Related papers: Geometric Operator Learning with Optimal Transport

Forecasting motion of a specific target object is a common problem for surgical interventions, e.g. for localization of a target region, guidance for surgical interventions, or motion compensation. Optical coherence tomography (OCT) is an…

This work introduces AD-SVFD, a deep learning model for the deformable registration of vascular shapes to a pre-defined reference and for the generation of synthetic anatomies. AD-SVFD operates by representing each geometry as a weighted…

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient(PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on…

Sampling from diffusion probabilistic models (DPMs) can be viewed as a piecewise distribution transformation, which generally requires hundreds or thousands of steps of the inverse diffusion trajectory to get a high-quality image. Recent…

Unbalanced Optimal Transport (UOT) has emerged as a robust relaxation of standard Optimal Transport, particularly effective for handling outliers and mass variations. However, scalable algorithms for UOT, specifically those based on…

Optimal transport (OT) is a powerful tool in mathematics and data science but faces severe computational and statistical challenges in high dimensions. We propose convex relaxation approaches based on marginal and cluster moment relaxations…

We introduce ODE-GS, a novel approach that integrates 3D Gaussian Splatting with latent neural ordinary differential equations (ODEs) to enable future extrapolation of dynamic 3D scenes. Unlike existing dynamic scene reconstruction methods,…

OD matrix estimation is a critical problem in the transportation domain. The principle method uses the traffic sensor measured information such as traffic counts to estimate the traffic demand represented by the OD matrix. The problem is…

While 3D Gaussian Splatting (3DGS) has revolutionized 3D reconstruction, it suffers from significant overhead due to massive redundant primitives. Existing compression methods typically rely on local sampling or fixed pruning thresholds,…

Imbalanced data pose challenges for deep learning based classification models. One of the most widely-used approaches for tackling imbalanced data is re-weighting, where training samples are associated with different weights in the loss…

Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural…

Combinatorial optimization problems (COPs) are an important research topic in various fields. In recent times, there have been many attempts to solve COPs using deep learning-based approaches. We propose a novel neural network model that…

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional…

In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep…

Dynamic imaging is critical for understanding and visualizing dynamic biological processes in medicine and cell biology. These applications often encounter the challenge of a limited amount of time series data and time points, which hinders…

Optimal Transport (OT) based distances are powerful tools for machine learning to compare probability measures and manipulate them using OT maps. In this field, a setting of interest is semi-discrete OT, where the source measure $\mu$ is…

We present a neural framework for learning conditional optimal transport (OT) maps between probability distributions. Our approach introduces a conditioning mechanism capable of processing both categorical and continuous conditioning…

We improve the accuracy of Guidance & Control Networks (G&CNETs), trained to represent the optimal control policies of a time-optimal transfer and a mass-optimal landing, respectively. In both cases we leverage the dynamics of the…

Neural networks have been applied to control problems, typically by combining data, differential equation residuals, and objective costs in the training loss or by incorporating auxiliary architectural components. Instead, we propose a…

We propose the geometry-informed neural operator (GINO), a highly efficient approach to learning the solution operator of large-scale partial differential equations with varying geometries. GINO uses a signed distance function and…