Data-driven radiative hydrodynamics simulations of the solar photosphere using physics-informed neural networks: proof of concept

TL;DR

This paper demonstrates a novel physics-informed neural network approach to simulate the solar photosphere's radiative hydrodynamics, aiming to produce more physically consistent and detailed models that match observations.

Contribution

It introduces the first proof of concept for using PINNs to solve solar radiative hydrodynamics equations, enabling continuous and detailed modeling of the solar photosphere.

Findings

PINNs can approximate solar radiative hydrodynamics equations.

Models are continuous and can focus on local regions.

Provides estimates of unobserved physical parameters.

Abstract

Current, realistic numerical simulations of the solar atmosphere reproduce observations in a statistical sense; they do not replicate observations such as a movie of solar granulation. Inversions on the other hand reproduce observations by design, but the resulting models are often not physically self-consistent. Physics-informed neural networks (PINNs) offer a new approach to solving the time-dependent radiative hydrodynamics equations and matching observations as boundary conditions. PINNs approximate the solution of the integro-differential equations with a deep neural network. The parameters of this network are determined by minimizing the residuals with respect to the physics equations and the observations. The resulting models are continuous in all dimensions, can zoom into local areas of interest in space and time, and provide information on physical parameters that are not necessarily directly observed such as horizontal velocities. Here we present the first proof of concept of this novel approach, explain the underlying methodology in detail, and provide an outlook to the many applications that PINNs enable.