NITO: Neural Implicit Fields for Resolution-free Topology Optimization

TL;DR

Topology optimization is computation-heavy and traditionally limited by CNN-based, fixed-domain approaches. This work introduces NITO, a Neural Implicit Topology Optimizer that uses BPOM to condition implicit neural fields on sparse boundary constraints, enabling resolution-free, domain-agnostic topology generation. With a few-step direct optimization and an updated SIMP training regime, NITO achieves state-of-the-art performance across 64x64 and 256x256 domains while using far fewer parameters and offering substantial speedups over diffusion baselines. The results demonstrate strong cross-domain generalization and practical feasibility on consumer hardware, suggesting a new paradigm of deep optimization for engineering design. Overall, NITO offers a scalable, generalizable path to rapid topology optimization across diverse problem domains and resolutions.

Abstract

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.

Figures (21)

• Figure 1: NITO framework leveraging BPOM. Left: ground truth obtained using a SIMP optimizer. Second From Left: the raw output of neural fields using BPOM. Right Two: the NITO framework output leveraging a few steps (5 and 10 steps) of optimization. We see that NITO is amenable to deep optimization and can generate high-quality, constraint-satisfying, and high-performance topologies with fast inference. See Appendix \ref{['appx:visualizations']} for more visualizations.
• Figure 2: Topology Optimization. Given a domain, boundary conditions, loads, and volume fraction, TO aims to find the design variables $\phi$ that maximize performance (in this case minimizing compliance $f$) for the system, fulfilling all the prescribed constraints and respecting the underlying physics (Static Equilibrium).
• Figure 3: The NITO framework for topology optimization. The boundary conditions are processed as point clouds using the BPOM approach and a neural field is conditioned on these representations by modulating layer normalization based on the latent representation of the constraints to predict the optimal density field given the boundary conditions of the problem. Finally, the predicted density field is further refined through a few steps of direct optimization.
• Figure 4: Comparison of field-based such as stress fields (middle), and point-cloud-based (right) representations, given a TO problem (left). Unlike the expensive and domain-limiting iterative FEA method, the point clouds offer a generalizable and memory efficient, representation of the boundary conditions.
• Figure 5: Visual comparison of samples generated for the out-of-distribution test. Each row is labeled. Ground truth samples are SIMP-optimized samples.