相关论文: Efficient and accurate nonlinear model reduction v…
Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However, solving these PDEs repeatedly can be prohibitively…
We present a method for approximating the solution of a parameterized, nonlinear dynamical system using an affine combination of solutions computed at other points in the input parameter space. The coefficients of the affine combination are…
The Empirical Interpolation Method (EIM) and its generalized version (GEIM) can be used to approximate a physical system by combining data measured from the system itself and a reduced model representing the underlying physics. In presence…
Nonlinear parametric inverse problems appear in several prominent applications; one such application is Diffuse Optical Tomography (DOT) in medical image reconstruction. Such inverse problems present huge computational challenges, mostly…
We develop and analyze a posteriori error estimators for a proper orthogonal decomposition-discrete empirical interpolation method (Pod-Deim) reduced order model applied to a parametric Poisson equation posed on a parameter-dependent domain…
In present paper we propose seemingly new method for finding solutions of some types of nonlinear PDEs in closed form. The method is based on decomposition of nonlinear operators on sequence of operators of lower orders. It is shown that…
In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties that originate from active forces generated from…
In this paper, we study numerically the linear damped second-order hyperbolic partial differential equation (PDE) with affine parameter dependence using a goal-oriented approach by finite element (FE) and reduced basis (RB) methods. The…
This paper is concerned with the numerical approximation of quantities of interest associated with solutions to parametric elliptic partial differential equations (PDEs). The key novelty of this work is in its focus on the quantities of…
Most simulation schemes for partial differential equations (PDEs) focus on minimizing a simple error norm of a discretized version of a field. This paper takes a fundamentally different approach; the discretized field is interpreted as data…
This paper presents a structure-exploiting nonlinear model reduction method for systems with general nonlinearities. First, the nonlinear model is lifted to a model with more structure via variable transformations and the introduction of…
In recent years, the immersed finite element methods (IFEM) introduced in \cite{Li2003}, \cite{Li2004} to solve elliptic problems having an interface in the domain due to the discontinuity of coefficients are getting more attentions of…
In this work, we aim at efficiently solving a parametrized family of optimal transport problems by using model order reduction methods. We propose a reduced-order model by adding to the primal (respectively dual) version of the…
The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction…
In this paper we consider the numerical approximation of a semilinear reaction-diffusion model problem (PDEs) by means of reduced order methods (ROMs) based on proper orthogonal decomposition (POD). We focus on the time integration of the…
We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancements in loss functions and network architectures have…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
This work investigates the use of sparse polynomial interpolation as a model order reduction method for the incompressible Navier-Stokes equations. Numerical results are presented underscoring the validity of sparse polynomial…