# Geometric Priors for Scientific Generative Models in Inertial Confinement Fusion

arXiv: https://arxiv.org/abs/2111.12798 · HTML: https://mlsanity.com/paper/2111.12798/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 12 references that are in the map.
- First posted on arXiv 24 Nov 2021.

## Builds on (most cited first, 9 of 9)

- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Wasserstein Auto-Encoders](https://mlsanity.com/paper/1711.01558/) (2017)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Hyperspherical Variational Auto-Encoders](https://mlsanity.com/paper/1804.00891/) (2018)
- [CaloGAN: Simulating 3D High Energy Particle Showers in Multi-Layer Electromagnetic Calorimeters with Generative Adversarial Networks](https://mlsanity.com/paper/1712.10321/) (2017)
- [CosmoGAN: creating high-fidelity weak lensing convergence maps using Generative Adversarial Networks](https://mlsanity.com/paper/1706.02390/) (2017)
- [Improved Surrogates in Inertial Confinement Fusion with Manifold and Cycle Consistencies](https://mlsanity.com/paper/1912.08113/) (2019)

## Abstract (arXiv)

In this paper, we develop a Wasserstein autoencoder (WAE) with a hyperspherical prior for multimodal data in the application of inertial confinement fusion. Unlike a typical hyperspherical generative model that requires computationally inefficient sampling from distributions like the von Mis Fisher, we sample from a normal distribution followed by a projection layer before the generator. Finally, to determine the validity of the generated samples, we exploit a known relationship between the modalities in the dataset as a scientific constraint, and study different properties of the proposed model.