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Explicit time integration for immersed finite element discretizations severely suffers from the influence of poorly cut elements. In this contribution, we propose a generalized eigenvalue stabilization (GEVS) strategy for the element mass…

The problem of combined state and input estimation of linear structural systems based on measured responses and a priori knowledge of structural model is considered. A novel methodology using Gaussian process latent force models is proposed…

This paper presents the first sufficient conditions that guarantee the stability and almost sure convergence of multi-timescale stochastic approximation (SA) iterates. It extends the existing results on one-timescale and two-timescale SA…

State estimation techniques for continuum robots (CRs) typically involve using computationally complex dynamic models, simplistic shape approximations, or are limited to quasi-static methods. These limitations can be sensitive to unmodelled…

The conditional Gaussian nonlinear system (CGNS) is a broad class of nonlinear stochastic dynamical systems. Given the trajectories for a subset of state variables, the remaining follow a Gaussian distribution. Despite the conditionally…

Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions…

State-space models (SSMs) are a powerful statistical tool for modelling time-varying systems via a latent state. In these models, the latent state is never directly observed. Instead, a sequence of observations related to the state is…

Stochastic resonance (SR) is a prominent phenomenon in many natural and engineered noisy system, whereby the response to a periodic forcing is greatly amplified when the intensity of the noise is tuned to within a specific range of values.…

We propose an end-to-end trained neural networkarchitecture to robustly predict the complex dynamics of fluid flows with high temporal stability. We focus on single-phase smoke simulations in 2D and 3D based on the incompressible…

We propose consistent locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of non-autonomous parabolic evolution problems under the assumption of maximal…

Gaussian processes are frequently deployed as part of larger machine learning and decision-making systems, for instance in geospatial modeling, Bayesian optimization, or in latent Gaussian models. Within a system, the Gaussian process model…

This paper proposes an online learning method of Gaussian process state-space model (GP-SSM). GP-SSM is a probabilistic representation learning scheme that represents unknown state transition and/or measurement models as Gaussian processes…

In this paper, we develop and analyze an integral fixed-time sliding mode control method for a scenario in which the system model is only partially known, utilizing Gaussian processes. We present two theorems on fixed-time convergence. The…

Forecasting the evolution of complex systems is one of the grand challenges of modern data science. The fundamental difficulty lies in understanding the structure of the observed stochastic process. In this paper, we show that every…

For the simulations of unsteady flow, the global time step becomes really small with a large variation of local cell size. In this paper, an implicit high-order gas-kinetic scheme (HGKS) is developed to remove the restrictions on the time…

Stochastic averaging allows for the reduction of the dimension and complexity of stochastic dynamical systems with multiple time scales, replacing fast variables with statistically equivalent stochastic processes in order to analyze…

We introduce a new class of algorithms, Stochastic Generalized Method of Moments (SGMM), for estimation and inference on (overidentified) moment restriction models. Our SGMM is a novel stochastic approximation alternative to the popular…

We propose a novel Skew Gradient Embedding (SGE) framework for systematically reformulating thermodynamically consistent partial differential equation (PDE) models-capturing both reversible and irreversible processes-as generalized gradient…

Contraction theory is a powerful tool for proving asymptotic properties of nonlinear dynamical systems including convergence to an attractor and entrainment to a periodic excitation. We consider three generalizations of contraction with…

Fuzzy systems (FSs) have enjoyed wide applications in various fields, including pattern recognition, intelligent control, data mining and bioinformatics, which is attributed to the strong interpretation and learning ability. In traditional…