NITO 是一种基于神经隐式场的无分辨率、领域无关的拓扑优化方法，通过边界点顺序不变 MLP 表示边界条件，比最先进扩散模型结构效率高七倍、速度快十倍，且模型更小，可泛化至任意领域。
摘要：
拓扑优化是工程设计中的一项关键任务，其目标是在给定空间中优化材料分布以实现最大性能。我们引入了神经隐式拓扑优化（NITO），一种利用深度学习加速拓扑优化问题的新方法。NITO 是深度学习拓扑优化领域中首批提供无分辨率和领域无关解决方案的框架之一。与最先进的扩散模型相比，NITO 合成结构的结构效率提高了多达七倍，且耗时仅为后者的十分之一。在 NITO 框架中，我们提出了一种新方法——边界点顺序不变多层感知器（BPOM），以稀疏且领域无关的方式表示边界条件，从而摆脱了昂贵的基于仿真的方法。至关重要的是，NITO 规避了限制卷积神经网络（CNN）模型只能处理固定大小结构化领域的领域和分辨率限制——这些限制阻碍了 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和生成解决方案，从而无需大量特定领域的 CNN 及其庞大的数据集。尽管具有泛化能力，NITO 在专门任务中仍优于最先进的模型，其规模小一个数量级，并且实际上可以在对 CNN 而言受限的高分辨率下进行训练。这种多功能性、高效性和性能的结合，凸显了 NITO 通过隐式场改变工程设计优化问题格局的潜力。
英文摘要：
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.
Université de Montréal（蒙特利尔大学）；ETH Zurich（苏黎世联邦理工学院）
Recent advances in implicit neural representations show great promise when it comes to generating numerical solutions to partial differential equations. Compared to conventional alternatives, such representations employ parameterized neural networks to define, in a mesh-free manner, signals that are highly-detailed, continuous, and fully differentiable. In this work, we present a novel machine learning approach for topology optimization -- an important class of inverse problems with high-dimensional parameter spaces and highly nonlinear objective landscapes. To effectively leverage neural repr…
Implicit Generative Models (IGMs) such as GANs have emerged as effective data-driven models for generating samples, particularly images. In this paper, we formulate the problem of learning an IGM as minimizing the expected distance between characteristic functions. Specifically, we minimize the distance between characteristic functions of the real and generated data distributions under a suitably-chosen weighting distribution. This distance metric, which we term as the characteristic function distance (CFD), can be (approximately) computed with linear time-complexity in the number of samples, …
State University of New York at Buffalo（纽约州立大学布法罗分校）
Learning with kernels is an important concept in machine learning. Standard approaches for kernel methods often use predefined kernels that require careful selection of hyperparameters. To mitigate this burden, we propose in this paper a framework to construct and learn a data-dependent kernel based on random features and implicit spectral distributions that are parameterized by deep neural networks. The constructed network (called KernelNet) can be applied to deep generative modeling in various scenarios, including two popular learning paradigms in deep generative models, MMD-GAN and implicit…
Automatically selecting the best performing algorithm for a given dataset or ranking multiple algorithms by their expected performance supports users in developing new machine learning applications. Most approaches for this problem rely on pre-computed dataset meta-features and landmarking performances to capture the salient topology of the datasets and those topologies that the algorithms attend to. Landmarking usually exploits cheap algorithms not necessarily in the pool of candidate algorithms to get inexpensive approximations of the topology. While somewhat indicative, hand-crafted dataset…
University of Wisconsin - Madison（威斯康星大学麦迪逊分校）；Palo Alto Research Center（帕洛阿尔托研究中心）
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 distrib…
NVIDIA（英伟达）；University of Toronto（多伦多大学）；Vector Institute（矢量研究所）
We introduce DMTet, a deep 3D conditional generative model that can synthesize high-resolution 3D shapes using simple user guides such as coarse voxels. It marries the merits of implicit and explicit 3D representations by leveraging a novel hybrid 3D representation. Compared to the current implicit approaches, which are trained to regress the signed distance values, DMTet directly optimizes for the reconstructed surface, which enables us to synthesize finer geometric details with fewer artifacts. Unlike deep 3D generative models that directly generate explicit representations such as meshes, o…
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；The Chinese University of Hong Kong（香港中文大学）；SenseTime Research（商汤科技研究院）
Controversy exists on whether differentiable neural architecture search methods discover wiring topology effectively. To understand how wiring topology evolves, we study the underlying mechanism of several existing differentiable NAS frameworks. Our investigation is motivated by three observed searching patterns of differentiable NAS: 1) they search by growing instead of pruning; 2) wider networks are more preferred than deeper ones; 3) no edges are selected in bi-level optimization. To anatomize these phenomena, we propose a unified view on searching algorithms of existing frameworks, transfe…
Masaryk University（马萨里克大学）；University of Twente（特文特大学）
Methods allowing the synthesis of realistic cell shapes could help generate training data sets to improve cell tracking and segmentation in biomedical images. Deep generative models for cell shape synthesis require a light-weight and flexible representation of the cell shape. However, commonly used voxel-based representations are unsuitable for high-resolution shape synthesis, and polygon meshes have limitations when modeling topology changes such as cell growth or mitosis. In this work, we propose to use level sets of signed distance functions (SDFs) to represent cell shapes. We optimize a ne…
Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to decrease the computational expense while retaining dominant solution features and behavior. Traditional Convolutional Neural Network-based frameworks for surrogate modeling require lossy pixelization and data-preprocessing, and generally are not effective in realistic engineering applications. We propose alternative deep-learning based surrogate models for discr…
