JULES DUMONT

Explored physics-informed approaches to learning chaotic dynamical systems, embedding known governing equations (Lorenz-63 and Lorenz-96) directly into neural network loss functions. On the Lorenz-63 attractor, a Transformer-based HyperNetwork dynamically generates the weights of a prediction MLP from context trajectories. On the higher-dimensional Lorenz-96 weather model, an LSTM and an encoder-decoder Transformer reconstruct full system states from partial observations and reproduce statistical properties of the chaotic system.

Trained a deep neural network to predict Critical Heat Flux in nuclear reactor fuel elements, replacing traditional look-up table interpolation. The full pipeline extracts data from the Groeneveld 2006 LUT PDF, applies physical filtering and normalization, and uses a parallelized Bayesian hyperparameter optimization via Optuna with multiprocessing to search over architectures, learning rates, and regularization.

Implemented a geometric multigrid solver and multigrid-preconditioned conjugate gradient in C for the 2D Laplace equation on rectangular domains with rectangular holes. The system is discretized with the 5-point finite difference stencil and stored in CSR format. Supports V-, W-, and F-cycles with Gauss-Seidel smoothing, full-weighting restriction, bilinear prolongation, and a choice of coarse-level solvers including UMFPACK.

Implemented the CSI (Capture, Score, Integrate) model for classifying social media threads as rumor or non-rumor. User behavior is embedded via truncated SVD of a user-thread incidence matrix, tweet text is compressed from 384 to 100 dimensions using Gaussian random projection, and temporal engagement patterns are captured by an LSTM over hourly bins. A feedforward network scores user credibility before final classification. Tested on PHEME (Twitter) and Weibo datasets.

Built a complete 2048-bit RSA cryptosystem from scratch in C, including a custom arbitrary-precision integer library using uint64 arrays with all arithmetic reduced to bitwise operations. Prime candidates are validated with 12-round Miller-Rabin tests, keys are derived via the extended Euclidean algorithm, and decryption uses blinding to resist timing side-channel attacks. A minimum-d threshold guards against Wiener's attack.

Developed a probabilistic framework for QAOA by modeling the variational algorithm as a continuous-time Markov process, where switching between Hamiltonians is governed by stochastic rates rather than fixed angles. Entropy regularization yields exact analytical solutions for the transition density in terms of modified Bessel functions. A spectral analysis links the Fourier spectrum of the cost landscape to trainability, producing a polynomial-time Monte Carlo diagnostic that detects Barren Plateaus at first round of the optimization process by simulating quantum signal-to-noise ratio.

Teaching assistant for practical sessions of the second-year undergraduate course "Introduction to Quantum Physics and Statistics" at École polytechnique de Bruxelles during academic years 2024-2025 and 2025-2026.