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.

翻译：拓扑优化是工程设计中的关键任务，其目标是在给定空间内最优分布材料以实现最大性能。我们提出神经隐式拓扑优化（NITO），这是一种利用深度学习加速拓扑优化问题的新方法。NITO 是基于深度学习的拓扑优化中首批提供无分辨率、领域无关解决方案的框架之一。NITO 合成的结构相比最先进的扩散模型具有高达七倍的结构效率提升，且仅需其十分之一的时间。在 NITO 框架中，我们引入了一种新方法——边界点排序不变 MLP（BPOM），以稀疏且领域无关的方式表示边界条件，从而摒弃了昂贵的基于仿真的方法。关键的是，NITO 突破了将卷积神经网络（CNN）模型限制在固定大小结构化领域中的领域与分辨率局限——这些局限阻碍了 CNN 在工程应用中的广泛采用。这种泛化能力使得单个 NITO 模型能够在无数领域中训练并生成解决方案，无需大量领域特定的 CNN 及其庞大的数据集。尽管具有泛化性，NITO 在专门任务中仍优于最先进的模型，模型规模小一个数量级，并且能在 CNN 受限的高分辨率下实际训练。这种通用性、效率与性能的结合，突显了 NITO 通过隐式场变革工程设计优化问题领域的潜力。