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Mean-field approximations are useful in determining numerical values for order parameters in phase transitions like in superconductivity. Considering the computational complexities of iterativaly diagonalizations in a self consistent approach, one might wonder: could a machine learn the patterns existing in the determination of Δ and find a function f such that Δ ← f(T,V,N,Ec,etc)?

The project aimed to answer this question by training a Random Forest model to predict the superconducting gap Δ in a 1D system with periodic and non-periodic boundary conditions. The model was trained on a dataset of 1000 samples, each with 10 features, and achieved a twofold increase in computational speed while solving for Δ in continuous space simulations. The results also suggested potential new physical behaviors for conditions where V≈t, indicating unusual phase transitions in the bulk and at the edges.

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Could a machine learn to recreate the unique brushstrokes of Van Gogh or the textures of the Mona Lisa while preserving the essence of a modern photograph? This project aimed to answer that question by applying neural networks to the artistic challenge of style transfer. Our goal was to take the stylistic elements of renowned artworks, like the swirling patterns of Van Gogh’s Starry Night or the fine details of the Mona Lisa, and seamlessly apply them to photographs, while keeping the original colors and content intact.

We used a modified version of the Gatys et al. neural style transfer algorithm, designed to selectively transfer textures and artistic features through different layers of the network. The result? A balanced fusion of style and content, where the artistic feel of the painting meets the structural integrity of the photograph, without losing its natural color.

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Detecting and classifying skin lesions is key to diagnosing various skin conditions, including skin cancer, which is a major global health concern. Computer-aided diagnosis (CAD) systems have become promising tools in this area, providing efficient and accurate ways to classify lesions. By integrating machine learning algorithms with medical imaging, CAD systems offer valuable support to doctors, helping them make quick and informed decisions for diagnosis and treatment planning.

In this context, this project the development and results of skin lesion classification into eight different diagnostic categories.

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Detecting and classifying skin lesions is key to diagnosing various skin conditions, including skin cancer, which is a major global health concern. Computer-aided diagnosis (CAD) systems have become promising tools in this area, providing efficient and accurate ways to classify lesions. By integrating machine learning algorithms with medical imaging, CAD systems offer valuable support to doctors, helping them make quick and informed decisions for diagnosis and treatment planning.

In this context, this project the development and results of skin lesion classification into eight different diagnostic categories.

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I contributed to the development of a Open-Source Python library that generates 1- and 2-electron integrals for molecular quantum chemistry simulations. This software allows the simulation of new molecules and provides data for machine learning applications.

My work involved designing user-friendly APIs for Pariser-Parr-Pople approximations, extending support to include all atom types, and developing new models that integrate occupation- and spin-based Hamiltonians.

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In the medical field, accurate segmentation plays a critical role in diagnosing conditions like skin cancer. By precisely extracting the lesion area from the surrounding skin, segmentation allows healthcare professionals to focus on the affected region, leading to more accurate diagnoses and informed treatment plans. Segmentation also enhances machine learning workflows, acting as a vital pre-processing step that improves classification performance by providing clean, well-defined inputs.

This project aimed to implement a segmentation pipeline to extract lesion areas from skin lesion images, using classical image processing techniques. As part of Télécom Paris's Image Processing course, the project successfully applied these tools to address a real-world medical challenge. The pipeline achieved impressive results, with a Dice coefficient exceeding 80%, demonstrating its high accuracy and effectiveness. Below are examples of the pipeline's output, highlighting its capability in extracting lesion areas.

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This project explores how nighttime satellite imagery can be utilized to predict energy consumption in the state of Rio Grande do Sul, Brazil. Using data from the VIIRS-DNB satellite and the Brazilian Energy Research Company (EPE), we performed econometric analyses including correlation and causality to evaluate the relationship between luminosity and energy consumption.

We compared ARIMA and LSTM models with and without the luminosity variable to assess their forecasting effectiveness. Preliminary results indicate that including nighttime luminosity data improves energy consumption predictions, providing a low-cost approach for optimizing energy management.

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Data streaming algorithms must address limited memory and real-time processing needs, especially in applications such as anomaly detection, fraud prevention, and network monitoring. Traditional methods struggle with these constraints due to their batch nature and the lack of labeled datasets.

In this project, we implement and evaluate the StreamRHF algorithm—an unsupervised, tree-based method for streaming anomaly detection—within the CapyMOA Python library. StreamRHF uses kurtosis-based splits to build Random Histogram Forests incrementally, enabling adaptation to concept drifts.

We replicate and extend the original work by normalizing anomaly scores for full CapyMOA compatibility. Experimental results show StreamRHF achieves competitive or superior performance compared to state-of-the-art methods like HalfSpaceTrees and Online Isolation Forests.

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Large-scale language models (LLMs) have demonstrated remarkable capabilities in capturing world knowledge and performing reasoning tasks. However, aligning these models with human expectations remains a major challenge due to their unsupervised training.

Reinforcement Learning from Human Feedback (RLHF) offers a framework to fine-tune these models using human preferences. But RLHF often involves training an unstable and complex reward model. This project explores Direct Preference Optimization (DPO), a simplified and stable alternative to traditional RLHF.

DPO reformulates the reward model and derives an optimal policy using only a classification loss. We dissect the theoretical underpinnings, including the Bradley-Terry model and reward reparameterization. Our implementation replicates the original results and further analyzes performance trade-offs, providing a more stable pathway to human-aligned LLMs.

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This project re-implements the DPM-Solver-1/2/3 algorithms and dives into the mathematical foundations of diffusion probabilistic models. It explores the transformation of stochastic differential equations into a deterministic probability flow ODE.

We review the methods of the original paper "DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps", deriving closed-form solutions using exponential integrators and provide step-by-step demonstrations of forward and reverse SDEs. The focus is on high-order solvers, the variation of constants method, and the role of the transformation function \( \lambda(t) = \log(\alpha(t)/\sigma(t)) \).

Also, a comparisson with the previous existent methods was performed based on the ideas of the paper.