拓扑引导：通过向量场拓扑控制生成模型的输出
Topology Guidance: Controlling the Outputs of Generative Models via Vector Field Topology
AI总结：
针对场生成模型难以控制输出拓扑的问题，提出 topology guidance，通过基于坐标的网络提供拓扑信号引导扩散模型去噪，使生成向量场满足指定临界点位置与类型并保持数据分布。
摘要：
对于涉及数值模拟的领域，运行覆盖用户感兴趣参数空间的模拟集合可能在计算上非常昂贵。为此，一种有吸引力的模拟替代方案是对由集合产生的场进行生成建模，从而允许人们以计算成本低廉且准确的方式合成场。然而，就视觉分析而言，生成模型的一个局限是缺乏可控性，因为当从模型中采样一个场时，人们并不清楚应期待什么。本文研究如何使场的生成模型更具可控性，以便用户能够指定他们希望在输出中看到的感兴趣特征，尤其是拓扑特征。我们提出 topology guidance（拓扑引导），这是一种引导生成模型（具体为扩散模型）采样过程的方法，使生成输出满足作为输入指定的拓扑描述。该方法的核心是将用于表示场的基于坐标的神经网络与用于生成的扩散模型相结合。我们展示了如何利用基于坐标的网络提供的与拓扑相关的信号来帮助引导扩散模型的去噪过程。这使我们能够忠实地表示用户指定的拓扑，同时确保输出场仍处于生成数据分布内。具体而言，我们研究二维向量场拓扑，在一组流体流集合上评估该方法，并表明生成的向量场在整个空间域上忠实地符合临界点的位置和类型。我们进一步展示了该方法在辅助集合比较方面的优势，使人们能够沿规定的拓扑特征探索分布中的共性与差异。
英文摘要：
For domains that involve numerical simulation, it can be computationally expensive to run an ensemble of simulations spanning a parameter space of interest to a user. To this end, an attractive surrogate for simulation is the generative modeling of fields produced by an ensemble, allowing one to synthesize fields in a computationally cheap, yet accurate, manner. However, for the purposes of visual analysis, a limitation of generative models is their lack of control, as it is unclear what one should expect when sampling a field from a model. In this paper we study how to make generative models of fields more controllable, so that users can specify features of interest, in particular topological features, that they wish to see in the output. We propose topology guidance, a method for guiding the sampling process of a generative model, specifically a diffusion model, such that a topological description specified as input is satisfied in the generated output. Central to our method, we couple a coordinate-based neural network used to represent fields, with a diffusion model used for generation. We show how to use topologically-relevant signals provided by the coordinate-based network to help guide the denoising process of a diffusion model. This enables us to faithfully represent a user's specified topology, while ensuring that the output field remains within the generative data distribution. Specifically, we study 2D vector field topology, evaluating our method over an ensemble of fluid flows, where we show that generated vector fields faithfully adhere to the location, and type, of critical points over the spatial domain. We further show the benefits of our method in aiding the comparison of ensembles, allowing one to explore commonalities and differences in distributions along prescribed topological features.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
