Multivariate time series modeling requires capturing complex dependencies both within individual time series and across different variables. Existing graph-based approaches are limited to pairwise interactions, while recent product cell complex methods assume homogeneous higher-order relationships. This thesis proposes the Simplicial Product Complex (SPC), a topological framework that constructs simplicial complexes in the product space to capture heterogeneous higher-order interactions across space and time. The key innovation is the ability to distinguish between different relationship types and learn their relative importance from data. We develop the Simplicial Product Complex Convolutional Neural Network (SPCCNN) to perform data-adaptive learning over these structures. Experimental evaluation shows SPCCNN achieves competitive performance with state-of-the-art methods while offering enhanced flexibility through parameterized structures. The model adapts to dataset-specific patterns and maintains computational efficiency through sparsity regularization. Our findings demonstrate the effectiveness of higher-order simplicial modeling for capturing complex temporal dynamics in multivariate time series data.

Graph Neural Networks are widely used as useful tools to investigate graphs because they can learn from the topological structure of graphs. In practical applications, the graph’s structure can change over time, have errors or be subject to adversarial attacks. These perturbations negatively impact the accuracy of the neural network. The theoretical stability of graph neural networks has been analysed already and in this paper, the stability of graph neural networks is investigated experimentally. The performance of different perturbation strategies is compared to see how different perturbations impact stability.

GNNs are a powerful tool for learning tasks on data with a graph structure. However, the topology of the graph in which GNNs are trained is often subject to change due to random, external perturbations. This research investigates the relationship between 5 topological properties of graphs (assortativity, density, edge connectivity, closeness centrality, diameter) and how stable GNNs trained on graphs with different topological properties are against different perturbations. The analysis is conducted by first synthetically generating graphs with different topological properties and training a GNN using the generated graphs. The synthetic graphs are then perturbed, and the relative change in the GNNs' output is measured. These results are further supported by conducting the same process on three popular GNN datasets: Cora, CiteSeer and PubMed citations. Finally, relationships between the graph properties under investigation and GNN stability are inferred using the results obtained from both synthetic and real-world datasets.

Graph Neural Networks (GNNs) have emerged as a powerful tool for learning from relational data. The real-world graphs such models are trained on are susceptible to changes in their topology. A growing body of work in the field of GNNs' stability to topology perturbations is trying to characterise how models respond to those changes, providing valuable insights that have enhanced the robustness of GNNs to adversarial attacks. The past work in this field, however, has only approached stability analysis using spectral graph theory, which is not applicable to all kinds of GNN models. In this paper, we aim to extend the past work in GNN stability by proposing an algorithm for analysing the stability of GNNs with model-agnostic GNN explainability tools instead of the mathematical framework of spectral graph theory. We demonstrate that the outputs of explainability tools can encode useful insights into the stability of GNNs and present a case study on using those insights to analyse node removal, edge removal, and edge weight perturbations.

Graph Neural Network holds significant impor- tance in various applications. Pioneering research has demonstrated state-of-the-art performance in practical applications such as Fraud Detection, Recommender Systems, or Traffic Forecasting by utilizing various Graph Neural Networks (GNNs) architectures. For these applications, one of the most important properties that needs to hold is the stability of GNN under stochastic perturbation as real-life networks undergo changes in topology on a frequent basis. However, it remains unclear how different architectures preserve this property under different perturbations. In this research, we aim to shed light on if this stability property undergoes drastic changes in the graph underlying topology, and if it affects the overall performance of the GNN in Traffic Forecasting problems. We demonstrate that the architectures differ in the stability property measured by different metrics, while some archi- tectures retains their state-of-the-art performance, providing useful insight on the analysis of stability property on different graph neural network archi- tectures in Traffic Forecasting problem.

Graph Neural Networks (GNN) are Machine Learning models which are trained on graph data in order to handle complex state-of-the-art tasks such as recommender systems and molecular property prediction. However, the graphs that these models are trained on can be perturbed in various ways post training resulting in reductions in performance. This study compares the stability of various Graph Neural Network task types (Node Classification, Link Prediction, and Graph Classification) by investigating each of their performances across a range of perturbation severities performed on graphs. Further experiments explore whether this performance ranking changes for different types of perturbations and GNN architectures. Through results, it is shown that there is a noticeable difference in stability between the investigated tasks. However, it is also shown that under certain conditions, such as different types of perturbations or architectures, the performance ranking may shift. This paper highlights weak points in GNNs that should be explored for stronger defenses against potential attacks.

Earthquakes can have tremendous effects. They can result in casualties, massive damage, and hurt the economy. Therefore, one would like to predict earthquakes as early as possible and with the highest accuracy possible. This paper contains the proposal for the optimal prediction-time, which is the time between the execution of a prediction and the actual earthquake strike, for deep learning models. Only short-term predictions and high-magnitude earthquakes are considered. A prediction means to define whether an earthquake happens or does not happen in an upcoming amount of seconds. A short-term prediction means a forecast to the extent of seconds. A high-magnitude earthquake means an earthquake with a magnitude of 2.5 or higher. This research uses the Long Short Term Memory deep learning model to test the optimal prediction-time value for earthquake predictions.
The optimal value for the prediction-time is found by testing the model with different values for the prediction-time and concluding when the model performs best. For prediction-times from moments before the strike until 40 seconds, the model is performing worse compared to higher prediction-times. The model's performance peaks at a prediction-time of 70. When increasing further than 70, the performance decreases until a prediction-time of one hundred. When rising even further, the performance is stabilising. Thus, for predictions with the highest performance, one should use a prediction-time of 70 seconds.

Earthquake prediction is the field of seismology concerned with predicting the time, location, and magnitude of earthquakes within a small time frame, usually defined in terms of minutes or seconds before an event. Such predictions can have a large impact on minimizing the damage caused by these seismic events, by providing early warnings to the affected population and allowing them to respond appropriately. Although the methods used to predict earthquakes are often limited to larger magnitude events, predicting micro-earthquakes is also an important task, especially in locations that are more vulnerable to seismic shocks. Concentrations of localized micro-earthquakes can also hint at larger future seismic events, and their location can be used to locate moving fault lines underground. Deep learning methods perform particularly well in this context, due to their ability to quickly identify patterns in large volumes of data, and Long-Short Term Memory (LSTM) neural networks are very well suited to handling time-sequenced data such as the seismic waves used in earthquake prediction problems. In this paper, an LSTM network is trained to predict micro-earthquakes three seconds before the event, using seismic recordings from the New Zealand dataset: the goal is to find the optimal size of these recordings and understand how different values affect the model. Our results suggest that larger recordings do not provide any benefit in performance and that high levels of accuracy can be reached with smaller samples. This means that in the context of micro-earthquake prediction, primary waves can be easily detected in short recordings, and are likely to travel close to shear waves. This can be attributed to the low strength of signals that micro-earthquakes generate, as they will travel shorter distances than major earthquakes.

Due to the devastating consequences of earthquakes, predicting their occurrence before the first strike has been a long standing research topic. Deep learning models have been used to facilitate prediction, using seismograph data to attempt to classify an earthquake right before it happens. However, this is a difficult task and research needs to be conducted into how properties of earthquakes impact the accuracy of models. Thus earthquake focal depth was studied as a factor in prediction accuracy, specifically comparing deep and shallow earthquakes, split along a depth of 70km. An LSTM model was trained using these different data sets, providing 30 seconds of seismic waveform data and given the task to predict the occurrence of an earthquake 3 seconds in the future. Training this model 20 times with each data set resulted in the accuracies of 0.869 for shallow earthquakes and 0.850 for deep ones. Thus the results show that both shallow and deep earthquake trained models performed similarly well.

Earthquakes are one of the most destructive natural phenomena, both in terms of human lives, and property damage. Although they are treated as a random phenomenon, the ability to predict them, even few seconds before they occur, could be of great benefit to society. Lots of research has been done on this topic but without any significant results. With the increase of seismic wave measurements data and since in recent years deep learning has solved many difficult problems, this paper aims to answer the impact of the seismic wave length in detecting high-magnitude earthquakes via Long Short-Term Memory (LSTM) neural network. Although the performance of the model was unsatisfactory, given the complex task of predicting earthquakes, as well as the resulting metrics not indicating any significant data in order to extrapolate a certain conclusion, it is worth further researching a duration of seismic waveform recordings of length 30 seconds, with sampling rate between 10 and 20 HZ, as these seismic waves seem to perform relatively best in our research.

Different methods have been studied to predict earthquakes, but the results are still far from optimal. Due to their seemingly dynamic and unpredictable nature, it has been very hard to find data correlating with earthquakes happening. But recently, various research has been done using neural networks, and some has suggested that it could extract valuable information from preceding seismic data. To get a better sense of how seismic data can contain this information, we need to look at how long before an earthquake seismic precursor signals can exist. This paper uses an LSTM model to perform binary classification of the task: ”Given the seismic wave recordings of N stations during T seconds, will an earthquake happen after H seconds?” By varying the parameter H and studying its effect on the prediction accuracy of the NN, results suggest that sensitive information is very present in the seismic data 10 to 15 minutes before a low-magnitude (less than 2.5 on Richters scale) earthquake strikes. We aim to open the way for further research about precursor-based earthquake prediction using neural networks, showing that LSTM can be a good option. We also hope for further research to dig deeper in understanding what the signals in the seismic data are to further improve earthquake prediction.

Multi-Layer Perceptron and Support Vector Machine have both been widely used in machine learning. In this research paper, these models have been applied to binary classification on an individual time series basis. The goal was to see whether they can predict earthquakes, using earthquakes measured at specific stations across New Zealand. As it turns out, both models serve as satisfactory classifiers. However, their performances are dependent on the stations the data was accumulated from.

Earthquake prediction has raised many concerns nowadays, due to the massive loss caused by earthquakes, as well as the significance of accurate forecasting. Lots of trials have been investigated and experimented but few achieved satisfying results on short-term prediction (i.e., usually those earthquakes that will happen in three months). It is cardinal to detect strikes within a few minutes or hours in advance. In this paper, given thirty seconds of waveform signal before earthquakes happen, we compare the performances of three different recurrent neural networks, namely vanilla recurrent neural network (RNN), long short-term memory (LSTM) and bidirectional LSTM, on earthquake prediction. We choose recurrent neural networks because their inner structures take advantage of learning the temporal dependencies from time series sequence. Results show that LSTM has better performance predicting on unseen data than the other two networks.

Earthquakes can do great harm to the environment and people's daily lives. Being able to predict an earthquake moments before it happens could therefore reduce harm and save human lives. Traditional methods have not been successful yet, but with the rise of techniques focused on deep learning, there is a growing interest to apply them to the field of earthquakes. The placement of stations measuring seismic waves at various locations across regions has also greatly contributed to the possibility of applying data-driven techniques to the problem. A neural network that has been previously successful in the prediction of epileptic seizures - is a CNN mixed with RNN methods. In this paper, we validate the use of this model in predicting earthquakes and compare its performance to individual models. We do this based on seismic measurements before the earthquakes of different stations across New Zealand. The results suggest that our method is not capable of predicting earthquakes with higher accuracy than random guessing.

Earthquakes are one of the most dangerous natural disasters that occur worldwide. Predicting them is one of the unsolved problems in the field of science. In the past decade, there has been an increase in seismic monitoring stations worldwide, which has allowed us to design and implement data-driven and deep learning solutions. In this paper, we will investigate how CNN mixed with LSTM methods compare to the individual ones in predicting earthquakes given 30 seconds of seismic data before an earthquake occurs, also known as precursor data. Preliminary results show that a CNN mixed with LSTM has the best training accuracy while an individual LSTM performs best on unseen data.