Learning Similarity Metrics for Numerical Simulations

Georg Kohl, Kiwon Um, Nils Thuerey

Keywords: metric learning, CNNs, PDEs, numerical simulation, perceptual evaluation, physics simulation

TL;DR: We propose a novel CNN-based metric to robustly compare field data from PDE-based numerical simulations.

Abstract: We propose a novel approach to compute a stable and generalizing metric (LNSM) with convolutional neural networks (CNN) to compare field data from a variety of numerical simulation sources. Our method employs a Siamese network architecture that is motivated by the mathematical properties of a metric and is known to work well for finding similarities of other data modalities. We leverage a controllable data generation setup with partial differential equation (PDE) solvers to create increasingly different outputs from a reference simulation. In addition, the data generation allows for adjusting the difficulty of the resulting learning task. 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 simple 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 using the proposed correlation loss and the impact of an adjustable training data difficulty.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2002.07863/code)