相关论文: Taylor approximation and variance reduction for PD…

We introduce a framework for approximate dynamic programming that we apply to discrete time chains on $\mathbb{Z}_+^d$ with countable action sets. Our approach is grounded in the approximation of the (controlled) chain's generator by that…

We consider the optimal control of a PDE with random source term subject to probabilistic or almost sure state constraints. In the main theoretical result, we provide an exact formula for the Clarke subdifferential of the probability…

Hyperparameter tuning is a challenging problem especially when the system itself involves uncertainty. Due to noisy function evaluations, optimization under uncertainty can be computationally expensive. In this paper, we present a novel…

We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element…

Brittle optimization has been observed to adversely impact model likelihoods for regression and VAEs when simultaneously fitting neural network mappings from a (random) variable onto the mean and variance of a dependent Gaussian variable.…

A novel inner approximation algorithm is proposed for dynamic optimization problems to ensure strict satisfaction of path constraints. Distinct from traditional methods relying on interval analysis, the proposed algorithm leverages the…

To help resolve issues of non-realizability and restriction to homogeneity faced by analytical theories of turbulence, we explore three-dimensional homogeneous shear turbulence of incompressible Newtonian fluids via optimal control and…

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…

We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a "budget"…

Variability in multiple independent input parameters makes it difficult to estimate the resultant variability in the system's overall response. The Propagation of Errors and Monte-Carlo techniques are two major methods to predict the…

We present a parameter estimation method in Ordinary Differential Equation (ODE) models. Due to complex relationships between parameters and states the use of standard techniques such as nonlinear least squares can lead to the presence of…

Model predictive control is an advanced control approach for multivariable systems with constraints, which is reliant on an accurate dynamic model. Most real dynamic models are however affected by uncertainties, which can lead to…

Computing partial differential equation (PDE) operators via nested backpropagation is expensive, yet popular, and severely restricts their utility for scientific machine learning. Recent advances, like the forward Laplacian and randomizing…

We present a novel control variate technique for enhancing the efficiency of Monte Carlo (MC) estimation of expectations involving solutions to stochastic differential equations (SDEs). Our method integrates a primary fine-time-step…

In this paper we study model reduction of linear and bilinear quadratic stochastic control problems with parameter uncertainties. Specifically, we consider slow-fast systems with unknown diffusion coefficient and study the convergence of…

We describe and analyze a variance reduction approach for Monte Carlo (MC) sampling that accelerates the estimation of statistics of computationally expensive simulation models using an ensemble of models with lower cost. These lower cost…

Taylor's formula holds significant importance in function representation, such as solving differential difference equations, ordinary differential equations, partial differential equations, and further promotes applications in visual…

Variational inference has become one of the most widely used methods in latent variable modeling. In its basic form, variational inference employs a fully factorized variational distribution and minimizes its KL divergence to the posterior.…

In this paper, we propose the uncertain volatility models with stochastic bounds. Like the regular uncertain volatility models, we know only that the true model lies in a family of progressively measurable and bounded processes, but instead…

Enlightened from the inverse consideration of the stable continuous-time dynamics evolution, the Variation Evolving Method (VEM) analogizes the optimal solution to the equilibrium point of an infinite-dimensional dynamic system and solves…