# Data-Driven Shadowgraph Simulation of a 3D Object

arXiv: https://arxiv.org/abs/2106.00317 · HTML: https://mlsanity.com/paper/2106.00317/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 15 references that are in the map.
- First posted on arXiv 1 Jun 2021.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)

## Built on by (most cited first, 3 of 3)

- [Data-driven Science and Machine Learning Methods in Laser-Plasma Physics](https://mlsanity.com/paper/2212.00026/) (2022)
- [Continual learning autoencoder training for a particle-in-cell simulation via streaming](https://mlsanity.com/paper/2211.04770/) (2022)
- [Ensuring Topological Data-Structure Preservation under Autoencoder Compression due to Latent Space Regularization in Gauss--Legendre nodes](https://mlsanity.com/paper/2309.08228/) (2023)

## Abstract (arXiv)

In this work we propose a deep neural network based surrogate model for a plasma shadowgraph - a technique for visualization of perturbations in a transparent medium. We are substituting the numerical code by a computationally cheaper projection based surrogate model that is able to approximate the electric fields at a given time without computing all preceding electric fields as required by numerical methods. This means that the projection based surrogate model allows to recover the solution of the governing 3D partial differential equation, 3D wave equation, at any point of a given compute domain and configuration without the need to run a full simulation. This model has shown a good quality of reconstruction in a problem of interpolation of data within a narrow range of simulation parameters and can be used for input data of large size.