Related papers: Interval-based parameter identification for struct…
In this paper, we address the identification problem for the systems characterized by linear time-invariant dynamics with bilinear observation models. More precisely, we consider a suitable parametric description of the system and formulate…
Interval identification of parameters such as average treatment effects, average partial effects and welfare is particularly common when using observational data and experimental data with imperfect compliance due to the endogeneity of…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
The Intrinsic Surface Finite Element Method (ISFEM) was recently proposed to solve Partial Differential Equations (PDEs) on surfaces. ISFEM proceeds by writing the PDE with respect to a local coordinate system anchored to the surface and…
A problem of identification of piecewise-constant unknown parameters of a linear regression equation (LRE) is considered. Such parameters change their values over the interval of the regressor finite (rather than persistent) excitation. To…
We present the Finite Element Method (FEM) for the numerical solution of the multidimensional coefficient inverse problem (MCIP) in two dimensions. This method is used for explicit reconstruction of the coefficient in the hyperbolic…
In this paper, we develop a class of interacting particle Langevin algorithms to solve inverse problems for partial differential equations (PDEs). In particular, we leverage the statistical finite elements (statFEM) formulation to obtain a…
The numerical approximation of an inverse problem subject to the convection--diffusion equation when diffusion dominates is studied. We derive Carleman estimates that are on a form suitable for use in numerical analysis and with explicit…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to allow for piecewise stationarity, where the model is allowed to change at given time points. We propose a three-stage procedure for…
We discuss methods for {\em a priori} selection of parameters to be estimated in inverse problem formulations (such as Maximum Likelihood, Ordinary and Generalized Least Squares) for dynamical systems with numerous state variables and an…
A boundary element method (BEM) simulation is used to compare the efficiency of numerical inverse Laplace transform strategies, considering general requirements of Laplace-space numerical approaches. The two-dimensional BEM solution is used…
Control and state estimation procedures need to be robust against imprecisely known parameters, uncertainty in initial conditions, and external disturbances. Interval methods and other set-based techniques form the basis for the…
We present a new fixed mesh algorithm for solving a class of interface inverse problems for the typical elliptic interface problems. These interface inverse problems are formulated as shape optimization prob- lems whose objective…
This paper presents a new parameter free partially penalized immersed finite element method and convergence analysis for solving second order elliptic interface problems. A lifting operator is introduced on interface edges to ensure the…
The use of ensemble methods to solve inverse problems is attractive because it is a derivative-free methodology which is also well-adapted to parallelization. In its basic iterative form the method produces an ensemble of solutions which…
Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in…
This paper presents a new methodology for structural reliability analysis via stochastic finite element method (SFEM). A novel sample-based SFEM is firstly used to compute structural stochastic responses of all spatial points at the same…
The article considers the nonlinear inverse problem of identifying the material parameters in viscoelastic structures based on a generalized Maxwell model. The aim is to reconstruct the model parameters from stress data acquired from a…
In this paper, we develop interval estimation methods for means of bounded random variables based on a sequential procedure such that the sampling is continued until the sample sum is no less than a prescribed threshold.