Related papers: Dynamic Conditional Optimal Transport through Simu…
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…
Optimal Transport (OT) problem aims to find a transport plan that bridges two distributions while minimizing a given cost function. OT theory has been widely utilized in generative modeling. In the beginning, OT distance has been used as a…
Data driven methods for time series forecasting that quantify uncertainty open new important possibilities for robot tasks with hard real time constraints, allowing the robot system to make decisions that trade off between reaction time and…
We study dynamic measure transport for generative modeling, focusing on transport maps that connect a source measure $P_0$ to a target measure $P_1$ by integrating a velocity field of the form $v_t(x) = \mathbb{E}[\dot X_t \mid X_t = x]$,…
Conditional score-based diffusion model (SBDM) is for conditional generation of target data with paired data as condition, and has achieved great success in image translation. However, it requires the paired data as condition, and there…
We have developed a new data-driven paradigm for the rapid inference, modeling and simulation of the physics of transport phenomena by deep learning. Using conditional generative adversarial networks (cGAN), we train models for the direct…
We extend the Benamou-Brenier formula from classical optimal transport to weak optimal transport and show that the barycentric optimal transport problem studied by Gozlan and Juillet has a dynamic analogue. We also investigate a martingale…
We present a mathematical framework and computational methods to optimally design a finite number of sequential experiments. We formulate this sequential optimal experimental design (sOED) problem as a finite-horizon partially observable…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
Deep generative models and neural operators have demonstrated significant potential for 3D aerodynamic inference. However, they often face inherent challenges in maintaining physical consistency and preserving high-frequency features,…
To determine causal relationships between two variables, approaches based on Functional Causal Models (FCMs) have been proposed by properly restricting model classes; however, the performance is sensitive to the model assumptions, which…
This paper presents a novel method to generate spatial constraints for motion planning in dynamic environments. Motion planning methods for autonomous driving and mobile robots typically need to rely on the spatial constraints imposed by a…
Generating realistic 3D point clouds is a fundamental problem in computer vision with applications in remote sensing, robotics, and digital object modeling. Existing generative approaches primarily capture geometry, and when semantics are…
The ability to predict the future trajectories of traffic participants is crucial for the safe and efficient operation of autonomous vehicles. In this paper, a diffusion-based generative model for multi-agent trajectory prediction is…
We systematically derive the dissipationless quantum kinetic equation for a multi-band free fermionic system with U(1) symmetry. Using the Moyal product formalism, we fully band-diagonalize the dynamics. Expanding to the second order in…
Flow matching has emerged as a powerful framework for generative modeling, offering computational advantages over diffusion models by leveraging deterministic Ordinary Differential Equations (ODEs) instead of stochastic dynamics. While…
A likelihood-free transport filtering method is proposed based on the couplings between state and observation variables. By exploiting a block-triangular structure in the transport map, the analysis step of filtering is reformulated as the…
Trajectory prediction and generation are crucial for autonomous robots in dynamic environments. While prior research has typically focused on either prediction or generation, our approach unifies these tasks to provide a versatile framework…
We propose a new method for collision-free planning using Conditional Generative Adversarial Networks (cGANs) to transform between the robot's joint space and a latent space that captures only collision-free areas of the joint space,…
We propose a novel conditional diffusion model for contextual portfolio optimization that learns the cross-sectional distribution of next-day stock returns conditioned on high-dimensional asset-specific factors. Our model leverages a…