Related papers: Interpolatory Model Reduction of Parameterized Bil…

Micromagnetics simulations require accurate approximation of the magnetization dynamics described by the Landau-Lifshitz-Gilbert equation, which is nonlinear, nonlocal, and has a non-convex constraint, posing interesting challenges in…

We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…

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…

This paper develops a novel Bayesian approach for nonlinear regression with symmetric matrix predictors, often used to encode connectivity of different nodes. Unlike methods that vectorize matrices as predictors that result in a large…

Projection-based reduced order models are effective at approximating parameter-dependent differential equations that are parametrically separable. When parametric separability is not satisfied, which occurs in both linear and nonlinear…

In this paper, for a variety of nonholonomic (reducible) Hamiltonian systems, we first give to various distributional Hamiltonian systems, by analyzing carefully the dynamics and structures of the nonholonomic Hamiltonian systems. Secondly,…

This paper studies the model order reduction of second-order index-1 descriptor systems using a tangential interpolation projection method based on the Iterative Rational Krylov Algorithm (IRKA). Our primary focus is to reduce the system…

Diffusion models are powerful deep generative models, but unlike classical models, they lack an explicit low-dimensional latent space that parameterizes the data manifold. This absence makes it difficult to perform manifold-aware…

On the basis of input-output time-domain data collected from a complex simulator, this paper proposes a constructive methodology to infer a reduced-order linear, bilinear or quadratic time invariant dynamical model reproducing the…

A primary goal of computer experiments is to reconstruct the function given by the computer code via scattered evaluations. Traditional isotropic Gaussian process models suffer from the curse of dimensionality, when the input dimension is…

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…

Continuous-time projected dynamical systems are an elementary class of discontinuous dynamical systems with trajectories that remain in a feasible domain by means of projecting outward-pointing vector fields. They are essential when…

The four-dimensional nonlinear model is extended to include the inter-channel stimulated Raman scattering, enabling accurate prediction of dual-polarization four-dimensional modulation formats and probabilistically shaped constellations in…

Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…

Non-Hermitian systems exploiting the synergy between gain and loss have recently become the focus of interest to discover novel physical phenomena. The spatial symmetry breaking in such systems allows tailoring the wave propagation at will.…

Optimal dimensionality reduction methods are proposed for the Bayesian inference of a Gaussian linear model with additive noise in presence of overabundant data. Three different optimal projections of the observations are proposed based on…

Bayesian optimisation is a popular technique for hyperparameter learning but typically requires initial exploration even in cases where similar prior tasks have been solved. We propose to transfer information across tasks using learnt…

We demonstrate the synthesis of sparse sampling and machine learning to characterize and model complex, nonlinear dynamical systems over a range of bifurcation parameters. First, we construct modal libraries using the classical proper…

Though ubiquitous as first-principles models for conservative phenomena, Hamiltonian systems present numerous challenges for model reduction even in relatively simple, linear cases. Here, we present a method for the projection-based model…

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…