arXiv subjects

Xavier Tricoche

Publications and source records attributed to Xavier Tricoche.

5 recordsLinked to original sources

arXiv2025

Deep Representation Learning for Unsupervised Clustering of Myocardial Fiber Trajectories in Cardiac Diffusion Tensor Imaging

Understanding the complex myocardial architecture is critical for diagnosing and treating heart disease. However, existing methods often struggle to accurately capture this intricate structure from Diffusion Tensor Imaging (DTI) data, particularly due to the lack of ground truth labels and the ambiguous, intertwined nature of fiber trajectories. We present a novel deep learning framework for unsupervised clustering of myocardial fibers, providing a data-driven approach to identifying distinct fiber bundles. We uniquely combine a Bidirectional Long Short-Term Memory network to capture local sequential information along fibers, with a Transformer autoencoder to learn global shape features, with pointwise incorporation of essential anatomical context. Clustering these representations using a density-based algorithm identifies 33 to 62 robust clusters, successfully capturing the subtle distinctions in fiber trajectories with varying levels of granularity. Our framework offers a new, flexible, and quantitative way to analyze myocardial structure, achieving a level of delineation that, to our knowledge, has not been previously achieved, with potential applications in improving surgical planning, characterizing disease-related remodeling, and ultimately, advancing personalized cardiac care.

eess.IV↗

arXiv2025

Meshing of High-Dimensional Toroidal Manifolds from Quasi-Periodic Three-Body Problem Dynamics using Parameterization via Discrete One-Forms

High-dimensional visual computer models are poised to revolutionize the space mission design process. The circular restricted three-body problem (CR3BP) gives rise to high-dimensional toroidal manifolds that are of immense interest to mission designers. We present a meshing technique which leverages an embedding-agnostic parameterization to enable topologically accurate modelling and intuitive visualization of toroidal manifolds in arbitrarily high-dimensional embedding spaces. This work describes the extension of a discrete one-form-based toroidal point cloud meshing method to high-dimensional point clouds sampled along quasi-periodic orbital trajectories in the CR3BP. The resulting meshes are enhanced through the application of an embedding-agnostic triangle-sidedness assignment algorithm. This significantly increases the intuitiveness of interpreting the meshes after they are downprojected to 3D for visualization. These models provide novel surface-based representations of high-dimensional topologies which have so far only been shown as points or curves. This success demonstrates the effectiveness of differential geometric methods for characterizing manifolds with complex, high-dimensional embedding spaces, laying the foundation for new models and visualizations of high-dimensional solution spaces for dynamical systems. Such representations promise to enhance the utility of the three-body problem for the visual inspection and design of space mission trajectories by enabling the application of proven computational surface visualization and analysis methods to underlying solution manifolds.

cs.GR↗

arXiv2023

Out-of-distributional risk bounds for neural operators with applications to the Helmholtz equation

Despite their remarkable success in approximating a wide range of operators defined by PDEs, existing neural operators (NOs) do not necessarily perform well for all physics problems. We focus here on high-frequency waves to highlight possible shortcomings. To resolve these, we propose a subfamily of NOs enabling an enhanced empirical approximation of the nonlinear operator mapping wave speed to solution, or boundary values for the Helmholtz equation on a bounded domain. The latter operator is commonly referred to as the ''forward'' operator in the study of inverse problems. Our methodology draws inspiration from transformers and techniques such as stochastic depth. Our experiments reveal certain surprises in the generalization and the relevance of introducing stochastic depth. Our NOs show superior performance as compared with standard NOs, not only for testing within the training distribution but also for out-of-distribution scenarios. To delve into this observation, we offer an in-depth analysis of the Rademacher complexity associated with our modified models and prove an upper bound tied to their stochastic depth that existing NOs do not satisfy. Furthermore, we obtain a novel out-of-distribution risk bound tailored to Gaussian measures on Banach spaces, again relating stochastic depth with the bound. We conclude by proposing a hypernetwork version of the subfamily of NOs as a surrogate model for the mentioned forward operator.

cs.LG↗

arXiv2022

A Hybrid Lagrangian-Eulerian Model for the Structural Analysis of Multifield Datasets

Multifields datasets are common in a large number of research and engineering applications of computational science. The effective visualization of the corresponding datasets can facilitate their analysis by elucidating the complex and dynamic interactions that exist between the attributes that describe the physics of the phenomenon. We present in this paper a new hybrid Lagrangian-Eulerian model that extends existing Lagrangian visualization techniques to the analysis of multifields problems. In particular, our approach factors in the entire data space to reveal the structure of multifield datasets, thereby combining both Eulerian and Lagrangian perspectives. We evaluate our technique in the context of several fluid dynamics applications. Our results indicate that our proposed approach is able to characterize important structural features that are missed by existing methods.

cs.GR↗

arXiv2022

Improved characterization of Lagrangian coherent structures through time-scale analysis

The computation of Lagrangian coherent structures (LCS) has established itself as a prominent means to reveal significant geometric structures in time-dependent vector fields. Their characterization, however, requires the selection of a suitable time parameter for the construction of the flow map that may not be known in advance. We present in this paper a continuous time-scale framework for LCS extraction and visualization. Specifically, we treat the time axis as a continuum from which a best temporal scale is automatically determined at each spatial location for the extraction of LCS. Beyond its effectiveness with vector fields we show that this method can be successfully applied to improve the characterization of salient structures in tensor fields and discrete maps. We present applications of our method to problems spanning fluid dynamics, medical imaging, and orbital mechanics. The results show that our approach can reveal important structural features that are missed by existing LCS extraction methods.

physics.flu-dyn↗