# Neural networks: solving the chemistry of the interstellar medium

arXiv: https://arxiv.org/abs/2211.15688 · HTML: https://mlsanity.com/paper/2211.15688/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 8 references that are in the map.
- First posted on arXiv 28 Nov 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)

## Built on by (most cited first, 7 of 7)

- [Speeding up astrochemical reaction networks with autoencoders and neural ODEs](https://mlsanity.com/paper/2312.06015/) (2023)
- [CODES: Benchmarking Coupled ODE Surrogates](https://mlsanity.com/paper/2410.20886/) (2024)
- [3D-PDR Orion dataset and NeuralPDR: Neural Differential Equations for Photodissociation Regions](https://mlsanity.com/paper/2412.00758/) (2024)
- [NeuralPDR: Neural Differential Equations as surrogate models for Photodissociation Regions](https://mlsanity.com/paper/2506.14270/) (2025)
- [A comparative study of NeuralODE and Universal ODE approaches to solving Chandrasekhar White Dwarf equation](https://mlsanity.com/paper/2410.14998/) (2024)
- [Neural-Network Chemical Emulator for First-Star Formation: Robust Iterative Predictions over a Wide Density Range](https://mlsanity.com/paper/2508.16114/) (2025)
- [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)

Non-equilibrium chemistry is a key process in the study of the InterStellar Medium (ISM), in particular the formation of molecular clouds and thus stars. However, computationally it is among the most difficult tasks to include in astrophysical simulations, because of the typically high (>40) number of reactions, the short evolutionary timescales (about 104 times less than the ISM dynamical time) and the characteristic non-linearity and stiffness of the associated Ordinary Differential Equations system (ODEs). In this proof of concept work, we show that Physics Informed Neural Networks (PINN) are a viable alternative to traditional ODE time integrators for stiff thermo-chemical systems, i.e. up to molecular hydrogen formation (9 species and 46 reactions). Testing different chemical networks in a wide range of densities (-2< log n/rm cm-3< 3) and temperatures (1 < log T/rm K< 5), we find that a basic architecture can give a comfortable convergence only for simplified chemical systems: to properly capture the sudden chemical and thermal variations a Deep Galerkin Method is needed. Once trained (~ 103 GPUhr), the PINN well reproduces the strong non-linear nature of the solutions (errors lesssim 10%) and can give speed-ups up to a factor of ~ 200 with respect to traditional ODE solvers. Further, the latter have completion times that vary by about ~ 30% for different initial n and T, while the PINN method gives negligible variations. Both the speed-up and the potential improvement in load balancing imply that PINN-powered simulations are a very palatable way to solve complex chemical calculation in astrophysical and cosmological problems.