Learning Similarity Metrics for Numerical Simulations
This work addresses the need for stable and generalizing similarity metrics in numerical simulations, particularly for motion and transport-based PDEs, but it is incremental as it builds on Siamese network architectures.
The authors tackled the problem of comparing data from numerical simulations by proposing a neural network-based metric (LSiM) that outperforms existing metrics on a range of test data, demonstrating robustness on three real-world datasets.
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.