Related papers: Nonlinear Moment Matching for the Simulation-Free …
Compositional simulation is challenging, because of highly nonlinear couplings between multi-component flow in porous media with thermodynamic phase behavior. The coupled nonlinear system is commonly solved by the fully-implicit scheme.…
Direct simulation of physical processes on a kinetic level is prohibitively expensive in aerospace applications due to the extremely high dimension of the solution spaces. In this paper, we consider the moment system of the Boltzmann…
We present a novel algorithm for reducing the state dimension, i.e. order, of linear parameter varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable. The input-output behavior of the reduced…
This paper deals with the balanced truncation model reduction of discrete-time, linear time-varying, heterogeneous subsystems interconnected over finite arbitrary directed graphs. The information transfer between the subsystems is subject…
The paper deals with measures of nonlinearity. In state estimation, they are utilized i) to select a suitable state estimation algorithm by assessing the nonlinearity of a system model, ii) to adapt the estimation algorithm structure or…
We study mixed finite element methods for the rotating shallow water equations with linearized momentum terms but nonlinear drag. By means of an equivalent second-order formulation, we prove long-time stability of the system without energy…
Fixed-point or Newton-methods are typically employed for the numerical solution of nonlinear systems arising from discretization of nonlinear magnetic field problems. We here discuss an alternative strategy which uses local Quasi-Newton…
In this work, the issue of obtaining consistent parameter estimators for nonlinear regression models where the regressors are second-order modulus functions is explored. It is shown that consistent instrumental variable estimators can be…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
To be feasible for computationally intensive applications such as parametric studies, optimization and control design, large-scale finite element analysis requires model order reduction. This is particularly true in nonlinear settings that…
We present a fast method for nonlinear data-driven model reduction of dynamical systems onto their slowest nonresonant spectral submanifolds (SSMs). We use observed data to locate a low-dimensional, attracting slow SSM and compute a…
A recently introduced technique of topology sensitivity in method of moments is extended by the possibility of adding degrees-of-freedom (reconstruct) into underlying structure. The algebraic formulation is inversion-free, suitable for…
The paper studies identification of linear systems with multiplicative noise from multiple-trajectory data. An algorithm based on the least-squares method and multiple-trajectory data is proposed for joint estimation of the nominal system…
Two-time-scale stochastic approximation, a generalized version of the popular stochastic approximation, has found broad applications in many areas including stochastic control, optimization, and machine learning. Despite its popularity,…
Model order reduction in high-dimensional, nonlinear dynamical systems if often enabled through fast-slow timescale separation. One such approach involves identifying a low-dimensional slow manifold to which the state rapidly converges and…
Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications…
In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…
This work provides a framework for nonlinear model-free control of systems with unknown input-output dynamics, but outputs that can be controlled by the inputs. This framework leads to real-time control of the system such that a feasible…
The thermal dynamics in thermo-mechanical systems exhibits a much slower time scale compared to the structural dynamics. In this work, we use the method of multiple scales to reduce the thermo-mechanical structural models with a…