Drift vehicle control offers valuable insights to support safe autonomous driving in extreme conditions, which hinges on tracking a particular path while maintaining the vehicle states near the drift equilibrium points (DEP). However, conventional tracking methods are not adaptable for drift vehicles due to their opposite steering angle and yaw rate. In this paper, we propose an adaptive path tracking (APT) control method to dynamically adjust drift states to follow the reference path, improving the commonly utilized predictive path tracking methods with released computation burden. Furthermore, existing control strategies necessitate a precise system model to calculate the DEP, which can be more intractable due to the highly nonlinear drift dynamics and sensitive vehicle parameters. To tackle this problem, an adaptive learning-based model predictive control (ALMPC) strategy is proposed based on the APT method, where an upper-level Bayesian optimization is employed to learn the DEP and APT control law to instruct a lower-level MPC drift controller. This hierarchical system architecture can also resolve the inherent control conflict between path tracking and drifting by separating these objectives into different layers. The ALMPC strategy is verified on the Matlab-Carsim platform, and simulation results demonstrate its effectiveness in controlling the drift vehicle to follow a clothoid-based reference path even with the misidentified road friction parameter.

High-performance computing and modern numerical algorithms have made high-fidelity fluid-thermal analysis tractable in geometries of ever increasing complexity. Despite continued advances in these areas, direct numerical (DNS), large eddy simulation (LES), and even unsteady Reynolds-averaged Navier-Stokes (URANS) simulations of turbulent thermal transport remain too costly for routine analysis and design of thermal-hydraulic systems, where hundreds of cases must be considered. Reduced order models (ROMs) offer a promising alternative by leveraging expensive high-fidelity simulations (referred to as full order models or FOMs) to first extract a low-dimensional basis that captures the principal features of the underlying flow fields, and then construct computational models whose dimensions are orders of magnitude lower than the FOM dimension. In the numerical simulation of fluid flows, Galerkin ROMs (G-ROMs), which use data-driven basis functions in a Galerkin framework, have provided efficient and accurate approximations of laminar flows, such as the two-dimensional flow past a circular cylinder at low Reynolds numbers [1, 2]. However, turbulent flows are notoriously hard for the standard G-ROM. Indeed, to capture the complex dynamics, a large number [3] of ROM basis functions is required, which yields high-dimensional ROMs that cannot be used in realistic applications. Thus, computationally efficient, low-dimensional ROMs are used instead. Unfortunately, these ROMs are inaccurate since the ROM basis functions that were not used to build the G-ROM have an important role in dissipating the energy from the system [4].

The twenty-first century is a data-driven era where human activities and behavior, physical phenomena, scientific discoveries, technology advancements, and almost everything that happens in the world resulting in massive generation, collection, and utilization of data. Connectivity in data is a crucial property. A straightforward example is the World Wide Web, where every webpage is connected to other web pages through hyperlinks, providing a form of directed connectivity. Combinatorial data refers to combinations of data items based on certain connectivity rules. Other forms of combinatorial data include social networks, meshes, community clusters, set systems, and molecules. This Ph.D. dissertation focuses on learning and computing with combinatorial data. We study and examine topological and connectivity features within and across connected data to improve the performance of learning and achieve high algorithmic efficiency.

Artificial intelligence commonly refers to the science and engineering of artificial systems that can carry out tasks generally associated with requiring aspects of human intelligence, such as playing games, translating languages, and driving cars. In recent years, there have been exciting advances in learning-based, data-driven approaches towards AI, and machine learning and deep learning have enabled computer systems to perceive the world in unprecedented ways. Reinforcement learning has enabled breakthroughs in complex games such as Go and challenging robotics tasks such as quadrupedal locomotion. A key aspect of intelligence is to not only make predictions, but reason about the uncertainty in these predictions, and to consider this uncertainty when making decisions. This is what this manuscript on "Probabilistic Artificial Intelligence" is about. The first part covers probabilistic approaches to machine learning. We discuss the differentiation between "epistemic" uncertainty due to lack of data and "aleatoric" uncertainty, which is irreducible and stems, e.g., from noisy observations and outcomes. We discuss concrete approaches towards probabilistic inference and modern approaches to efficient approximate inference. The second part of the manuscript is about taking uncertainty into account in sequential decision tasks. We consider active learning and Bayesian optimization -- approaches that collect data by proposing experiments that are informative for reducing the epistemic uncertainty. We then consider reinforcement learning and modern deep RL approaches that use neural network function approximation. We close by discussing modern approaches in model-based RL, which harness epistemic and aleatoric uncertainty to guide exploration, while also reasoning about safety.

Turbulent flow fields are characterized by extreme events that are statistically intermittent and carry a significant amount of energy and physical importance. To emulate these flows, we introduce the extreme variational Autoencoder (xVAE), which embeds a max-infinitely divisible process with heavy-tailed distributions into a standard VAE framework, enabling accurate modeling of extreme events. xVAEs are neural network models that reduce system dimensionality by learning non-linear latent representations of data. We demonstrate the effectiveness of xVAE in large-eddy simulation data of wildland fire plumes, where intense heat release and complex plume-atmosphere interactions generate extreme turbulence. Comparisons with the commonly used Proper Orthogonal Decomposition (POD) modes show that xVAE is more robust in capturing extreme values and provides a powerful uncertainty quantification framework using variational Bayes. Additionally, xVAE enables analysis of the so-called copulas of fields to assess risks associated with rare events while rigorously accounting for uncertainty, such as simultaneous exceedances of high thresholds across multiple locations. The proposed approach provides a new direction for studying realistic turbulent flows, such as high-speed aerodynamics, space propulsion, and atmospheric and oceanic systems that are characterized by extreme events.

Bivariate structural causal models (SCM) are often used to infer causal direction by examining their goodness-of-fit under restricted model classes. In this paper, we describe a parametrization of bivariate SCMs in terms of a causal velocity by viewing the cause variable as time in a dynamical system. The velocity implicitly defines counterfactual curves via the solution of initial value problems where the observation specifies the initial condition. Using tools from measure transport, we obtain a unique correspondence between SCMs and the score function of the generated distribution via its causal velocity. Based on this, we derive an objective function that directly regresses the velocity against the score function, the latter of which can be estimated non-parametrically from observational data. We use this to develop a method for bivariate causal discovery that extends beyond known model classes such as additive or location scale noise, and that requires no assumptions on the noise distributions. When the score is estimated well, the objective is also useful for detecting model non-identifiability and misspecification. We present positive results in simulation and benchmark experiments where many existing methods fail, and perform ablation studies to examine the method's sensitivity to accurate score estimation.

Black-box algorithms are designed to optimize functions without relying on their underlying analytical structure or gradient information, making them essential when gradients are inaccessible or difficult to compute. Traditional methods for solving black-box optimization (BBO) problems predominantly rely on non-parametric models and struggle to scale to large input spaces. Conversely, parametric methods that model the function with neural estimators and obtain gradient signals via backpropagation may suffer from significant gradient errors. A recent alternative, Explicit Gradient Learning (EGL), which directly learns the gradient using a first-order Taylor approximation, has demonstrated superior performance over both parametric and non-parametric methods. In this work, we propose two novel gradient learning variants to address the robustness challenges posed by high-dimensional, complex, and highly non-linear problems. Optimistic Gradient Learning (OGL) introduces a bias toward lower regions in the function landscape, while Higher-order Gradient Learning (HGL) incorporates second-order Taylor corrections to improve gradient accuracy. We combine these approaches into the unified OHGL algorithm, achieving state-of-the-art (SOTA) performance on the synthetic COCO suite. Additionally, we demonstrate OHGLs applicability to high-dimensional real-world machine learning (ML) tasks such as adversarial training and code generation. Our results highlight OHGLs ability to generate stronger candidates, offering a valuable tool for ML researchers and practitioners tackling high-dimensional, non-linear optimization challenges

SQL Injection (SQLi) continues to pose a significant threat to the security of web applications, enabling attackers to manipulate databases and access sensitive information without authorisation. Although advancements have been made in detection techniques, traditional signature-based methods still struggle to identify sophisticated SQL injection attacks that evade predefined patterns. As SQLi attacks evolve, the need for more adaptive detection systems becomes crucial. This paper introduces an innovative approach that leverages generative models to enhance SQLi detection and prevention mechanisms. By incorporating Variational Autoencoders (VAE), Conditional Wasserstein GAN with Gradient Penalty (CWGAN-GP), and U-Net, synthetic SQL queries were generated to augment training datasets for machine learning models. The proposed method demonstrated improved accuracy in SQLi detection systems by reducing both false positives and false negatives. Extensive empirical testing further illustrated the ability of the system to adapt to evolving SQLi attack patterns, resulting in enhanced precision and robustness.

Abstract--Accurate estimation of voltage drop (IR drop) in modern Application-Specific Integrated Circuits (ASICs) is highly time and resource demanding, due to the growing complexity and the transistor density in recent technology nodes. To mitigate this challenge, we investigate how Machine Learning (ML) techniques, including Extreme Gradient Boosting (XGBoost), Convolutional Neural Network (CNN), and Graph Neural Network (GNN) can aid in reducing the computational effort and implicitly the time required to estimate the IR drop in Integrated Circuits (ICs). ML algorithms, on the other hand, are explored as an alternative solution to offer quick and precise IR drop estimation, but in considerably less time. This study illustrates the effectiveness of ML algorithms in precisely estimating IR drop and optimizing ASIC sign-off. Thus, a new round of simulations is required for verification. This process is a standard routine in every ASIC design and manufacturing process, and it is defined as the "sign-off" REDICTION of IR drop is an important problem faced today often by ASIC designers. As the current (I) flows With the transition to larger density integration of transistors, through the Power Distribution Network (PDN), a part of the number of connection layers and interconnections the applied voltage inherently drops across the current path, have increased exponentially over the last decades, driven which is, in simple terms, the definition of IR drop. As a result, while commercial results in voltage drop, or to the grounding (GND), which tools are trying to keep up with the up-scaling demand, results in a ground bounce.

Molecular Relational Learning (MRL) is widely applied in natural sciences to predict relationships between molecular pairs by extracting structural features. The representational similarity between substructure pairs determines the functional compatibility of molecular binding sites. Nevertheless, aligning substructure representations by attention mechanisms lacks guidance from chemical knowledge, resulting in unstable model performance in chemical space (\textit{e.g.}, functional group, scaffold) shifted data. With theoretical justification, we propose the \textbf{Re}presentational \textbf{Align}ment with Chemical Induced \textbf{Fit} (ReAlignFit) to enhance the stability of MRL. ReAlignFit dynamically aligns substructure representation in MRL by introducing chemical Induced Fit-based inductive bias. In the induction process, we design the Bias Correction Function based on substructure edge reconstruction to align representations between substructure pairs by simulating chemical conformational changes (dynamic combination of substructures). ReAlignFit further integrates the Subgraph Information Bottleneck during fit process to refine and optimize substructure pairs exhibiting high chemical functional compatibility, leveraging them to generate molecular embeddings. Experimental results on nine datasets demonstrate that ReAlignFit outperforms state-of-the-art models in two tasks and significantly enhances model's stability in both rule-shifted and scaffold-shifted data distributions.