相关论文: Efficient Computation of Mean field Control based …

We consider probabilistic models for sequential observations which exhibit gradual transitions among a finite number of states. We are particularly motivated by applications such as human activity analysis where observed accelerometer time…

This work is motivated by the need to study the impact of data uncertainties and material imperfections on the solution to optimal control problems constrained by partial differential equations. We consider a pathwise optimal control…

Many partial differential equations (PDEs) such as Navier--Stokes equations in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do not have an exact, primal variational structure. Recently,…

Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…

With the rapidly growing model complexity and data volume, training deep generative models (DGMs) for better performance has becoming an increasingly more important challenge. Previous research on this problem has mainly focused on…

Numerical simulation of flow problems and wave propagation in heterogeneous media has important applications in many engineering areas. However, numerical solutions on the fine grid are often prohibitively expensive, and multiscale model…

We design and compute first-order implicit-in-time variational schemes with high-order spatial discretization for initial value gradient flows in generalized optimal transport metric spaces. We first review some examples of gradient flows…

We prove quasi-optimal $L^\infty$ norm error estimates (up to logarithmic factors) for the solution of Poisson's problem by the standard Hybridizable Discontinuous Galerkin (HDG) method. Although such estimates are available for conforming…

We present a unified, finite-element-native variational inference framework for very high-dimensional Bayesian spatial field reconstruction in physics-based problems governed by partial differential equations (PDEs) that are nonlinear in…

Sampling from nonsmooth target probability distributions is essential in various applications, including the Bayesian Lasso. We propose a splitting-based sampling algorithm for the time-implicit discretization of the probability flow for…

Liquid droplet dynamics are widely used in biological and engineering applications, which contain complex interfacial instabilities and pattern formation such as droplet merging, splitting, and transport. This paper studies a class of mean…

Distributionally robust control (DRC) aims to effectively manage distributional ambiguity in stochastic systems. While most existing works address inaccurate distributional information in fully observable settings, we consider a partially…

Dataset Distillation (DD) aims to generate a compact synthetic dataset that enables models to achieve performance comparable to training on the full large dataset, significantly reducing computational costs. Drawing from optimal transport…

Many engineering systems are subject to spatially distributed uncertainty, i.e. uncertainty that can be modeled as a random field. Altering the mean or covariance of this uncertainty will in general change the statistical distribution of…

This paper presents Density-based Predictive Control (DPC), a novel multi-agent control strategy for efficient non-uniform area coverage, grounded in optimal transport theory. In large-scale scenarios such as search and rescue or…

Large-scale competitive market equilibrium problems arise in a wide range of important applications, including economic decision-making and intelligent manufacturing. Traditional solution methods, such as interior-point algorithms and…

We propose a new hybridizable discontinuous Galerkin (HDG) method to approximate the solution of a Dirichlet boundary control problem governed by an elliptic convection diffusion PDE. Even without a convection term, Dirichlet boundary…

A method is presented for the numerical solution of optimal boundary control problems governed by parabolic partial differential equations. The continuous space-time optimal control problem is transcribed into a sparse nonlinear programming…

In black-box function optimization, we need to consider not only controllable design variables but also uncontrollable stochastic environment variables. In such cases, it is necessary to solve the optimization problem by taking into account…

We present a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. We consider a symmetric integral form of these nonlocal equations defined on general geometries and in arbitrary bounded…