Neural Flow Map Reconstruction
Neural Flow Map Reconstruction
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DOI：
10.1111/cgf.14549
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发表时间：
2022-06
影响因子：
2.5
通讯作者：
Saroj Sahoo;Y. Lu;M. Berger
中科院分区：
文献类型：
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作者：
Saroj Sahoo;Y. Lu;M. Berger
在本文中，我们提出了一种重建技术的基础上减少非定常流数据的神经表示的时变矢量场。我们的方法是由大量的数据通常在数值模拟中生成的动机，反过来，域科学家可以生成的数据类型在原位是紧凑的，但有用的，事后分析。在模拟期间通常获取的一种类型的数据是流图的样本，其中单个样本是在指定的持续时间内对基础向量场进行积分的结果。在我们的工作中，我们将单个数据集的流图样本集合视为一个有意义的，紧凑的，但不完整的，不稳定流的表示，我们的中心目标是找到一个表示，使我们能够最好地恢复任意流图样本。为此，我们介绍了一种用于学习时变向量场的隐式神经表示的技术，该技术经过专门优化，以重现稀疏覆盖数据时空域的流图样本。我们表明，尽管积极的数据减少，我们的优化问题-学习函数空间神经网络在固定的积分方案下重现流图样本-导致表现出很强的泛化能力的表示，无论是在字段本身，还是使用字段来近似流图。通过对不同数据集的定量和定性分析，我们表明我们的方法是对各种数据简化方法的改进，以及对各种措施的改进，包括改进的向量场、流图和从流图中导出的特征。
In this paper we present a reconstruction technique for the reduction of unsteady flow data based on neural representations of time‐varying vector fields. Our approach is motivated by the large amount of data typically generated in numerical simulations, and in turn the types of data that domain scientists can generate in situ that are compact, yet useful, for post hoc analysis. One type of data commonly acquired during simulation are samples of the flow map, where a single sample is the result of integrating the underlying vector field for a specified time duration. In our work, we treat a collection of flow map samples for a single dataset as a meaningful, compact, and yet incomplete, representation of unsteady flow, and our central objective is to find a representation that enables us to best recover arbitrary flow map samples. To this end, we introduce a technique for learning implicit neural representations of time‐varying vector fields that are specifically optimized to reproduce flow map samples sparsely covering the spatiotemporal domain of the data. We show that, despite aggressive data reduction, our optimization problem — learning a function‐space neural network to reproduce flow map samples under a fixed integration scheme — leads to representations that demonstrate strong generalization, both in the field itself, and using the field to approximate the flow map. Through quantitative and qualitative analysis across different datasets we show that our approach is an improvement across a variety of data reduction methods, and across a variety of measures ranging from improved vector fields, flow maps, and features derived from the flow map.