<div>Following a natural disaster, one of the most important facet that influence a persons chances of survival/being found out is the time with which they are rescued. Traditional means of search operations involving dogs, ground robots, humanitarian intervention; are time intensive and can be a major bottleneck in search operations. The main aim of these operations is to rescue victims without critical delay in the shortest time possible which can be realized in real-time by using UAVs. With advancements in computational devices and the ability to learn from complex data, deep learning can be leveraged in real time environment for purpose of search and rescue operations. This research aims to solve the traditional means of search operation using the concept of deep learning for real time object detection and Photogrammetry for precise geo-location mapping of the objects(person,car) in real time. In order to do so, various pre-trained algorithms like Mask-RCNN, SSD300, YOLOv3 and trained algorithms like YOLOv3 have been deployed with their results compared with means of addressing the search operation in</div><div>real time.</div><div><br></div>

<p>High-dimensional regression problems are ubiquitous in science and engineering. Deep learning has been a critical tool for solving a wide range of high-dimensional problems with surprising performance. Even though in theory neural networks have good properties in terms of approximation and optimization, numerically obtaining an accurate neural network solution is a challenging problem due to the highly non-convex objective function and implicit bias of least square optimization. In this dissertation, we mainly discuss two topics involving the high dimensional regression using efficient deep learning algorithms. These two topics include solving PDEs with high dimensional domains and data-driven dynamical modeling. </p> <p><br></p> <p>In the first topic, we aim to develop an efficient solver for PDE problems. Firstly, we focus on neural network structures to increase efficiency. We propose a data-driven activation function called reproducing activation function which can reproduce traditional approximation tools and enable faster convergence of deep neural network training with smaller parameter cost. Secondly, we target the application of neural networks to mitigate the numerical issues that hamper the traditional approach. As an example, we develop a neural network solver for elliptic PDEs on unknown manifolds and verify its effectiveness for the large-scale problem. </p> <p><br></p> <p>In the second topic, we aim to enhance the accuracy of learning the dynamical system from data by incorporating the prior. In the missing dynamics problem, taking advantage of known partial dynamics, we propose a framework that approximates a map that takes the memories of the resolved and identifiable unresolved variables to the missing components in the resolved dynamics. With this framework, we achieve a low error to predict the missing component, enabling the accurate prediction of the resolved variables. In the recovering Hamiltonian dynamics, by the energy conservation property, we learn the conserved Hamiltonian function instead of its associated vector field. To better learn the Hamiltonian from the stiff dynamics, we identify and splits the</p> <p>training data into stiff and nonstiff portions, and adopt different learning strategies based on the classification to reduce the training error. </p>

<p> In computer vision, accurately detecting objects of varying sizes is essential for various applications, such as autonomous vehicle navigation and medical imaging diagnostics. Addressing the variance in object sizes presents a significant challenge requiring advanced computational solutions for reliable object recognition and processing. This research introduces a size-adaptive Convolutional Neural Network (CNN) framework to enhance detection performance across different object sizes. By dynamically adjusting the CNN’s configuration based on the observed distribution of object sizes, the framework employs statistical analysis and algorithmic decision-making to improve detection capabilities. Further innovation is presented through the Parameterized-Swish activation function. Distinguished by its dynamic parameters, this function is designed to better adapt to varying input patterns. It exceeds the performance of traditional activation functions by enabling faster model convergence and increasing detection accuracy, showcasing the effectiveness of adaptive activation functions in enhancing object detection systems. The implementation of this model has led to notable performance improvements: a 11.4% increase in mean Average Precision (mAP) and a 40.63% increase in frames per second (FPS) for small objects, demonstrating enhanced detection speed and accuracy. The model has achieved a 48.42% reduction in training time for medium-sized objects while still improving mAP, indicating significant efficiency gains without compromising precision. Large objects have seen a 16.9% reduction in training time and a 76.04% increase in inference speed, showcasing the model’s ability to expedite processing times substantially. Collectively, these advancements contribute to a more than 12% increase in detection efficiency and accuracy across various scenarios, highlighting the model’s robustness and adaptability in addressing the critical challenge of size variance in object detection. </p>

<p>Temporal point processes (TPP) are mathematical approaches for modeling asynchronous event sequences by considering the temporal dependency of each event on past events and its instantaneous rate. Temporal point processes can model various problems, from earthquake aftershocks, trade orders, gang violence, and reported crime patterns, to network analysis, infectious disease transmissions, and virus spread forecasting. In each of these cases, the entity's behavior with the corresponding information is noted over time as an asynchronous event sequence, and the analysis is done using temporal point processes, which provides a means to define the generative mechanism of the sequence of events and ultimately predict events and investigate causality.</p> <p><br></p> <p>Among point processes, Hawkes process as a stochastic point process is able to model a wide range of contagious and self-exciting patterns. One of Hawkes process's well-known applications is predicting the evolution of viral processes on networks, which is an important problem in biology, the social sciences, and the study of the Internet. In existing works, mean-field analysis based upon degree distribution is used to predict viral spreading across networks of different types. However, it has been shown that degree distribution alone fails to predict the behavior of viruses on some real-world networks. Recent attempts have been made to use assortativity to address this shortcoming. This thesis illustrates how the evolution of such a viral process is sensitive to the underlying network's structure. </p> <p><br></p> <p>In Chapter 3, we show that adding assortativity does not fully explain the variance in the spread of viruses for a number of real-world networks. We propose using the graphlet frequency distribution combined with assortativity to explain variations in the evolution of viral processes across networks with identical degree distribution. Using a data-driven approach, by coupling predictive modeling with viral process simulation on real-world networks, we show that simple regression models based on graphlet frequency distribution can explain over 95\% of the variance in virality on networks with the same degree distribution but different network topologies. Our results highlight the importance of graphlets and identify a small collection of graphlets that may have the most significant influence over the viral processes on a network.</p> <p><br></p> <p>Due to the flexibility and expressiveness of deep learning techniques, several neural network-based approaches have recently shown promise for modeling point process intensities. However, there is a lack of research on the possible adversarial attacks and the robustness of such models regarding adversarial attacks and natural shocks to systems. Furthermore, while neural point processes may outperform simpler parametric models on in-sample tests, how these models perform when encountering adversarial examples or sharp non-stationary trends remains unknown. </p> <p><br></p> <p>In Chapter 4, we propose several white-box and black-box adversarial attacks against deep temporal point processes. Additionally, we investigate the transferability of white-box adversarial attacks against point processes modeled by deep neural networks, which are considered a more elevated risk. Extensive experiments confirm that neural point processes are vulnerable to adversarial attacks. Such a vulnerability is illustrated both in terms of predictive metrics and the effect of attacks on the underlying point process's parameters. Expressly, adversarial attacks successfully transform the temporal Hawkes process regime from sub-critical to into a super-critical and manipulate the modeled parameters that is considered a risk against parametric modeling approaches. Additionally, we evaluate the vulnerability and performance of these models in the presence of non-stationary abrupt changes, using the crimes and Covid-19 pandemic dataset as an example.</p> <p><br></p> <p> Considering the security vulnerability of deep-learning models, including deep temporal point processes, to adversarial attacks, it is essential to ensure the robustness of the deployed algorithms that is despite the success of deep learning techniques in modeling temporal point processes.</p> <p> </p> <p>In Chapter 5, we study the robustness of deep temporal point processes against several proposed adversarial attacks from the adversarial defense viewpoint. Specifically, we investigate the effectiveness of adversarial training using universal adversarial samples in improving the robustness of the deep point processes. Additionally, we propose a general point process domain-adopted (GPDA) regularization, which is strictly applicable to temporal point processes, to reduce the effect of adversarial attacks and acquire an empirically robust model. In this approach, unlike other computationally expensive approaches, there is no need for additional back-propagation in the training step, and no further network is required. Ultimately, we propose an adversarial detection framework that has been trained in the Generative Adversarial Network (GAN) manner and solely on clean training data. </p> <p><br></p> <p>Finally, in Chapter 6, we discuss implications of the research and future research directions.</p>

<p>Domain adaptation is one of the hottest directions in solving annotation insufficiency problem of deep learning. General domain adaptation is not consistent with the practical scenarios in the industry. In this thesis, we focus on two concerns as below.</p> <p>  </p> <p>  First is that labeled data are generally collected from multiple domains. In other words, multi-source adaptation is a more common situation. Simply extending these single-source approaches to the multi-source cases could cause sub-optimal inference, so specialized multi-source adaptation methods are essential. The main challenge in the multi-source scenario is a more complex divergence situation. Not only the divergence between target and each source plays a role, but the divergences among distinct sources matter as well. However, the significance of maintaining consistency among multiple sources didn't gain enough attention in previous work. In this thesis, we propose an Enhanced Consistency Multi-Source Adaptation (EC-MSA) framework to address it from three perspectives. First, we mitigate feature-level discrepancy by cross-domain conditional alignment, narrowing the divergence between each source and target domain class-wisely. Second, we enhance multi-source consistency via dual mix-up, diminishing the disagreements among different sources. Third, we deploy a target distilling mechanism to handle the uncertainty of target prediction, aiming to provide high-quality pseudo-labeled target samples to benefit the previous two aspects. Extensive experiments are conducted on several common benchmark datasets and demonstrate that our model outperforms the state-of-the-art methods.</p> <p>  </p> <p>  Second is that data privacy and security is necessary in practice. That is, we hope to keep the raw data stored locally while can still obtain a satisfied model. In such a case, the risk of data leakage greatly decreases. Therefore, it is natural for us to combine the federated learning paradigm with domain adaptation. Under the source-private setting, the main challenge for us is to expose information from the source domain to the target domain while make sure that the communication process is safe enough. In this thesis, we propose a method named Fourier Transform-Assisted Federated Domain Adaptation (FTA-FDA) to alleviate the difficulties in two ways. We apply Fast Fourier Transform to the raw data and transfer only the amplitude spectra during the communication. Then frequency space interpolations between these two domains are conducted, minimizing the discrepancies while ensuring the contact of them and keeping raw data safe. What's more, we make prototype alignments by using the model weights together with target features, trying to reduce the discrepancy in the class level. Experiments on Office-31 demonstrate the effectiveness and competitiveness of our approach, and further analyses prove that our algorithm can help protect privacy and security.</p>

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