This is the poster presentation of the paper "Learning Similarity Metrics for Numerical Simulations" by G. Kohl, K. Um, and N. Thuerey at the virtual ICML 2020 conference. Paper, source code, and data sets are available at: https://ge.in.tum.de/publications/2020-lsim-kohl/
The two live poster sessions will take place at 11pm (CEST) on 14.07.2020 and at 10pm (CEST) on 15.07.2020 at: https://icml.cc/virtual/2020/paper/6024
Abstract: 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.