Differentiable Conservative Radially Symmetric Fluid Simulations and Stellar Winds -- jf1uids

TL;DR

jf1uids is a GPU-compatible, fully differentiable 1D fluid solver for radially symmetric problems like stellar winds, enabling efficient simulations and parameter inference with gradient-based methods.

Contribution

A novel geometric formulation of Euler equations for 1D radial fluid simulations that is conservative, differentiable, and computationally efficient.

Findings

Successfully retrieved stellar wind parameters via gradient descent.

Reduced computational costs compared to 3D simulations.

Demonstrated differentiability for physics-informed machine learning applications.

Abstract

We present jf1uids, a one-dimensional fluid solver that can, by virtue of a geometric formulation of the Euler equations, model radially symmetric fluid problems in a conservative manner, i.e., without losing mass or energy. For spherical problems, such as ideal supernova explosions or stellar wind-blown bubble expansions, simulating only along a radial dimension drastically reduces compute and memory demands compared to a full three-dimensional method. This simplification also alleviates constraints on backpropagation through the solver. Written in JAX, jf1uids is a GPU-compatible and fully differentiable simulator. We demonstrate the advantages of this differentiable physics simulator by retrieving the wind's parameters for an adiabatic stellar wind expansion from the final fluid state using gradient descent. As part of a larger "stellar winds, cosmic rays and machine learning" research track, jf1uids serves as a solid foundation to be extended with additional physics modules, foremost cosmic rays and a neural-net powered gas-cooling surrogate and improved by higher order and more accurate numerical schemes. All code is available under https://github.com/leo1200/jf1uids/.