Spatiotemporal Predictive Learning (SPL) is an essential research topic involving many practical and real-world applications, e.g., motion detection, video generation, precipitation forecasting, and traffic flow prediction. The problems and challenges of this field come from numerous data characteristics in both time and space domains, and they vary depending on the specific task. For instance, spatial analysis refers to the study of spatial features, such as spatial location, latitude, elevation, longitude, the shape of objects, and other patterns. From the time domain perspective, the temporal analysis generally illustrates the time steps and time intervals of data points in the sequence, also known as interval recording or time sampling. Typically, there are two types of time sampling in temporal analysis: regular time sampling (i.e., the time interval is assumed to be fixed) and the irregular time sampling (i.e., the time interval is considered arbitrary) related closely to the continuous-time prediction task when data are in continuous space. Therefore, an efficient spatiotemporal predictive method has to model spatial features properly at the given time sampling types. In this thesis, by taking advantage of Machine Learning (ML) and Deep Learning (DL) methods, which have achieved promising performance in many complicated computational tasks, we propose three DL-based models used for Spatiotemporal Sequence Prediction (SSP) with several types of time sampling. First, we design the Trajectory Gated Recurrent Unit Attention (TrajGRU-Attention) with novel attention mechanisms, namely Motion-based Attention (MA), to improve the performance of the standard Convolutional Recurrent Neural Networks (ConvRNNs) in the SSP tasks. In particular, the TrajGRU-Attention model can alleviate the impact of the vanishing gradient, which leads to the blurry effect in the long-term predictions and handle both regularly sampled and irregularly sampled time series. Consequently, this model can work effectively with different scenarios of spatiotemporal sequential data, especially in the case of time series with missing time steps. Second, by taking the idea of Neural Ordinary Differential Equations (NODEs), we propose Trajectory Gated Recurrent Unit integrating Ordinary Differential Equation techniques (TrajGRU-ODE) as a continuous time-series model. With Ordinary Differential Equation (ODE) techniques and the TrajGRU neural network, this model can perform continuous-time spatiotemporal prediction tasks and generate resulting output with high accuracy. Compared to TrajGRU-Attention, TrajGRU-ODE benefits from the development of efficient and accurate ODE solvers. Ultimately, we attempt to combine those two models to create TrajGRU-Attention-ODE. NODEs are still in their early stage of research, and recent ODE-based models were designed for many relatively simple tasks. In this thesis, we will train the models with several video datasets to verify the ability of the proposed models in practical applications. To evaluate the performance of the proposed models, we select four available spatiotemporal datasets based on the complexity level, including the MovingMNIST, MovingMNIST++, and two real-life datasets: the weather radar HKO-7 and KTH Action. With each dataset, we train, validate, and test with distinct types of time sampling to justify the prediction ability of our models. In summary, the experimental results on the four datasets indicate the proposed models can generate predictions properly with high accuracy and sharpness. Significantly, the proposed models outperform state-of-the-art ODE-based approaches under SSP tasks with different circumstances of interval recording.