Related papers: Semi-implicit Integration and Data-Driven Model Or…

This paper aims to investigate the numerical approximation of semilinear non-autonomous stochastic partial differential equations (SPDEs) driven by multiplicative or additive noise. Such equations are more realistic than autonomous SPDEs…

Hysteresis is a highly nonlinear phenomenon, showing up in a wide variety of science and engineering problems. The identification of hysteretic systems from input-output data is a challenging task. Recent work on black-box polynomial…

Systems with nonreciprocal interactions generically display time-dependent states. These are routinely observed in finite systems, from neuroscience to active matter, in which globally ordered oscillations exist. However, the stability of…

We propose a model order reduction framework for incompressible fluid-structure interaction (FSI) problems based on high-order implicit Runge-Kutta (IRK) methods. We consider separate reduced spaces for fluid velocity, fluid pressure and…

This paper proposes a new substructuring technique for hybrid simulation of steel braced frame structures under seismic loading in which a new machine learning-based model is used to predict the hysteretic response of steel braces.…

Reliable inference of system degradation from sensor data is fundamental to condition monitoring and prognostics in mechanical and infrastructural systems. Since degradation is rarely directly observable and measurable, it must be inferred…

Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems…

We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection-diffusion equations and extend our previous analysis in [Numer. Math. 144, 451--477, 2020] to the convection-dominated regime.…

Data-driven reduced order modeling of chaotic dynamics can result in systems that either dissipate or diverge catastrophically. Leveraging non-linear dimensionality reduction of autoencoders and the freedom of non-linear operator inference…

In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…

Numerical investigations of partial differential equations with hysteresis have largely focused on simulations, leaving numerical error analysis unexplored and relying mainly on derivative-free nonlinear solvers. This work establishes…

Second-order continuous-time dissipative dynamical systems with viscous and Hessian driven damping have inspired effective first-order algorithms for solving convex optimization problems. While preserving the fast convergence properties of…

In this paper, we propose a numerical model to describe the adhesive normal contact between a "rigid" spherical indenter and a viscoelastic rough substrate. The model accounts for dissipative process under the assumption that viscoelastic…

We consider a fully discrete loosely coupled scheme for incompressible fluid-structure interaction based on the time semi-discrete splitting method introduced in {\emph{[Burman, Durst \& Guzm\'an, arXiv:1911.06760]}}. The splittling method…

Complex dynamical systems are notoriously difficult to model because some degrees of freedom (e.g., small scales) may be computationally unresolvable or are incompletely understood, yet they are dynamically important. For example, the small…

Dynamic hysteresis, viz., delay in switching of a bistable system on account of the finite sweep rate of the drive has been extensively studied in dynamical and thermodynamic systems. Dynamic hysteresis results from slowing of the response…

Second-order optimization methods exhibit fast convergence to critical points, however, in nonconvex optimization, these methods often require restrictive step-sizes to ensure a monotonically decreasing objective function. In the presence…

We consider data assimilation for the heat equation using a finite element space semi-discretization. The approach is optimization based, but the design of regularization operators and parameters rely on techniques from the theory of…

In ecological studies of pattern formation, models of the competitive-diffusion type are generally singularly perturbed, and the numerical approximation of such models is challenging. In this paper, we present finite element discretization…

We introduce a new class of integrators for stiff ODEs as well as SDEs. These integrators are (i) {\it Multiscale}: they are based on flow averaging and so do not fully resolve the fast variables and have a computational cost determined by…