# M-ENIAC: A machine learning recreation of the first successful numerical weather forecasts

arXiv: https://arxiv.org/abs/2304.09070 · HTML: https://mlsanity.com/paper/2304.09070/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 18 Apr 2023.

## Builds on (most cited first, 13 of 13)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1801.06637/) (2018)
- [Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast](https://mlsanity.com/paper/2211.02556/) (2022)
- [Respecting causality is all you need for training physics-informed neural networks](https://mlsanity.com/paper/2203.07404/) (2022)
- [Long-time integration of parametric evolution equations with physics-informed DeepONets](https://mlsanity.com/paper/2106.05384/) (2021)
- [A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions](https://mlsanity.com/paper/2302.14227/) (2023)
- [Physics-informed neural networks for the shallow-water equations on the sphere](https://mlsanity.com/paper/2104.00615/) (2021)
- [Improving physics-informed neural networks with meta-learned optimization](https://mlsanity.com/paper/2303.07127/) (2023)
- [A generative adversarial network approach to (ensemble) weather prediction](https://mlsanity.com/paper/2006.07718/) (2020)
- [Computing the ensemble spread from deterministic weather predictions using conditional generative adversarial networks](https://mlsanity.com/paper/2205.09182/) (2022)

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

- [Improving physics-informed DeepONets with hard constraints](https://mlsanity.com/paper/2309.07899/) (2023)
- [Towards replacing precipitation ensemble predictions systems using machine learning](https://mlsanity.com/paper/2304.10251/) (2023)
- [Low-rank adaptive physics-informed HyperDeepONets for solving differential equations](https://mlsanity.com/paper/2507.18346/) (2025)

## Abstract (arXiv)

In 1950 the first successful numerical weather forecast was obtained by solving the barotropic vorticity equation using the Electronic Numerical Integrator and Computer (ENIAC), which marked the beginning of the age of numerical weather prediction. Here, we ask the question of how these numerical forecasts would have turned out, if machine learning based solvers had been used instead of standard numerical discretizations. Specifically, we recreate these numerical forecasts using physics-informed neural networks. We show that physics-informed neural networks provide an easier and more accurate methodology for solving meteorological equations on the sphere, as compared to the ENIAC solver.