# On the reproducibility of fully convolutional neural networks for modeling time-space evolving physical systems

arXiv: https://arxiv.org/abs/2105.05482 · HTML: https://mlsanity.com/paper/2105.05482/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 53 references that are in the map.
- First posted on arXiv 12 May 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [Improving Reproducibility in Machine Learning Research (A Report from the NeurIPS 2019 Reproducibility Program)](https://mlsanity.com/paper/2003.12206/) (2020)
- [Deep multi-scale video prediction beyond mean square error](https://mlsanity.com/paper/1511.05440/) (2015)
- [Random Search and Reproducibility for Neural Architecture Search](https://mlsanity.com/paper/1902.07638/) (2019)
- [Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networks](https://mlsanity.com/paper/1506.05751/) (2015)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Accelerating Eulerian Fluid Simulation With Convolutional Networks](https://mlsanity.com/paper/1607.03597/) (2016)
- [A unified deep artificial neural network approach to partial differential equations in complex geometries](https://mlsanity.com/paper/1711.06464/) (2017)
- [PPINN: Parareal Physics-Informed Neural Network for time-dependent PDEs](https://mlsanity.com/paper/1909.10145/) (2019)
- [A Step Toward Quantifying Independently Reproducible Machine Learning Research](https://mlsanity.com/paper/1909.06674/) (2019)
- [Poisson CNN: Convolutional neural networks for the solution of the Poisson equation on a Cartesian mesh](https://mlsanity.com/paper/1910.08613/) (2019)
- [Comparing recurrent and convolutional neural networks for predicting wave propagation](https://mlsanity.com/paper/2002.08981/) (2020)
- [Cyberbullying Detection in Social Networks Using Deep Learning Based Models; A Reproducibility Study](https://mlsanity.com/paper/1812.08046/) (2018)
- [Approximating the solution to wave propagation using deep neural networks](https://mlsanity.com/paper/1812.01609/) (2018)

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

- [Sources of Irreproducibility in Machine Learning: A Review](https://mlsanity.com/paper/2204.07610/) (2022)
- [Beyond Reproducibility: Token Probabilities Expose Large Language Model Nondeterminism](https://mlsanity.com/paper/2601.06118/) (2026)
- [Training Variation of Physically-Informed Deep Learning Models](https://mlsanity.com/paper/2510.03416/) (2025)

## Abstract (arXiv)

Reproducibility of a deep-learning fully convolutional neural network is evaluated by training several times the same network on identical conditions (database, hyperparameters, hardware) with non-deterministic Graphics Processings Unit (GPU) operations. The propagation of two-dimensional acoustic waves, typical of time-space evolving physical systems, is studied on both recursive and non-recursive tasks. Significant changes in models properties (weights, featured fields) are observed. When tested on various propagation benchmarks, these models systematically returned estimations with a high level of deviation, especially for the recurrent analysis which strongly amplifies variability due to the non-determinism. Trainings performed with double floating-point precision provide slightly better estimations and a significant reduction of the variability of both the network parameters and its testing error range.