RHINE: R-process Heating Implementation in hydrodynamic simulations with NEural networks

# Overview

RHINE (R-process Heating Implementation in hydrodynamic simulations with NEural networks) is a machine-learning based Fortran code for modeling r-process heating in astrophysical hydrodynamic simulations. The code uses trained neural networks to provide fast and accurate estimates of r-process related rates of change for a set of characteristic quantities. RHINE is designed for integration into hydrodynamic simulations of astrophysical environments with r-process viable conditions such as neutron-star mergers. While maintaining a high accuracy comparable to detailed nuclear reaction networks, it avoids their large computational demands.

For more details see:

Phys. Rev. D 113, 083022

# Features

- Provides nuclear rates of change for the electron fraction, mass fractions of neutrons, protons, alphas, and remaining ("heavy") nuclei, average mass number of heavy nuclei, average mass excess per baryon, and energy-loss rates due to neutrino emission from beta-decays.
- Trained on large datasets from full nuclear network calculations.
- Lightweight and fast: neural network inference is orders of magnitude faster than full nuclear reaction networks.

# Modules

RHINE contains two modules `RHINE_neural()` and `RHINE_model()`.

1. Module `RHINE_neural()` provides

  - subroutine `load_model()` to load specific neural network,

  - function `forward()` to evaluate a neural network, i.e. obtain the output for given input quantities,

  - functions `scale_data()` and `rescale_data()` for scaling and rescaling functions for data standardization,

  - functions `expo()`, `sigmoid()`, and `elu()` for the activation functions.

2. Module `RHINE_model()` provides

  - subroutine `load_model_RHINE()` to load all neural networks,

  - subroutine `run_RHINE()` to provide all source terms used to update the hydro quantities within a time step dt,

  - subroutine `get_derivative()` to predict all variables and time derivatives given all input quantities,

  - subroutine `get_QSE()` to predict the abundances in QSE regime given the density, temperature, and electron fraction,

  - subroutine `get_ma()` to predict the mass excess and fraction of neutrino losses,

  - subroutine `normalization()` to ensure physical consistency of the source terms such as mass and charge conservation.

# Usage

1. Load the model

```fortran
use RHINE_model

call load_model_RHINE(<model_path>)
```

2. Predict the source terms

```fortran
call run_RHINE(<arguments>)
```

3. See also more detailed demonstration in `demo.f90`.

# Citation

If you use RHINE in your research, please include the following two references:

```
@misc{RHINE2025,
  author = {{Just}, Oliver and {Xiong}, Zewei and {Martı́nez-Pinedo}, Gabriel},
  title  = {RHINE: R-process Heating Implementation in Hydrodynamic Simulations with Neural Networks},
  year   = {2025},
  url    = {https://git.gsi.de/nucastro_public/rhine}
}

```

# License

RHINE is released under the BSD 3-Clause License. See LICENSE file for details.

# Contact

For questions or requests please contact:

o.just@gsi.de
z.xiong@gsi.de
g.martinez@gsi.de