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In this paper we investigate infinite horizon optimal control problems for parametrized partial differential equations. We are interested in feedback control via dynamic programming equations which is well-known to suffer from the curse of…
Stochastic domain decomposition is proposed as a novel method for solving the two-dimensional Maxwell's equations as used in the magnetotelluric method. The stochastic form of the exact solution of Maxwell's equations is evaluated using…
This paper presents a novel partial differential equation (PDE)-based framework for controlling an ensemble of robots, which have limited sensing and actuation capabilities and exhibit stochastic behaviors, to perform mapping and coverage…
This paper investigates the well-posedness and small-noise asymptotics of a class of stochastic partial differential equations defined on a bounded domain of $\mathbb{R}^d$, where the diffusion coefficient depends nonlinearly and…
Stochastic differential equations (SDEs) are increasingly used in longitudinal data analysis, compartmental models, growth modelling, and other applications in a number of disciplines. Parameter estimation, however, currently requires…
Given multiple images that describe chaotic reaction-diffusion dynamics, parameters of a PDE model are estimated using autosynchronization, where parameters are controlled by synchronization of the model to the observed data. A…
In the task of predicting spatio-temporal fields in environmental science using statistical methods, introducing statistical models inspired by the physics of the underlying phenomena that are numerically efficient is of growing interest.…
Polynomial chaos methods have been extensively used to analyze systems in uncertainty quantification. Furthermore, several approaches exist to determine a low-dimensional approximation (or sparse approximation) for some quantity of interest…
Some recent methods for lossy signal and image compression store only a few selected pixels and fill in the missing structures by inpainting with a partial differential equation (PDE). Suitable operators include the Laplacian, the…
We propose an approach to domain adaptation for semantic segmentation that is both practical and highly accurate. In contrast to previous work, we abandon the use of computationally involved adversarial objectives, network ensembles and…
Partial differential equations (PDEs) are a fundamental tool in the modeling of many real world phenomena. In a number of such real world phenomena the PDEs under consideration contain gradient-dependent nonlinearities and are…
Linear systems with large differences between coefficients ("discontinuous coefficients") arise in many cases in which partial differential equations(PDEs) model physical phenomena involving heterogeneous media. The standard approach to…
The accurate numerical solution of partial differential equations is a central task in numerical analysis allowing to model a wide range of natural phenomena by employing specialized solvers depending on the scenario of application. Here,…
Diffusion models have proven effective for various applications such as images, audio and graph generation. Other important applications are image super-resolution and the solution of inverse problems. More recently, some works have used…
We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…
We propose a new numerical method for one dimensional stochastic differential equations (SDEs). The main idea of this method is based on a representation of a weak solution of a SDE with a time changed Brownian motion, dated back to Doeblin…
This paper proposes a novel computationally efficient dynamic bi-orthogonality based approach for calibration of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on a…
We consider an elliptic partial differential equation with a random diffusion parameter discretized by a stochastic collocation method in the parameter domain and a finite element method in the spatial domain. We prove convergence of an…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…