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Efficient modeling of the Richtmyer-Meshkov instability (RMI) is essential to many engineering tasks, including high-speed combustion and drive and capsule geometry optimization in Inertial Confinement Fusion (ICF). In the latter, RMI…

The dynamic behavior of jointed assemblies exhibiting friction nonlinearities features amplitude-dependent dissipation and stiffness. To develop numerical simulations for predictive and design purposes, macro-scale High Fidelity Models…

Deep learning methods for unsupervised registration often rely on objectives that assume a uniform noise level across the spatial domain (e.g. mean-squared error loss), but noise distributions are often heteroscedastic and input-dependent…

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…

Electrical Impedance Tomography gives rise to the severely ill-posed Calder\'on problem of determining the electrical conductivity distribution in a bounded domain from knowledge of the associated Dirichlet-to-Neumann map for the governing…

The paper is concerned with locally stabilized space-time IgA approximations to initial boundary value problems of the parabolic type. Originally, similar schemes (but weighted with a global mesh parameter) was presented and studied by U.…

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…

By incorporating physical consistency as inductive bias, deep neural networks display increased generalization capabilities and data efficiency in learning nonlinear dynamic models. However, the complexity of these models generally…

We present iDARR, a scalable iterative Data-Adaptive RKHS Regularization method, for solving ill-posed linear inverse problems. The method searches for solutions in subspaces where the true solution can be identified, with the data-adaptive…

In this paper we propose a nonconforming finite element method for the solution of the ill-posed elliptic Cauchy problem. We prove error estimates using continuous dependence estimates in the $L^2$-norm. The effect of perturbations in data…

We present a new adaptive method for electronic structure calculations based on novel fast algorithms for reduction of multivariate mixtures. In our calculations, spatial orbitals are maintained as Gaussian mixtures whose terms are selected…

We present a method for contraction-based feedback motion planning of locally incrementally exponentially stabilizable systems with unknown dynamics that provides probabilistic safety and reachability guarantees. Given a dynamics dataset,…

We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…

A large number of theoretically predicted waveforms are required by matched-filtering searches for the gravitational-wave signals produced by compact binary coalescence. In order to substantially alleviate the computational burden in…

This work presents a Finite Element Model Updating inverse methodology for reconstructing heterogeneous material distributions based on an efficient isogeometric shell formulation. It uses nonlinear hyperelastic material models suitable for…

The present paper develops a reduced-order model capable of modeling unsteady aerodynamic loads in the transonic regime using system identification techniques. The computational fluid dynamics (CFD) calculations are based on the Euler…

In this paper, we propose a reduced order approach for 3D variational data assimilation governed by parametrized partial differential equations. In contrast to the classical 3D-VAR formulation that penalizes the measurement error directly,…

In electrical impedance tomography the electrical conductivity inside a physical body is computed from electro-static boundary measurements. The focus of this paper is to extend recent result for the 2D problem to 3D. Prior information…

Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically…

In this paper we address the numerical solution of nonlinear ill-posed systems by iterative regularization methods in the classes of Levenberg-Marquardt, trust-region and adaptive quadratic regularization procedures. Both with exact and…