# Learning Similarity Metrics for Volumetric Simulations with Multiscale CNNs

arXiv: https://arxiv.org/abs/2202.04109 · HTML: https://mlsanity.com/paper/2202.04109/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 57 references that are in the map.
- First posted on arXiv 8 Feb 2022.

## Builds on (most cited first, 22 of 22)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Perceptual Losses for Real-Time Style Transfer and Super-Resolution](https://mlsanity.com/paper/1603.08155/) (2016)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Generating Images with Perceptual Similarity Metrics based on Deep Networks](https://mlsanity.com/paper/1602.02644/) (2016)
- [PieAPP: Perceptual Image-Error Assessment through Pairwise Preference](https://mlsanity.com/paper/1806.02067/) (2018)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [Incorporating Symmetry into Deep Dynamics Models for Improved Generalization](https://mlsanity.com/paper/2002.03061/) (2020)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [Revisiting Training Strategies and Generalization Performance in Deep Metric Learning](https://mlsanity.com/paper/2002.08473/) (2020)
- [Visual Interaction Networks](https://mlsanity.com/paper/1706.01433/) (2017)
- [Understanding SSIM](https://mlsanity.com/paper/2006.13846/) (2020)
- [Deep Dynamical Modeling and Control of Unsteady Fluid Flows](https://mlsanity.com/paper/1805.07472/) (2018)
- [Physics-based Deep Learning](https://mlsanity.com/paper/2109.05237/) (2021)
- [tempoGAN: A Temporally Coherent, Volumetric GAN for Super-resolution Fluid Flow](https://mlsanity.com/paper/1801.09710/) (2018)
- [Learned Perceptual Image Enhancement](https://mlsanity.com/paper/1712.02864/) (2017)
- [Learning Similarity Metrics for Numerical Simulations](https://mlsanity.com/paper/2002.07863/) (2020)
- [Audio-based Near-Duplicate Video Retrieval with Audio Similarity Learning](https://mlsanity.com/paper/2010.08737/) (2020)
- [PerceptNet: Learning Perceptual Similarity of Haptic Textures in Presence of Unorderable Triplets](https://mlsanity.com/paper/1905.03302/) (2019)
- [Perceptual Evaluation of Liquid Simulation Methods](https://mlsanity.com/paper/2011.10257/) (2020)

## Built on by (most cited first, 1 of 1)

- [Guarantees by Construction for Learned Finite Volume Schemes on Steady Supersonic Flow](https://mlsanity.com/paper/2607.20171/) (2026)

## Abstract (arXiv)

Simulations that produce three-dimensional data are ubiquitous in science, ranging from fluid flows to plasma physics. We propose a similarity model based on entropy, which allows for the creation of physically meaningful ground truth distances for the similarity assessment of scalar and vectorial data, produced from transport and motion-based simulations. Utilizing two data acquisition methods derived from this model, we create collections of fields from numerical PDE solvers and existing simulation data repositories. Furthermore, a multiscale CNN architecture that computes a volumetric similarity metric (VolSiM) is proposed. To the best of our knowledge this is the first learning method inherently designed to address the challenges arising for the similarity assessment of high-dimensional simulation data. Additionally, the tradeoff between a large batch size and an accurate correlation computation for correlation-based loss functions is investigated, and the metric's invariance with respect to rotation and scale operations is analyzed. Finally, the robustness and generalization of VolSiM is evaluated on a large range of test data, as well as a particularly challenging turbulence case study, that is close to potential real-world applications.