signal-Agnostic Manifolds of Neural Fields](https://mlsanity.com/paper/2111.06387/) (2021)
- [NTopo: Mesh-free Topology Optimization using Implicit Neural Representations](https://mlsanity.com/paper/2102.10782/) (2021)
- [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)

## Built on by (most cited first, 3 of 3)

- [Multi-scale Topology Optimization using Neural Networks](https://mlsanity.com/paper/2404.08708/) (2024)
- [Heterogeneous Metamaterials Design via Multiscale Neural Implicit Representation](https://mlsanity.com/paper/2511.03012/) (2025)
- [TopoEdit: Fast Post-Optimization Editing of Topology Optimized Structures](https://mlsanity.com/paper/2602.22430/) (2026)

## Abstract (arXiv)

Topology optimization is a critical task in engineering design, where the goal is to optimally distribute material in a given space for maximum performance. We introduce Neural Implicit Topology Optimization (NITO), a novel approach to accelerate topology optimization problems using deep learning. NITO stands out as one of the first frameworks to offer a resolution-free and domain-agnostic solution in deep learning-based topology optimization. NITO synthesizes structures with up to seven times better structural efficiency compared to SOTA diffusion models and does so in a tenth of the time. In the NITO framework, we introduce a novel method, the Boundary Point Order-Invariant MLP (BPOM), to represent boundary conditions in a sparse and domain-agnostic manner, moving away from expensive simulation-based approaches. Crucially, NITO circumvents the domain and resolution limitations that restrict Convolutional Neural Network (CNN) models to a structured domain of fixed size -- limitations that hinder the widespread adoption of CNNs in engineering applications. This generalizability allows a single NITO model to train and generate solutions in countless domains, eliminating the need for numerous domain-specific CNNs and their extensive datasets. Despite its generalizability, NITO outperforms SOTA models even in specialized tasks, is an order of magnitude smaller, and is practically trainable at high resolutions that would be restrictive for CNNs. This combination of versatility, efficiency, and performance underlines NITO's potential to transform the landscape of engineering design optimization problems through implicit fields.