## 1 Introduction  
Ultrasonic wave propagation is used in various applications, including biomedical imaging [1], nondestructive evaluation [2; 3], seismic and geological studies [4], etc. The numerical modeling of the ultrasonic waves is critical, for improving the understanding of the underlying physics of these applications. The ultrasonic wave propagation phenomenon is widely modeled using Finite Element [5; 6; 7; 8], Finite Difference [9], and Finite Volume [10] techniques. Ultrasonic wave propagation is modeled by the widely used FE analysis, through solving the partial differential equations on discrete nodes, using iterative time-steeping schemes. Due to the transient nature of the wave propagation and the three-dimensional volume in which the ultrasonic wave is modeled, the computational resources and the time to complete the calculations are often extensive, thus limiting the utilization of modeling. We can develop a data-driven solver for modelling wave propagation, by capturing the underlying physics from numerical simulation datasets, as an alternative approach [11]. In recent years, modern deep-learning techniques, such as long short-term memory (LSTM) [12; 13], have been successful in many domains [14; 15]. These techniques are used in many applications, such as propagating the latent space to the future [16; 17], using [18] the LSTM network to realize gesture recognition, wave propagation [19], automating tumor segmentation in whole breast [20], and shear wave elastography [21]. Since the ultrasonic wave propagation prediction is a sequence of spatio-temporal images data, so, typically, the LSTM approach will not provide and capture the desired results [22]. The convolutional long short-term memory (ConvLSTM) networks, effectively, address the long-range simulation prediction [23; 24; 25; 26]. The ConvLSTM approach uses the convolutional operation inside the LSTM cell, to pair the temporal state with spatial information. On the other hand, the wave propagation simulation solver can be built using a convolutional neural network (CNN) architecture [27; 28]. Another group in the research community is adapting physics-informed neural networks to solve the partial differential equations [29; 30; 31]. In the current work, the authors have developed two separate spatio-temporal deep learning (SDL) models. In the prior work, [26] shows the modeling forward wave propagation simulation in a 2D domain with different physical settings. The authors, further, want to generalize the SDL network for modelling forward wave propagation in the different geometrical domains (i.e., other than the trained domains) and reflecting wave propagation simulation in the different geometrical boundaries. In the first SDL model, the network algorithm is tuned to incorporate geometrical domain information and trained using datasets containing numerous ultrasonic wave simulations, with single-point excitation to five-point excitation sources inside the solid medium, without reflection from the edges. This trained SDL model can be deployed for modelling real-time forward ultrasonic wave propagation in the different geometrical shapes. Whereas in the second SDL model, the learnable hyperparameters are tuned to generate wave propagation, without changing network architecture. The datasets used for training the second model have three distinct geometrical domains, with a single-point excitation source applied on the edges. This trained SDL model can be used to study the reflected wave propagation phenomenon from different geometrical boundaries, such as curved, T-shaped, triangular, and rectangular domains, with varying frequencies and cycles. Thus, depending on the availability of the datasets's structure, we should employ one of these models for generating wave propagation. These training datasets have spatial and temporal features; hence, algorithms based on the recurrent neural network (RNN) are treated as the most suitable for modelling ultrasonic wave propagation simulations [19].