# Hybridizing Physics and Neural ODEs for Predicting Plasma Inductance Dynamics in Tokamak Fusion Reactors

arXiv: https://arxiv.org/abs/2310.20079 · HTML: https://mlsanity.com/paper/2310.20079/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 16 references that are in the map.
- First posted on arXiv 30 Oct 2023.

## Builds on (most cited first, 5 of 5)

- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [On Neural Differential Equations](https://mlsanity.com/paper/2202.02435/) (2022)
- [Equinox: neural networks in JAX via callable PyTrees and filtered transformations](https://mlsanity.com/paper/2111.00254/) (2021)
- [Neural Controlled Differential Equations for Online Prediction Tasks](https://mlsanity.com/paper/2106.11028/) (2021)
- [Differentiable Multiple Shooting Layers](https://mlsanity.com/paper/2106.03885/) (2021)

## Built on by (most cited first, 4 of 4)

- [Full Shot Predictions for the DIII-D Tokamak via Deep Recurrent Networks](https://mlsanity.com/paper/2404.12416/) (2024)
- [Modeling chaotic Lorenz ODE System using Scientific Machine Learning](https://mlsanity.com/paper/2410.06452/) (2024)
- [A comparative study of NeuralODE and Universal ODE approaches to solving Chandrasekhar White Dwarf equation](https://mlsanity.com/paper/2410.14998/) (2024)
- [Forecasting N-Body Dynamics: A Comparative Study of Neural Ordinary Differential Equations and Universal Differential Equations](https://mlsanity.com/paper/2512.20643/) (2025)

## Abstract (arXiv)

While fusion reactors known as tokamaks hold promise as a firm energy source, advances in plasma control, and handling of events where control of plasmas is lost, are needed for them to be economical. A significant bottleneck towards applying more advanced control algorithms is the need for better plasma simulation, where both physics-based and data-driven approaches currently fall short. The former is bottle-necked by both computational cost and the difficulty of modelling plasmas, and the latter is bottle-necked by the relative paucity of data. To address this issue, this work applies the neural ordinary differential equations (ODE) framework to the problem of predicting a subset of plasma dynamics, namely the coupled plasma current and internal inductance dynamics. As the neural ODE framework allows for the natural inclusion of physics-based inductive biases, we train both physics-based and neural network models on data from the Alcator C-Mod fusion reactor and find that a model that combines physics-based equations with a neural ODE performs better than both existing physics-motivated ODEs and a pure neural ODE model.