Winds and Feedb
Black hole mass
accretion rate
(code units)
training test
cross-
validation
1 3 45 60 N+, arXiv:2011.1281
9
Duarte+, arXiv:2102.06242
Teaching machines to simulate black
hole weather
João Paulo Peçanha
NVIDIA
(Dated: December 10, 2019)
XXXXXXXXXXXXXXXXXXXXXXXX ABSTRACT XXXXXXXXXXXXXXXXXXXXXXXXXX
I. INTRODUCTION
Black holes (BHs) are astronomical objects that has
the strongest gravitational field. The escape velocity in
event horizon is equal the speed of light (c) (Misner et al.
1973). If matter gets close in this gravitational field it
gets trapped in orbit around them. This matter forms a
torus structure composed of fluids due to angular momen-
tum conservation. When it comes to accretion the fluid
needs to lose angular momentum otherwise this would be
orbiting around the black hole continually. The angular
momentum transport can be due to viscosity (Shakura
and Sunyaev 1973, Stone et al. 1999) or magnetic stress
(Balbus 2003), this transport allows matter to fall inside
the black hole creating a disk-like structure called accre-
tion disk composed of fluids.
The flow of incompressible fluids is described by the
Navier-Stokes equations. Navier-Stokes equations are a
set of partial differential equations which has to be solved
numerically with the exception of a few simple cases
(Temam 1977). Numerical simulations allow us to see
solutions of parameters in time and space. Density, pres-
sure and velocity fields are some of solutions possible due
to numerical simulations. In Figure 1, it is possible to see
a density field ⇢(r, t = 257387GM/c3) from a numerical
solution using Navier-Stokes to describe a hydrodynamic
fluid trapped inside a black hole’s gravity (Almeida and
Nemmen 2019).
Depending on the complexity of the problem we want
to study, numerical simulations may become very expen-
sive computationally and time consuming, even for visu-
alization (Kapferer and Riser 2008). This is the reason
why Astronomy deals with a challenge using traditional
methods to analyze the amount of data available (George
and Huerta 2018) and to have more complex and longer
simulations (He et al. 2019, Siemiginowska et al. 2019).
He et al. (2019) show us that deep learning may be a
method to overcome those challenges with numerical sim-
ulations. Also there is a enthusiasm to use deep learning
to study fluid dynamics (Mohan et al. 2019, Pathak et al.
2018).
⇤
A footnote to the article title
†
[email protected]
FIG. 1. Example of hydrodynamic simulations from Almeida
and Nemmen (2019) without magnetic field using PLUTO code
(Mignone et al. 2007). It is shown the logarithm of the density
field ⇢(r, t = 257387GM/c3). s. It is Euclidean-coordinates with
Rs ⌘ GM/c2
unit.
Neural networks are a deep learning method based on
the way biological neurons communicate between them-
selves (McCulloch and Pitts 1943). With the rise of neu-
ral networks new approaches are being build, one exam-
ple is convolutional neural networks (CNNs) that enable
us to extract information from a 2D image (LeCun 1989).
The use of CNNs for image extraction and video process-
ing are shown promising results (Chen et al. 2016, Karpa-
thy et al. 2014, Liu 2018, Shi et al. 2016). CNNs allow
us to extract information and analyse them in a practical
way, this is why CNNs are widely used. CNN are showing
better results even when compared with time-series neu-
ral networks such as recurrent neural networks (RNNs)
and long short term memory (LSTMs) (Bai et al. 2018,
Zhang et al. 2016). Here, we used an U-Net architecture
which is a U-shape architecture composed with layers of
convolutions and pooling. U-Net was first introduced for