Related papers: Uncertain Data in Initial Boundary Value Problems:…

Initial-boundary value problems in a bounded rectangle with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global well-posedness in the classes of weak and regular solution…

An effective approach to exploration in reinforcement learning is to rely on an agent's uncertainty over the optimal policy, which can yield near-optimal exploration strategies in tabular settings. However, in non-tabular settings that…

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods…

The stability theory for hyperbolic initial boundary value problems relies most of the time on the Laplace transform with respect to the time variable. For technical reasons, this usually restricts the validity of stability estimates to the…

When the underlying conditional density is known, conditional expectations can be computed analytically or numerically. When, however, such knowledge is not available and instead we are given a collection of training data, the goal of this…

In discrete choice panel data, estimation of average effects is crucial for quantifying the effect of covariates, and for policy evaluation and counterfactual analysis. However, in short panels with individual-specific effects, challenges…

We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…

Force fluctuations in granular materials are investigated. A continuum equation is derived starting from a discrete model proposed in the literature. The influence of boundary conditions is investigated. For periodic boundary conditions the…

We seek possible statistical consequences of the way a forcing term is added to the Navier--Stokes equations in the Direct Numerical Simulation (DNS) of incompressible channel flow. Simulations driven by constant flow rate, constant…

In this work, we study the initial boundary value problem for a non-strictly hyperbolic $2\times2$ system of equations in the quarter plane $x>0,t>0$ which is derived from Eulerian droplet model for air particle flow for velocity and volume…

The socioeconomic impact of pollution naturally comes with uncertainty due to, e.g., current new technological developments in emissions' abatement or demographic changes. On top of that, the trend of the future costs of the environmental…

We develop a cross-sectional research design to identify causal effects in the presence of unobservable heterogeneity without instruments. When units are dense in physical space, it may be sufficient to regress the "spatial first…

In a recent preprint (arXiv:1211.4285v1) we addressed the problem of constructing reduced models for time-dependent systems described by differential equations which involve uncertain parameters. In the current work, we focus on the…

We study identifying and estimating the causal effect of a treatment variable on a long-term outcome using data from an observational and an experimental domain. The observational data are subject to unobserved confounding. Furthermore,…

Using the quantum transition path time probability distribution we show that time averaging of weak values leads to unexpected results. We prove a weak value time energy uncertainty principle and time energy commutation relation. We also…

An uncertainty quantification framework is developed for Eulerian-Lagrangian models of particle-laden flows, where the fluid is modeled through a system of partial differential equations in the Eulerian frame and inertial particles are…

This paper discusses the fundamental principles of causal inference - the area of statistics that estimates the effect of specific occurrences, treatments, interventions, and exposures on a given outcome from experimental and observational…

The paper is devoted to constructing the global solutions around global Maxwellians to the initial-boundary value problem on the Boltzmann equation in general bounded domains with isothermal diffuse reflection boundaries. We allow a class…

In this paper, we consider an initial boundary value problem for Maxwell's equations. For this hyperbolic type problem, we derive guaranteed and computable upper bounds for the difference between the exact solution and any pair of vector…

We consider the large time asymptotic behavior of the global solutions to the initial value problem for the nonlinear damped wave equation with slowly decaying initial data. When the initial data decay fast enough, it is known that the…