相关论文: Generative modeling of time-dependent densities vi…

Flow-based methods for sampling and generative modeling use continuous-time dynamical systems to represent a {transport map} that pushes forward a source measure to a target measure. The introduction of a time axis provides considerable…

We propose a new framework for generative modeling based on a discrete-time stochastic control formulation of measure transport. Adapting classic results from control theory, we formulate our problem as a linear program whose dual variables…

Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…

We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the…

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent)…

The ability to compare two degenerate probability distributions (i.e. two probability distributions supported on two distinct low-dimensional manifolds living in a much higher-dimensional space) is a crucial problem arising in the…

By building upon the recent theory that established the connection between implicit generative modeling (IGM) and optimal transport, in this study, we propose a novel parameter-free algorithm for learning the underlying distributions of…

Given a set of $K$ probability densities, we consider the multimarginal generative modeling problem of learning a joint distribution that recovers these densities as marginals. The structure of this joint distribution should identify…

This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these…

Ray tracing has become a standard for accurate radio propagation modeling, but suffers from exponential computational complexity, as the number of candidate paths scales with the number of objects raised to the interaction order. This…

We propose the Selective Densification method for fast motion planning through configuration space. We create a sequence of roadmaps by iteratively adding configurations. We organize these roadmaps into layers and add edges between…

We present a general (i.e., independent of the underlying model) interpolation technique based on optimal transportation of Gaussian models for parametric advection-dominated problems. The approach relies on a scalar testing function to…

Sampling conditional distributions is a fundamental task for Bayesian inference and density estimation. Generative models, such as normalizing flows and generative adversarial networks, characterize conditional distributions by learning a…

We present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks, normalizing flows, variational auto-encoders, are usually considered as…

We propose the tensorizing flow method for estimating high-dimensional probability density functions from the observed data. The method is based on tensor-train and flow-based generative modeling. Our method first efficiently constructs an…

Traffic congestion has lead to an increasing emphasis on management measures for a more efficient utilization of existing infrastructure. In this context, this paper proposes a novel framework that integrates real-time optimization of…

Generative Design (GD) combines artificial intelligence (AI), physics-based modeling, and multi-objective optimization to autonomously explore and refine engineering designs. Despite its promise in aerospace, automotive, and other…

We investigate the problem of sampling from posterior distributions with intractable normalizing constants in Bayesian inference. Our solution is a new generative modeling approach based on optimal transport (OT) that learns a deterministic…

Generative models inspired by dynamical transport of measure -- such as flows and diffusions -- construct a continuous-time map between two probability densities. Conventionally, one of these is the target density, only accessible through…

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.…