# GRINN: A Physics-Informed Neural Network for solving hydrodynamic systems in the presence of self-gravity

arXiv: https://arxiv.org/abs/2308.08010 · HTML: https://mlsanity.com/paper/2308.08010/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 53 references that are in the map.
- First posted on arXiv 15 Aug 2023.

## Builds on (most cited first, 18 of 18)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data](https://mlsanity.com/paper/1901.06314/) (2019)
- [Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations](https://mlsanity.com/paper/2107.07871/) (2021)
- [A unified deep artificial neural network approach to partial differential equations in complex geometries](https://mlsanity.com/paper/1711.06464/) (2017)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [Evolutional Deep Neural Network](https://mlsanity.com/paper/2103.09959/) (2021)
- [DPM: A Novel Training Method for Physics-Informed Neural Networks in Extrapolation](https://mlsanity.com/paper/2012.02681/) (2020)
- [Deep Learning for Real-time Gravitational Wave Detection and Parameter Estimation: Results with Advanced LIGO Data](https://mlsanity.com/paper/1711.03121/) (2017)
- [Physics-Informed Neural Networks with Adaptive Localized Artificial Viscosity](https://mlsanity.com/paper/2203.08802/) (2022)
- [A physics-informed deep neural network for surrogate modeling in classical elasto-plasticity](https://mlsanity.com/paper/2204.12088/) (2022)
- [DPNNet-2.0 Part I: Finding hidden planets from simulated images of protoplanetary disk gaps](https://mlsanity.com/paper/2107.09086/) (2021)
- [Using Bayesian Deep Learning to infer Planet Mass from Gaps in Protoplanetary Disks](https://mlsanity.com/paper/2202.11730/) (2022)

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

- [ASURA-FDPS-ML: Star-by-star Galaxy Simulations Accelerated by Surrogate Modeling for Supernova Feedback](https://mlsanity.com/paper/2410.23346/) (2024)
- [Unraveling particle dark matter with Physics-Informed Neural Networks](https://mlsanity.com/paper/2502.17597/) (2025)
- [Neural Networks as Surrogate Solvers for Time-Dependent Accretion Disk Dynamics](https://mlsanity.com/paper/2509.20447/) (2025)

## Abstract (arXiv)

Modeling self-gravitating gas flows is essential to answering many fundamental questions in astrophysics. This spans many topics including planet-forming disks, star-forming clouds, galaxy formation, and the development of large-scale structures in the Universe. However, the nonlinear interaction between gravity and fluid dynamics offers a formidable challenge to solving the resulting time-dependent partial differential equations (PDEs) in three dimensions (3D). By leveraging the universal approximation capabilities of a neural network within a mesh-free framework, physics informed neural networks (PINNs) offer a new way of addressing this challenge. We introduce the gravity-informed neural network (GRINN), a PINN-based code, to simulate 3D self-gravitating hydrodynamic systems. Here, we specifically study gravitational instability and wave propagation in an isothermal gas. Our results match a linear analytic solution to within 1% in the linear regime and a conventional grid code solution to within 5% as the disturbance grows into the nonlinear regime. We find that the computation time of the GRINN does not scale with the number of dimensions. This is in contrast to the scaling of the grid-based code for the hydrodynamic and self-gravity calculations as the number of dimensions is increased. Our results show that the GRINN computation time is longer than the grid code in one- and two- dimensional calculations but is an order of magnitude lesser than the grid code in 3D with similar accuracy. Physics-informed neural networks like GRINN thus show promise for advancing our ability to model 3D astrophysical flows.