Related papers: Towards Generative Design Using Optimal Transport …
Optimal transport (OT), and in particular the Wasserstein distance, has seen a surge of interest and applications in machine learning. However, empirical approximation under Wasserstein distances suffers from a severe curse of…
This paper presents GO-GAN, a novel Generative Adversarial Network (GAN) architecture for geometry optimization (GO), specifically to generate structures based on user-specified input parameters. The architecture for GO-GAN proposed here…
When predicting observations across space and time, the spatial layout of errors impacts a model's real-world utility. For instance, in bike sharing demand prediction, error patterns translate to relocation costs. However, commonly used…
Diffusion models recently developed for generative AI tasks can produce high-quality samples while still maintaining diversity among samples to promote mode coverage, providing a promising path for learning stochastic closure models.…
Grassmannian manifold offers a powerful carrier for geometric representation learning by modelling high-dimensional data as low-dimensional subspaces. However, existing approaches predominantly rely on static single-subspace…
Recent progress in geometric deep learning has drawn increasing attention from the machine learning community toward domain adaptation on symmetric positive definite (SPD) manifolds, especially for neuroimaging data that often suffer from…
Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground…
The objective in statistical Optimal Transport (OT) is to consistently estimate the optimal transport plan/map solely using samples from the given source and target marginal distributions. This work takes the novel approach of posing…
We study the use of amortized optimization to predict optimal transport (OT) maps from the input measures, which we call Meta OT. This helps repeatedly solve similar OT problems between different measures by leveraging the knowledge and…
This paper addresses the practical challenge in Entropic Optimal Transport (EOT) where the underlying ground cost function is typically latent and unobserved. Rather than assuming a fixed geometric cost, we adopt a data-driven approach…
Effective monitoring of freight transportation is essential for advancing sustainable, low-carbon economies. Traditional methods relying on single-modal data and discrete simulations fall short in optimizing intermodal systems holistically.…
Generative modelling is a key tool in unsupervised machine learning which has achieved stellar success in recent years. Despite this huge success, even the best generative models such as Generative Adversarial Networks (GANs) and…
A key challenge in metasurface design is the development of algorithms that can effectively and efficiently produce high performance devices. Design methods based on iterative optimization can push the performance limits of metasurfaces,…
In machine learning and computer graphics, a fundamental task is the approximation of a probability density function through a well-dispersed collection of samples. Providing a formal metric for measuring the distance between probability…
Computing optimal transport maps between high-dimensional and continuous distributions is a challenging problem in optimal transport (OT). Generative adversarial networks (GANs) are powerful generative models which have been successfully…
The geometric multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared…
There is a recent surge in the development of spatio-temporal forecasting models in the transportation domain. Long-range traffic forecasting, however, remains a challenging task due to the intricate and extensive spatio-temporal…
Optimal transport (OT) is a powerful geometric and probabilistic tool for finding correspondences and measuring similarity between two distributions. Yet, its original formulation relies on the existence of a cost function between the…
In machine learning, Optimal Transport (OT) theory is extensively utilized to compare probability distributions across various applications, such as graph data represented by node distributions and image data represented by pixel…
In this paper, we introduce a neural network-based method to address the high-dimensional dynamic unbalanced optimal transport (UOT) problem. Dynamic UOT focuses on the optimal transportation between two densities with unequal total mass,…