Related papers: GeONet: a neural operator for learning the Wassers…

Neural ordinary differential equations (ODEs) provide expressive representations of invertible transport maps that can be used to approximate complex probability distributions, e.g., for generative modeling, density estimation, and Bayesian…

Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution…

We introduce Deep Set Linearized Optimal Transport, an algorithm designed for the efficient simultaneous embedding of point clouds into an $L^2-$space. This embedding preserves specific low-dimensional structures within the Wasserstein…

We introduce sliced optimal transport dataset distance (s-OTDD), a model-agnostic, embedding-agnostic approach for dataset comparison that requires no training, is robust to variations in the number of classes, and can handle disjoint label…

Dataset distillation seeks to synthesize a compact distilled dataset, enabling models trained on it to achieve performance comparable to models trained on the full dataset. Recent methods for large-scale datasets focus on matching global…

Despite the recent popularity of neural network-based solvers for optimal transport (OT), there is no standard quantitative way to evaluate their performance. In this paper, we address this issue for quadratic-cost transport --…

Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be…

Fast and accurate predictions for complex physical dynamics are a significant challenge across various applications. Real-time prediction on resource-constrained hardware is even more crucial in real-world problems. The deep operator…

Generative Adversarial Nets (GANs) are very successful at modeling distributions from given samples, even in the high-dimensional case. However, their formulation is also known to be hard to optimize and often not stable. While this is…

Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…

Optimal Transport (OT) has recently emerged as a powerful framework for learning minimal-displacement maps between distributions. The predominant approach involves a neural parametrization of the Monge formulation of OT, typically assuming…

The simulation of complex physical systems using a discretized mesh is a cornerstone of applied mechanics, but traditional numerical solvers are often computationally prohibitive for many-query tasks. While Graph Neural Networks (GNNs) have…

Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions. \OT~suffers however from a few drawbacks, computational and statistical, which have encouraged the proposal of several regularized variants…

We present GeGnn, a learning-based method for computing the approximate geodesic distance between two arbitrary points on discrete polyhedra surfaces with constant time complexity after fast precomputation. Previous relevant methods either…

This paper raises an implicit manifold learning perspective in Generative Adversarial Networks (GANs), by studying how the support of the learned distribution, modelled as a submanifold $\mathcal{M}_{\theta}$, perfectly match with…

Given a collection of probability measures, a practitioner sometimes needs to find an "average" distribution which adequately aggregates reference distributions. A theoretically appealing notion of such an average is the Wasserstein…

This paper provides a simple procedure to fit generative networks to target distributions, with the goal of a small Wasserstein distance (or other optimal transport costs). The approach is based on two principles: (a) if the source…

Nonlinear structural analyses in engineering often require extensive finite element simulations, limiting their applicability in design optimization and real-time control. Conventional deep learning surrogates often struggle with complex,…

Issued from Optimal Transport, the Wasserstein distance has gained importance in Machine Learning due to its appealing geometrical properties and the increasing availability of efficient approximations. In this work, we consider the problem…

Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data…