## 1 Introduction  
Attosecond transient absorption spectroscopy (ATAS) is a technique that employs attosecond laser pulses to probe modifications to the optical absorption in the time domain. Because its attosecond time-resolution is shorter than a typical time-scale of electron dynamics, which is on the order of femtosecond, it can naturally capture ultrafast electron dynamics in matter. Therefore, ATAS is one of the key experimental techniques to explore ultrafast phenomena where nonlinear electron dynamics play a significant role. Indeed, ATAS has been extensively applied to atoms and molecules over the past decade to investigate ultrafast electron dynamics in such relatively small systems [1; 2; 3; 4; 5; 6; 7]. Recently, ATAS has been further extended to solid-state materials to investigate rather complex electron dynamics in various phenomena such as band-gap renormalization [8], petahertz optical drive [9], dynamical Franz-Keldysh effect [10], photocarrier relaxation [11], exciton dynamics [12] as well as photocarrier injection [13]. Two-dimensional (2D) materials have been attracting great interest from both fundamental and technological points of view because of their remarkable properties. For example, graphene-like 2D materials such as hexagonal boron-nitride (\(h\)-BN) have been intensively studied for applications in optoelectronic devices and energy storage among others [14; 15; 16]. Transition metal dichalcogenides (TMDs), another kind of 2D materials, are also attracting attention because of their interesting properties deriving from strong spin-orbit coupling and a large direct-bandgap [17; 16; 18]. Thanks to recent development of laser technologies, laser-induced ultrafast electron dynamics in such 2 Dmaterials has been intensively studied both experimentally and theoretically [19; 20; 21; 22; 23; 24; 25]. For example, the high-order harmonic generation was recently studied in 2D materials [26; 27; 28; 29]. Surprisingly, it was demonstrated that elliptically polarized light can enhance the high-order harmonic generation in graphene [26]. In order to fully understand such laser-induced ultrafast electron dynamics, ATAS is one of the most desirable experimental techniques as it can resolve the dynamics with natural time-resolution. While ATAS for solid-state materials provides a wealth of information on microscopic electron dynamics in materials, the resulting experimental data are often very complicated due to complex electronic structure and highly-nonlinear effects in the dynamics. Therefore, it is hard to directly interpret the experimental results. Ab initio simulation based on the time-dependent density functional theory (TDDFT) [30] is a powerful tool to describe such complex electron dynamics and to provide microscopic insight into the phenomena. Indeed, ab initio TDDFT simulations have been applied to ATAS experiments for solid-state systems and played a significant role to construct the interpretation [8; 10; 11; 13]. Likewise, experimental results of ATAS for 2D materials are expected to be rather complicated. Therefore, ab initio TDDFT simulations are a good candidate to analyze ATAS for 2D materials. To realize such simulation methods, we extend the TDDFT pump-probe simulation [31] of transient absorption spectroscopy to 2D materials. To demonstrate the ab initio ATAS simulation, we employ monolayer \(h\)-BN as an example of a 2D material and investigate its transient optical property under intense infrared (IR) laser pulses. Because monolayer \(h\)-BN has a large band-gap among many 2D materials, ATAS for \(h\)-BN can be investigated in terms of knowledge from the recent ATAS experiments for bulk semiconductor materials [8; 10; 13]. Furthermore, we analyze the obtained transient absorption spectra of \(h\)-BN with a 2D parabolic two-band model and clarify the microscopic mechanism of the ultrafast modification of the optical property. This paper is organized as follows: in Section 2, we first describe the electron dynamics simulation based on TDDFT.