Related papers: Multi-parameter identification in systems of PDEs …
We introduce a conceptual framework for numerically solving linear elliptic, parabolic, and hyperbolic PDEs on bounded, polytopal domains in euclidean spaces by deep neural networks. The PDEs are recast as minimization of a least-squares…
Recent advances in stochastic differential equations (SDEs) have enabled robust modeling of real-world dynamical processes across diverse domains, such as finance, health, and systems biology. However, parameter estimation for SDEs…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
The estimation of distributed parameters in partial differential equations (PDE) from measures of the solution of the PDE may lead to under-determination problems. The choice of a parameterization is a usual way of adding a-priori…
We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary…
This paper investigates both biomechanical-constrained non-rigid medical image registrations and accurate identifications of material properties for soft tissues, using physics-informed neural networks (PINNs). The complex nonlinear…
Partial differential equation (PDE) models are widely used in engineering and natural sciences to describe spatio-temporal processes. The parameters of the considered processes are often unknown and have to be estimated from experimental…
In this paper, the simultaneous identification of damping or anti-damping coefficient and initial value for some PDEs is considered. An identification algorithm is proposed based on the fact that the output of system happens to be…
We present a computational technique for modeling the evolution of dynamical systems in a reduced basis, with a focus on the challenging problem of modeling partially-observed partial differential equations (PDEs) on high-dimensional…
This paper investigates adaptive model predictive control (MPC) for a class of constrained linear systems with unknown model parameters. This is also posed as the dual control problem consisting of system identification and regulation. We…
We present a framework for solving a broad class of ill-posed inverse problems governed by partial differential equations (PDEs), where the target coefficients of the forward operator are recovered through an iterative regularization scheme…
Fabrication process variations are a major source of yield degradation in the nano-scale design of integrated circuits (IC), microelectromechanical systems (MEMS) and photonic circuits. Stochastic spectral methods are a promising technique…
We consider the problem of deriving from experimental data an approximation of an unknown function, whose derivatives also approximate the unknown function derivatives. Solving this problem is useful, for instance, in the context of…
Recent developments in system identification have brought attention to regularized kernel-based methods. This type of approach has been proven to compare favorably with classic parametric methods. However, current formulations are not…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem…
Machine learning has been successfully applied to various fields of scientific computing in recent years. In this work, we propose a sparse radial basis function neural network method to solve elliptic partial differential equations (PDEs)…
We present a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of pattern-forming physics. The motivation comes from developmental…
The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…
Several novel imaging and non-destructive testing technologies are based on reconstructing the spatially dependent coefficient in an elliptic partial differential equation from measurements of its solution(s). In practical applications, the…