Related papers: DiffuSolve: Diffusion-based Solver for Non-convex …

Offline multi-objective optimization aims to identify Pareto-optimal solutions given a dataset of designs and their objective values. In this work, we propose a preference-guided diffusion model that generates Pareto-optimal designs by…

We propose DiffusionRollout, a novel selective rollout planning strategy for autoregressive diffusion models, aimed at mitigating error accumulation in long-horizon predictions of physical systems governed by partial differential equations…

Reliable and efficient trajectory generation methods are a fundamental need for autonomous dynamical systems of tomorrow. The goal of this article is to provide a comprehensive tutorial of three major convex optimization-based trajectory…

Diffusion probabilistic models (DPMs) have achieved impressive success in high-resolution image synthesis, especially in recent large-scale text-to-image generation applications. An essential technique for improving the sample quality of…

Evolutionary algorithms have been successful in solving multi-objective optimization problems (MOPs). However, as a class of population-based search methodology, evolutionary algorithms require a large number of evaluations of the objective…

The objective of trajectory optimization algorithms is to achieve an optimal collision-free path between a start and goal state. In real-world scenarios where environments can be complex and non-homogeneous, a robot needs to be able to…

Recent advances in motion planning for autonomous driving have led to models capable of generating high-quality trajectories. However, most existing planners tend to fix their policy after supervised training, leading to consistent but…

Gasoline blending scheduling uses resource allocation and operation sequencing to meet a refinery's production requirements. The presence of nonlinearity, integer constraints, and a large number of decision variables adds complexity to this…

Diffusion models have emerged as powerful generative tools with applications in computer vision and scientific machine learning (SciML), where they have been used to solve large-scale probabilistic inverse problems. Traditionally, these…

Motivated by the problem of pursuit-evasion, we present a motion planning framework that combines energy-based diffusion models with artificial potential fields for robust real time trajectory generation in complex environments. Our…

This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [20] and extends those…

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…

Our goal is to develop a flux limiter of the Flux-Corrected Transport method for a nonconservative convection-diffusion equation. For this, we consider a hybrid difference scheme that is a linear combination of a monotone scheme and a…

Diffusion model-based approaches have shown promise in data-driven planning, but there are no safety guarantees, thus making it hard to be applied for safety-critical applications. To address these challenges, we propose a new method,…

We present our deep learning framework to solve and accelerate the Time-Dependent partial differential equation's solution of one and two spatial dimensions. We demonstrate DiffusionNet solver by solving the 2D transient heat conduction…

Various bias-correction methods such as EXTRA, gradient tracking methods, and exact diffusion have been proposed recently to solve distributed {\em deterministic} optimization problems. These methods employ constant step-sizes and converge…

Abstract Diffusion models have recently gained prominence as a novel category of generative models. Despite their success, these models face a notable drawback in terms of slow sampling speeds, requiring a high number of function…

Diffusion models have shown remarkable potential in planning and control tasks due to their ability to represent multimodal distributions over actions and trajectories. However, ensuring safety under constraints remains a critical challenge…

Non-linear Trajectory Optimisation (TO) methods require good initial guesses to converge to a locally optimal solution. A feasible guess can often be obtained by allocating a large amount of time for the trajectory to complete. However for…

Drivable Free-space prediction is a fundamental and crucial problem in autonomous driving. Recent works have addressed the problem by representing the entire non-obstacle road regions as the free-space. In contrast our aim is to estimate…