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We develop a model reduction technique for non-smooth dynamical systems using spectral submanifolds. Specifically, we construct low-dimensional, sparse, nonlinear and non-smooth models on unions of slow and attracting spectral submanifolds…

This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…

Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…

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.…

We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…

Deep Neural Networks are known to be very demanding in terms of computing and memory requirements. Due to the ever increasing use of embedded systems and mobile devices with a limited resource budget, designing low-complexity models without…

We propose a projection-based model order reduction method for the solution of parameter-dependent dynamical systems. The proposed method relies on the construction of time-dependent reduced spaces generated from evaluations of the solution…

A variable screening procedure via correlation learning was proposed Fan and Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models. Even when the true model is linear, the marginal regression can be highly nonlinear. To…

Parametric system identification methods estimate the parameters of explicitly defined physical systems from data. Yet, they remain constrained by the need to provide an explicit function space, typically through a predefined library of…

Surrogate models provide compact relations between user-defined input parameters and output quantities of interest, enabling the efficient evaluation of complex parametric systems in many-query settings. Such capabilities are essential in a…

A methodology for non-intrusive, projection-based non-linear model reduction originally presented by Renganathan et. al. (2018)~\cite{renganathan2018koopman} is further extended towards parametric systems with focus on application to…

Functional graphical models have undergone extensive development during the recent years, leading to a variety models such as the functional Gaussian graphical model, the functional copula Gaussian graphical model, the functional Bayesian…

We introduce a novel data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system…

Reconstructing the equation of motion and thus the network topology of a system from time series is a very important problem. Although many powerful methods have been developed, it remains a great challenge to deal with systems in high…

The research paper addresses linear decomposition of time series of non-additive metrics that allows for the identification and interpretation of contributing factors (input features) of variance. Non-additive metrics, such as ratios, are…

Accurate models are essential for design, performance prediction, control, and diagnostics in complex engineering systems. Physics-based models excel during the design phase but often become outdated during system deployment due to changing…

In this paper, we propose a new approach to model reduction of parameterized partial differential equations (PDEs) based on the concept of adaptive reduced bases. The presented approach is particularly suited for large-scale nonlinear…

Many application areas rely on models that can be readily simulated but lack a closed-form likelihood, or an accurate approximation under arbitrary parameter values. Existing parameter estimation approaches in this setting are generally…

Many traditional robust control approaches assume linearity of the system and independence between the system state-input and the parameters of its approximant (possibly lower-order) model. This assumption implies that the application of…

We propose to address the common problem of linear estimation in linear statistical models by using a model selection approach via penalization. Depending then on the framework in which the linear statistical model is considered namely the…