Related papers: An ensemble algorithm for numerical solutions to d…
Convex regression is a promising area for bridging statistical estimation and deterministic convex optimization. New piecewise linear convex regression methods are fast and scalable, but can have instability when used to approximate…
This paper analyzes the SParareal algorithm for stochastic differential equations (SDEs). Compared to the classical Parareal algorithm, the SParareal algorithm accelerates convergence by introducing stochastic perturbations, achieving…
Conservation laws in the form of elliptic and parabolic partial differential equations (PDEs) are fundamental to the modeling of many problems such as heat transfer and flow in porous media. Many of such PDEs are stochastic due to the…
Weather forecasting has seen a shift in methods from numerical simulations to data-driven systems. While initial research in the area focused on deterministic forecasting, recent works have used diffusion models to produce skillful ensemble…
The purpose of this research work is to employ the Optimal Auxiliary Function Method (OAFM) for obtaining numerical approximations of time-dependent nonlinear partial differential equations (PDEs) that arise in many disciplines of science…
This article develops how to generalize the invariant subspace method for deriving the analytical solutions of the multi-component (N+1)-dimensional coupled nonlinear time-fractional PDEs (NTFPDEs) in the sense of Caputo fractional-order…
In this paper we describe a quantum algorithm to solve sparse systems of nonlinear differential equations whose nonlinear terms are polynomials. The algorithm is nondeterministic and its expected resource requirements are polylogarithmic in…
This paper presents a novel approach to binary classification using dynamic logistic ensemble models. The proposed method addresses the challenges posed by datasets containing inherent internal clusters that lack explicit feature-based…
The paper introduces a new finite element numerical method for the solution of partial differential equations on evolving domains. The approach uses a completely Eulerian description of the domain motion. The physical domain is embedded in…
The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution…
Solving partial differential equations (PDEs) by numerical methods meet computational cost challenge for getting the accurate solution since fine grids and small time steps are required. Machine learning can accelerate this process, but…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…
This work introduces an efficient novel approach for epistemic uncertainty estimation for ensemble models for regression tasks using pairwise-distance estimators (PaiDEs). Utilizing the pairwise-distance between model components, these…
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in…
In this paper, an efficient ensemble domain decomposition algorithm is proposed for fast solving the fully-mixed random Stokes-Darcy model with the physically realistic Beavers-Joseph (BJ) interface conditions. We utilize the Monte Carlo…
Parareal algorithms are studied for semilinear parabolic stochastic partial differential equations. These algorithms proceed as two-level integrators, with fine and coarse schemes, and have been designed to achieve a `parallel in real time'…
We present a hybrid quantum-classical framework for solving general time-dependent parabolic partial differential equations (PDEs) using quantum variational circuits. Building on the QPINN approach, this method applies broadly to parabolic…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
Developing algorithms for solving high-dimensional partial differential equations (PDEs) has been an exceedingly difficult task for a long time, due to the notoriously difficult problem known as the "curse of dimensionality". This paper…