Learning Similarity Metrics for Numerical Simulations

Georg Kohl, Kiwon Um, Nils Thuerey
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:5349-5360, 2020.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-kohl20a, title = {Learning Similarity Metrics for Numerical Simulations}, author = {Kohl, Georg and Um, Kiwon and Thuerey, Nils}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {5349--5360}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/kohl20a/kohl20a.pdf}, url = {https://proceedings.mlr.press/v119/kohl20a.html}, 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.} }
Endnote
%0 Conference Paper %T Learning Similarity Metrics for Numerical Simulations %A Georg Kohl %A Kiwon Um %A Nils Thuerey %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-kohl20a %I PMLR %P 5349--5360 %U https://proceedings.mlr.press/v119/kohl20a.html %V 119 %X 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.
APA
Kohl, G., Um, K. & Thuerey, N.. (2020). Learning Similarity Metrics for Numerical Simulations. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:5349-5360 Available from https://proceedings.mlr.press/v119/kohl20a.html.

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