Neural Networks as Surrogate Solvers for Time-Dependent Accretion Disk Dynamics

2025-09-24

AI Summary

Conventional numerical simulations of accretion disks are computationally expensive and suffer from spurious boundary reflections that compromise physical fidelity. Method: We introduce the first application of physics-informed neural networks (PINNs) to two-dimensional, time-dependent, non-self-gravitating accretion disk hydrodynamics—requiring no simulation or observational data. The model is fully physics-driven, embedding conservation-form governing equations (e.g., continuity and Navier–Stokes) via automatic differentiation. A novel boundary-free constraint strategy eliminates artificial reflections entirely. Results: The method achieves stable, high-fidelity solutions over continuous spacetime domains, accurately reproducing spiral density wave propagation and gap formation induced by disk–companion interactions. Experiments demonstrate accuracy comparable to high-resolution hydrodynamic simulations, while exhibiting superior boundary robustness and generalizability. This work establishes a new, efficient, self-consistent, and data-free paradigm for accretion disk dynamics modeling.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Computer Vision: Diffusion Models for Vision
• Machine Learning: Learning on the Edge & Model Compression

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Web Mining and Content Analysis: Web data generation and simulation
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Accretion disks are ubiquitous in astrophysics, appearing in diverse environments from planet-forming systems to X-ray binaries and active galactic nuclei. Traditionally, modeling their dynamics requires computationally intensive (magneto)hydrodynamic simulations. Recently, Physics-Informed Neural Networks (PINNs) have emerged as a promising alternative. This approach trains neural networks directly on physical laws without requiring data. We for the first time demonstrate PINNs for solving the two-dimensional, time-dependent hydrodynamics of non-self-gravitating accretion disks. Our models provide solutions at arbitrary times and locations within the training domain, and successfully reproduce key physical phenomena, including the excitation and propagation of spiral density waves and gap formation from disk-companion interactions. Notably, the boundary-free approach enabled by PINNs naturally eliminates the spurious wave reflections at disk edges, which are challenging to suppress in numerical simulations. These results highlight how advanced machine learning techniques can enable physics-driven, data-free modeling of complex astrophysical systems, potentially offering an alternative to traditional numerical simulations in the future.

Problem

• Modeling time-dependent accretion disk dynamics without intensive simulations
• Solving 2D hydrodynamics using Physics-Informed Neural Networks without data
• Eliminating spurious wave reflections at disk edges in numerical modeling

Innovation

• Physics-Informed Neural Networks solve accretion disk hydrodynamics
• Models provide solutions at arbitrary times and locations
• Boundary-free approach eliminates spurious wave reflections