We’re happy to report that the final version of our paper on “Learning Similarity Metrics for Numerical Simulations” to be presented at the International Conference on Machine Learning (ICML) is online now. We propose learning a metric for data produced by numerical simulations, i.e. PDEs such as Navier-Stokes, and a way to train Siamese networks with a correlation-based loss to improve the inference of similarities. The resulting deep learning based metric outperforms simpler metrics and other learned metrics such as LPIPS.
Assessing similarity for complex data is is a fundamental problem in all computational disciplines ranging from simulations of blood flow to aircraft design. Many practical problems rely on highly complex PDEs, where small perturbations in the input drastically alter the solutions. Regular vector space metrics like the L² distance are unreliable as they perform an element-wise comparison, and thus cannot compare contextual information or structures on different scales. Our approach, dubbed LSiM, employs convolutional neural networks (CNNs) as a method to extract and compare more meaningful features from a set of two simulation frames.