LDDMM stochastic interpolants: an application to domain uncertainty quantification in hemodynamics

• URL: http://arxiv.org/abs/2603.28324v1
• Date: Mon, 30 Mar 2026 11:52:36 GMT
• Title: LDDMM stochastic interpolants: an application to domain uncertainty quantification in hemodynamics
• Abstract summary: We introduce a novel conditional interpolant framework for generative modeling of three-dimensional shapes.<n>We present an application in the context of cardiovascular simulations, where aortic shapes are generated from an initial cohort of patients.
• Score: 2.003675800246271
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce a novel conditional stochastic interpolant framework for generative modeling of three-dimensional shapes. The method builds on a recent LDDMM-based registration approach to learn the conditional drift between geometries. By leveraging the resulting pull-back and push-forward operators, we extend this formulation beyond standard Cartesian grids to complex shapes and random variables defined on distinct domains. We present an application in the context of cardiovascular simulations, where aortic shapes are generated from an initial cohort of patients. The conditioning variable is a latent geometric representation defined by a set of centerline points and the radii of the corresponding inscribed spheres. This methodology facilitates both data augmentation for three-dimensional biomedical shapes, and the generation of random perturbations of controlled magnitude for a given shape. These capabilities are essential for quantifying the impact of domain uncertainties arising from medical image segmentation on the estimation of relevant biomarkers.

Related papers

• GenSP: Consistent Spherical Parameterization via Learning Shape Generative Models [45.68408819044841]
  We introduce GenSP, a data-driven framework that learns consistent spherical parameterizations across a collection of genus-0 shapes.<n>We address several key challenges in learning such a generative model.<n>Experiments on the ShapeNet dataset demonstrate that our approach significantly reduces geometric distortion.
  arXiv  Detail & Related papers  (2026-07-01T06:19:55Z)
• Riemannian geometry meets fMRI: the advantages of modeling correlation manifolds and eigenvector subspaces [0.0]
  Correlation matrices are fundamental summaries of functional brain networks.<n>Existing geometric methods frequently lack closed-form operations or depend on arbitrary region ordering.<n>We introduce a scalable geometric framework with two components: the Off-log metric and Grassmannian subspace discrimination.
  arXiv  Detail & Related papers  (2026-05-21T11:22:31Z)
• A Mean Curvature Approach to Boundary Detection: Geometric Insights for Unsupervised Learning [52.452902154360565]
  We introduce Mean Curvature Boundary Points (MCBP), a novel geometric framework grounded in Geometric Machine Learning.<n>MCBP explicitly models the intrinsic curvature of the data manifold and computes pointwise mean curvature without requiring principled manifold parametrization.<n>Experiments on synthetic and real-world datasets demonstrate that MCBP consistently improves clustering performance.
  arXiv  Detail & Related papers  (2026-05-05T20:19:09Z)
• ARC-Flow : Articulated, Resolution-Agnostic, Correspondence-Free Matching and Interpolation of 3D Shapes Under Flow Fields [4.706075725469252]
  This work presents a unified framework for the unsupervised prediction of physically plausibles between two 3D articulated shapes.<n>Interpolation is modelled as a diffeomorphic transformation using a smooth, time-varying flow field governed by Neural Ordinary Differential Equations (ODEs)<n>Correspondence is recovered using an efficient Varifold formulation, that is effective on high-fidelity surfaces with differing parameterisations.
  arXiv  Detail & Related papers  (2025-03-04T13:28:05Z)
• Geometric Trajectory Diffusion Models [58.853975433383326]
  Generative models have shown great promise in generating 3D geometric systems. Existing approaches only operate on static structures, neglecting the fact that physical systems are always dynamic in nature. We propose geometric trajectory diffusion models (GeoTDM), the first diffusion model for modeling the temporal distribution of 3D geometric trajectories.
  arXiv  Detail & Related papers  (2024-10-16T20:36:41Z)
• Relative Representations: Topological and Geometric Perspectives [50.85040046976025]
  Relative representations are an established approach to zero-shot model stitching.<n>We introduce a normalization procedure in the relative transformation, resulting in invariance to non-isotropic rescalings and permutations.<n>Second, we propose to deploy topological densification when fine-tuning relative representations, a topological regularization loss encouraging clustering within classes.
  arXiv  Detail & Related papers  (2024-09-17T08:09:22Z)
• Diffusion-Driven Generative Framework for Molecular Conformation Prediction [0.66567375919026]
  The rapid advancement of machine learning has revolutionized the precision of predictive modeling in this context. This research introduces a cutting-edge generative framework named method. Method views atoms as discrete entities and excels in guiding the reversal of diffusion.
  arXiv  Detail & Related papers  (2023-12-22T11:49:39Z)
• Geometric Neural Diffusion Processes [55.891428654434634]
  We extend the framework of diffusion models to incorporate a series of geometric priors in infinite-dimension modelling. We show that with these conditions, the generative functional model admits the same symmetry.
  arXiv  Detail & Related papers  (2023-07-11T16:51:38Z)
• Data-driven reduced-order modelling for blood flow simulations with geometry-informed snapshots [0.0]
  A data-driven surrogate model is proposed for the efficient prediction of blood flow simulations on similar but distinct domains. A non-intrusive reduced-order model for geometrical parameters is constructed using proper decomposition. A radial basis function interpolator is trained for predicting the reduced coefficients of the reduced-order model.
  arXiv  Detail & Related papers  (2023-02-21T21:18:17Z)
• Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data [50.23363975709122]
  We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing panel data. We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem. We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms.
  arXiv  Detail & Related papers  (2022-02-18T22:41:51Z)
• Inverse Learning of Symmetries [71.62109774068064]
  We learn the symmetry transformation with a model consisting of two latent subspaces. Our approach is based on the deep information bottleneck in combination with a continuous mutual information regulariser. Our model outperforms state-of-the-art methods on artificial and molecular datasets.
  arXiv  Detail & Related papers  (2020-02-07T13:48:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.