相关论文: Improved a posteriori Error Bounds for Reduced por…

Feedback control synthesis for nonlinear, parameter-dependent fluid flow control problems is considered. The optimal feedback law requires the solution of the Hamilton-Jacobi-Bellman (HJB) PDE suffering the curse of dimensionality. This is…

In this contribution we present how to obtain explicit state space models in port-Hamiltonian form when a mixed finite element method is applied to a linear mechanical system with non-uniform boundary conditions. The key is to express the…

This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, "on-the-fly", the reduced order modelling of highly…

We develop and analyse residual-based a posteriori error estimates for the virtual element discretisation of a nonlinear stress-assisted diffusion problem in two and three dimensions. The model problem involves a two-way coupling between…

A structure preserving proper orthogonal decomposition reduce-order modeling approach has been developed in [Gong et al. 2017] for the Hamiltonian system, which uses the traditional framework of Galerkin projection-based model reduction but…

Stability and stabilization of linear port-Hamiltonian systems on infinite-dimensional spaces are investigated. This class is general enough to include models of beams and waves as well as transport and Schr\"odinger equations with boundary…

Hybrid quantum/molecular mechanics models (QM/MM methods) are widely used in material and molecular simulations when MM models do not provide sufficient accuracy but pure QM models are computationally prohibitive. Adaptive QM/MM coupling…

In this paper the authors study a non-linear elliptic-parabolic system, which is motivated by mathematical models for lithium-ion batteries. One state satisfies a parabolic reaction diffusion equation and the other one an elliptic equation.…

In this paper we present a reduced basis method which yields structure-preservation and a tight a posteriori error bound for the simulation of the damped wave equations on networks. The error bound is based on the exponential decay of the…

In large-scale Bayesian inverse problems, it is often necessary to apply approximate forward models to reduce the cost of forward model evaluations, while controlling approximation quality. In the context of Bayesian inverse problems with…

Electric circuits are usually described by charge- and flux-oriented modified nodal analysis. In this paper, we derive models as port-Hamiltonian systems on several levels: overall systems, multiply coupled systems and systems within…

Motivated by a recently proposed error estimator for the transfer function of the reduced-order model of a given linear dynamical system, we further develop more theoretical results in this work. Furthermore, we propose several variants of…

In this work we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for elasticity problems in affinley parametrized geometries. The essential ingredients of the methodology are: a Galerkin…

This paper provides statistical guarantees on the accuracy of dynamical models learned from dependent data sequences. Specifically, we develop uniform error bounds that apply to quantized models and imperfect optimization algorithms…

In this article, we investigate the model based position control of soft hydraulic actuators arranged in an antagonistic pair. A dynamical model of the system is constructed by employing the port-Hamiltonian formulation. A control algorithm…

We consider a 1D periodic atomistic model, for which we formulate and analyze an adaptive variant of a quasicontinuum method. We establish a posteriori error estimates for the energy norm and for the energy, based on a posteriori residual…

This study presents incremental correction methods for refining neural network parameters or control functions entering into a continuous-time dynamic system to achieve improved solution accuracy in satisfying the interim point constraints…

Model order reduction (MOR) is often applied to spatially-discretized partial differential equations to reduce their order and hence decrease computational complexity. A reduced system can be obtained, e.g., by time-limited balanced…

In our work, we consider the classical density-based approach to the topology optimization. We propose to modify the discretized cost functional using a posteriori error estimator for the finite element method. It can be regarded as a new…

The parametrisation method for invariant manifolds is a powerful technique for deriving reduced-order models in the context of nonlinear vibrating systems, allowing accurate computations of nonlinear normal modes. Thanks to arbitrary order…