Thiago José Machado

Engineering education relies heavily on students' ability to apply mathematical reasoning to model, analyze, and solve complex problems across multiple domains. However, persistent difficulties in foundational mathematics courses remain a major challenge in undergraduate engineering programs, particularly in contexts marked by socioeconomic disparities. In this study, we present V‐MATH, a virtual tutoring system powered by large language models (LLMs) and designed to support engineering mathematics learning through a structured, computational, and pedagogically grounded approach. The system integrates optical character recognition for problem input validation, LaTeX‐based solution formatting, and WhatsApp‐based delivery to enhance accessibility, usability, and scalability. The architecture also incorporates retrieval‐augmented generation (RAG), auxiliary multi‐agent verification mechanisms, and graphical generation modules designed to improve mathematical consistency, reduce hallucinations, and support engineering‐oriented visualization tasks. Its instructional logic operationalizes Pólya's problem‐solving framework to provide step‐by‐step explanations aligned with engineering problem‐solving practices. The present work is explicitly framed as a proof of concept evaluated in a controlled, non‐classroom setting. Preliminary evaluations using items from national examinations (ENEM and ENA), employed as benchmarks of mathematical competencies relevant to engineering education, indicate that V‐MATH achieves accuracy above 90%, outperforming general‐purpose LLMs while offering greater pedagogical transparency. Given that V‐MATH is a complete workflow, rather than merely an isolated language model, this comparison should be interpreted as a system‐level contrast rather than a model‐level one, and the evidence presented here demonstrates the technical feasibility and pedagogically informed structuring of the proposed system. Overall, the findings suggest that V‐MATH represents a promising direction for the development of pedagogically grounded, multimodal, and reliability‐oriented AI tutoring systems for engineering education, motivating future validation in engineering classrooms.

Optimizing strategies in the Oil and Gas Industry, particularly within reservoir engineering and management, remains a significant challenge due to the prohibitive computational time costs and high resource demands of current simulation methods, even for medium-sized reservoirs. Notably, existing scientific approaches have not leveraged Deep Neural Networks (DNNs) for fine-grained predictions at the grid-cell level. This thesis introduces a novel approach that integrates DNNs with a Design of Experiments framework to develop a proxy model for reservoir simulation software. The methodology includes a robust feature selection process, model design, and training strategy, supplemented by comprehensive statistical evaluations and graphical tools. The proposed proxy models are validated using four distinct industrial scenarios based on the SPE9 black oil benchmark, incorporating production and injection wells across diverse temporal samples. The results demonstrate a significant improvement in computational efficiency without compromising accuracy, achieving over 80% accuracy across all scenarios, and reaching up to 99.9% under specific conditions. These findings highlight the potential of DNN-based proxy models to transform reservoir management practices, offering a scalable and resource-efficient alternative to traditional numerical simulations.

Directional drilling can be seen as a well-established technology that has advanced in the past few years, allowing higher productivity in petroleum exploration. On the other hand, the design of optimal multi-directional drilling paths has not gained much attention in the literature. Existing models and algorithms for the optimisation of directional drilling paths often disregard important petrophysical attributes or apply heuristic methods, which cannot guarantee the optimality of the generated solutions. In this paper, we employ mixed-integer programming (MIP) to optimize multiple directional drilling paths. This is achieved by integrating a screening step, capable of identifying the most promising target regions in terms of flow capacity, with an MIP model responsible for selecting and sequencing the identified targets. Our approach considers several constraints such as drift angles, maximum wellbore length, and minimum safety distances. In addition, a branch-and-cut algorithm is proposed for solving real-world multi-directional instances of challenging sizes. We carry out a case study in the Campos Basin to validate the proposed models. Preliminary results show that the optimized drilling paths have superior performance when compared to the historical average recovery factor of the Campos Basin.

In this work, a new pointwise source reconstruction method is proposed. From a single pair of boundary measurements, we want to completely characterize the unknown set of pointwise sources, namely, the number of sources and their locations and intensities. The idea is to rewrite the inverse source problem as an optimization problem, where a Kohn‐Vogelius type functional is minimized with respect to a set of admissible pointwise sources. The resulting second‐order reconstruction algorithm is non‐iterative and thus very robust with respect to noisy data. Finally, in order to show the effectiveness of the devised reconstruction algorithm, some numerical experiments into two spatial dimensions are presented. Copyright © 2016 John Wiley & Sons, Ltd.

O problema inverso do potencial consiste em reconstruir uma fonte desconhecida com suporte em um domínio geométrico a partir de uma única medição sobre a fronteira. A fim de tratar este problema inverso mal posto, este será reescrito como um problema de otimização onde um funcional de forma baseado no critério de Kohn-Vogelius é minimizado. Este funcional mede a diferença entre as soluções de dois problemas auxiliares, onde um deles contém a informação relativa a` leitura no contorno enquanto o outro e´ munido com a informação correspondente à excitação no contorno. As soluções dos problemas auxiliares coincidem quando se está sobre a solução do problema inverso. Para minimizar o critério de Kohn-Vogelius, sua variação total com respeito a um conjunto de fontes concentradas é avaliada explicitamente. Baseado na expressão obtida, constrói-se um novo método para resolver o problema inverso do potencial. Por fim, alguns resultados numéricos são apresentados a fim de mostrar a efetividade do algoritmo de reconstrução construído.