论文标题
学习数值模拟的相似性指标
Learning Similarity Metrics for Numerical Simulations
论文作者
论文摘要
我们提出了一种基于神经网络的方法，该方法计算稳定且概括的度量标准（LSIM），以比较来自各种数值仿真源的数据。我们专注于标量时间依赖性的2D数据，这些数据通常是由运动和基于运输的偏微分方程（PDE）引起的。我们的方法采用了由度量标准的数学属性激励的暹罗网络体系结构。我们利用使用PDE求解器的可控数据生成设置来创建与受控环境中参考模拟的越来越不同的输出。我们学到的指标的一个核心组成部分是一种专业的损失函数，它将有关单个数据样本之间相关性的知识引入训练过程中。为了证明所提出的方法的表现优于向量空间和其他学到的基于图像的指标的现有指标，我们评估了大量测试数据的不同方法。此外，我们分析了可调培训数据难度的概括益处，并通过对三个现实世界数据集的评估来证明LSIM的鲁棒性。
We propose a neural network-based approach that computes a stable and generalizing metric (LSiM) to compare data from a variety of numerical simulation sources. We focus on scalar time-dependent 2D data that commonly arises from motion and transport-based partial differential equations (PDEs). Our method employs a Siamese network architecture that is motivated by the mathematical properties of a metric. We leverage a controllable data generation setup with PDE solvers to create increasingly different outputs from a reference simulation in a controlled environment. A central component of our learned metric is a specialized loss function that introduces knowledge about the correlation between single data samples into the training process. To demonstrate that the proposed approach outperforms existing metrics for vector spaces and other learned, image-based metrics, we evaluate the different methods on a large range of test data. Additionally, we analyze generalization benefits of an adjustable training data difficulty and demonstrate the robustness of LSiM via an evaluation on three real-world data sets.
