arXiv subjects

Simon Ghyselincks

Publications and source records attributed to Simon Ghyselincks.

3 recordsLinked to original sources

arXiv2026

Preconditioned Flow Matching

Flow matching (FM) learns vector fields by regressing stochastic velocity targets along intermediate distributions $p_t$. We identify a geometric optimization bottleneck in this regression problem: when the covariance $Σ_t$ of $p_t$ is ill-conditioned, gradient-based training rapidly fits high-variance directions while making slow progress along low-variance ones. In an exactly solvable Gaussian setting, we prove that the excess risk is weighted by $Σ_t$, and that both gradient descent and stochastic gradient descent inherit condition-number-dependent convergence. We then extend the analysis to Gaussian mixtures, showing that multimodality does not average away this effect; instead, the slowest and worst-conditioned component can control optimization. Motivated by this analysis, we propose \emph{preconditioned flow matching}, a precondition-then-match framework that transforms the target distribution into a more isotropic representation, trains the main flow in the transformed space, and maps generated samples back through the inverse transformation. We show theoretically that preconditioning reshapes the intermediate FM path and improves its conditioning. Across controlled Gaussian and Gaussian-mixture experiments, latent MNIST and other high resolution image datasets up to $512{\times}512$ resolution, preconditioning improves path-conditioning diagnostics, low-eigenvalue recovery, FID, MMD, precision, and recall. Compute-matched baselines and preconditioner-quality ablations further show that the gains are not explained merely by additional preconditioner parameters, but by improved geometry of the downstream flow matching problem.

cs.LG↗

arXiv2026

Synthetic Geology: Structural Geology Meets Deep Learning

Reconstructing the structural geology and mineral composition of the first few kilometers of the Earth's subsurface from sparse or indirect surface observations remains a long-standing challenge with critical applications in mineral exploration, geohazard assessment, and geotechnical engineering. This inherently ill-posed problem is often addressed by classical geophysical inversion methods, which typically yield a single maximum-likelihood model that fails to capture the full range of plausible geology. The adoption of modern deep learning methods has been limited by the lack of large 3D training datasets. We address this gap with \textit{StructuralGeo}, a geological simulation engine that mimics eons of tectonic, magmatic, and sedimentary processes to generate a virtually limitless supply of realistic synthetic 3D lithological models. Using this dataset, we train both unconditional and conditional generative flow-matching models with a 3D attention U-Net architecture. The resulting foundation model can reconstruct multiple plausible 3D scenarios from surface topography and sparse borehole data, depicting structures such as layers, faults, folds, and dikes. By sampling many reconstructions from the same observations, we introduce a probabilistic framework for estimating the size and extent of subsurface features. While the realism of the output is bounded by the fidelity of the training data to true geology, this combination of simulation and generative AI functions offers a flexible prior for probabilistic modeling, regional fine-tuning, and use as an AI-based regularizer in traditional geophysical inversion workflows.

cs.CV↗

arXiv2025

Inversion of Magnetic Data using Learned Dictionaries and Scale Space

Magnetic data inversion is an important tool in geophysics, used to infer subsurface magnetic susceptibility distributions from surface magnetic field measurements. This inverse problem is inherently ill-posed, characterized by non-unique solutions, depth ambiguity, and sensitivity to noise. Traditional inversion approaches rely on predefined regularization techniques to stabilize solutions, limiting their adaptability to complex or diverse geological scenarios. In this study, we propose an approach that integrates variable dictionary learning and scale-space methods to address these challenges. Our method employs learned dictionaries, allowing for adaptive representation of complex subsurface features that are difficult to capture with predefined bases. Additionally, we extend classical variational inversion by incorporating multi-scale representations through a scale-space framework, enabling the progressive introduction of structural detail while mitigating overfitting. We implement both fixed and dynamic dictionary learning techniques, with the latter introducing iteration-dependent dictionaries for enhanced flexibility. Using a synthetic dataset to simulate geological scenarios, we demonstrate significant improvements in reconstruction accuracy and robustness compared to conventional variational and dictionary-based methods. Our results highlight the potential of learned dictionaries, especially when coupled with scale-space dynamics, to improve model recovery and noise handling. These findings underscore the promise of our data-driven approach for advance magnetic data inversion and its applications in geophysical exploration, environmental assessment, and mineral prospecting. The code is publicly available at: https://github.com/ahxmeds/magnetic-inversion-dictionary.git.

physics.geo-ph↗