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Variational-hemivariational inequalities are an important mathematical framework for nonsmooth problems. The framework can be used to study application problems from physical sciences and engineering that involve non-smooth and even…
The $G$-expectation framework is a generalization of the classical probabilistic system motivated by Knightian uncertainty, where the $G$-normal plays a central role. However, from a statistical perspective, $G$-normal distributions look…
We develop a pure Monte Carlo method to compute $E(g(X_T))$ where $g$ is a bounded and Lipschitz function and $X_t$ an Ito process. This approach extends a previously proposed method to the general multidimensional case with a SDE with…
In this paper, we present first-order accurate numerical methods for solution of the heat equation with uncertain temperature-dependent thermal conductivity. Each algorithm yields a shared coefficient matrix for the ensemble set improving…
In this paper we study mean-variance hedging under the G-expectation framework. Our analysis is carried out by exploiting the G-martingale representation theorem and the related probabilistic tools, in a contin- uous financial market with…
In this paper we consider two ways to generalize the mathematical expectation of a random variable, the Choquet expectation and Peng's g-expectation. An open question has been, after making suitable restrictions to the class of random…
Accurate characterization of entropy plays a pivotal role in capturing reversible and irreversible heating in supercapacitors during charging/discharging cycles. However, numerical methods that can faithfully capture entropy variation in…
Quantification and minimization of uncertainty is an important task in the design of electromagnetic devices, which comes with high computational effort. We propose a hybrid approach combining the reliability and accuracy of a Monte Carlo…
Multifidelity Monte Carlo methods rely on a hierarchy of possibly less accurate but statistically correlated simplified or reduced models, in order to accelerate the estimation of statistics of high-fidelity models without compromising the…
The present study concerns the numerical homogenization of second order hyperbolic equations in non-divergence form, where the model problem includes a rapidly oscillating coefficient function. These small scales influence the large scale…
We present iterative Monte Carlo algorithm for which the temperature variable is attracted by a critical point. The algorithm combines techniques of single histogram reweighting and linear filtering. The 2d Ising model of ferromagnet is…
In this paper, we propose and analyze a new stochastic homogenization method for diffusion equations with random and fast oscillatory coefficients. In the proposed method, the homogenized solutions are sought through a two-stage procedure.…
Counterfactual prediction is a fundamental task in decision-making. G-computation is a method for estimating expected counterfactual outcomes under dynamic time-varying treatment strategies. Existing G-computation implementations have…
There is growing interest in a hybrid control design for treatment evaluation, where a randomized controlled trial is augmented with external control data from a previous trial or a real world data source. The hybrid control design has the…
We develop a virtual element method to solve a convective Brinkman-Forchheimer problem coupled with a heat equation. This coupled model may allow for thermal diffusion and viscosity as a function of temperature. Under standard…
We investigate a weak space-time formulation of the heat equation and its use for the construction of a numerical scheme. The formulation is based on a known weak space-time formulation, with the difference that a pointwise component of the…
This paper presents a novel numerical method for the hybrid reliability analysis by using the uncertainty theory. Aleatory uncertainty and epistemic uncertainty are considered simultaneously in this method. Epistemic uncertainty is…
We propose a new approach to the numerical solution of ergodic problems arising in the homogenization of Hamilton-Jacobi (HJ) equations. It is based on a Newton-like method for solving inconsistent systems of nonlinear equations, coming…
In this paper a model for partial melts is constructed using two-scale homogenization theory. While this technique is well known to the mathematics and materials communities, it is relatively novel to problems in the solid Earth. This…
We present a hybrid asymptotic/numerical method for the accurate computation of single and double layer heat potentials in two dimensions. It has been shown in previous work that simple quadrature schemes suffer from a phenomenon called…