Related papers: Stochastic collocation schemes for Neural Field Eq…
Wideband communication receivers often deal with the problems of detecting weak signals from distant sources received together with strong nearby interferers. When the techniques of random modulation are used in communication system…
Stochastic parametrisations are used in weather and climate models to improve the representation of unpredictable unresolved processes. When compared to a deterministic model, a stochastic model represents `model uncertainty', i.e., sources…
In this paper we introduce concepts from uncertainty quantification (UQ) and numerical analysis for the efficient evaluation of stochastic high dimensional Newton iterates. In particular, we develop complex analytic regularity theory of the…
In this contribution, we provide convergence rates for a finite volume scheme of a stochastic non-linear parabolic equation with multiplicative Lipschitz noise and homogeneous Neumann boundary conditions. More precisely, we give an error…
We present a highly scalable strategy for developing mesh-free neuro-symbolic partial differential equation solvers from existing numerical discretizations found in scientific computing. This strategy is unique in that it can be used to…
We present an approach to deep estimation of discrete conditional probability distributions. Such models have several applications, including generative modeling of audio, image, and video data. Our approach combines two main techniques:…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…
We propose new numerical schemes for decoupled forward-backward stochastic differential equations (FBSDEs) with jumps, where the stochastic dynamics are driven by a $d$-dimensional Brownian motion and an independent compensated Poisson…
We address the problem of uncertainty calibration. While standard deep neural networks typically yield uncalibrated predictions, calibrated confidence scores that are representative of the true likelihood of a prediction can be achieved…
In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…
This paper presents a stabilized sequential quadratic programming (SQP) method for solving optimization problems in Banach spaces. The optimization problem considered in this study has a general form that enables us to represent various…
In this paper, we study discrete Carleman estimates for space semi-discrete approximations of one-dimensional stochastic parabolic equation. As applications of these discrete Carleman estimates, we apply them to study two inverse problems…
In this paper we investigate the numerical solution of stochastic partial differential equations (SPDEs) for a wider class of stochastic equations. We focus on non-diagonal colored noise instead of the usual space-time white noise. By…
We develop a distributed stochastic gradient descent algorithm for solving non-convex optimization problems under the assumption that the local objective functions are twice continuously differentiable with Lipschitz continuous gradients…
This work is concerned with the propagation of uncertainty across coupled domain problems with high-dimensional random inputs. A stochastic model reduction approach based on low-rank separated representations is proposed for the partitioned…
Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…
We propose an accurate data-driven numerical scheme to solve Stochastic Differential Equations (SDEs), by taking large time steps. The SDE discretization is built up by means of a polynomial chaos expansion method, on the basis of…
In this work, we investigate a stochastic gradient descent method for solving inverse problems that can be written as systems of linear or nonlinear ill-posed equations in Banach spaces. The method uses only a randomly selected equation at…
We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the…