Reduced Basis Methods: From Low-Rank Matrices To Low-Rank Tensors

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Electrochemical Impedance Spectroscopy (EIS) and Equivalent Circuit Models (ECMs) are widely used to characterize the impedance and estimate parameters of electrochemical systems such as batteries. We use a generic ECM with ten parameters grouped to model ...

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

This paper deals with the initial value problem for a semilinear wave equation on a bounded domain and solutions are required to vanish on the boundary of this domain. The essential feature of the situation considered here is that the ellipticity of the sp ...

We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of differential forms inv ...

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for time-dependent n ...

In engineering, oscillatory instabilities and resonances are often considered undesirable flow features and measures are taken to avoid them. This may include avoiding certain parametric regions or implementing control and mitigation strategies. However, t ...

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

Control systems operating in real-world environments often face disturbances arising from measurement noise and model mismatch. These factors can significantly impact the perfor- mance and safety of the system. In this thesis, we aim to leverage data to de ...

In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of basis vectors with r ...

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the solution of the li ...

We introduce HP, an implementation of density-functional perturbation theory, designed to compute Hubbard parameters (on-site U and inter-site V ) in the framework of DFT+U and DFT+U+V. The code does not require the use of computationally expensive superce ...

When learning from data, leveraging the symmetries of the domain the data lies on is a principled way to combat the curse of dimensionality: it constrains the set of functions to learn from. It is more data efficient than augmentation and gives a generaliz ...

The use of model-based numerical simulations of wave propagation in rooms for engineering applications requires that acoustic conditions for multiple parameters are evaluated iteratively, which is computationally expensive. We present a reduced basis metho ...

Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

Model-free data-driven computational mechanics (DDCM) is a new paradigm for simulations in solid mechanics. The modeling step associated to the definition of a material constitutive law is circumvented through the introduction of an abstract phase space in ...

We study the problem of learning unknown parameters of stochastic dynamical models from data. Often, these models are high dimensional and contain several scales and complex structures. One is then interested in obtaining a reduced, coarse-grained descript ...

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations ...

Reduced Basis Methods: From Low-Rank Matrices To Low-Rank Tensors

Chattez avec Graph Search

On the use of Cramér-Rao Lower Bound for least-variance circuit parameters identification of Li-ion cells

Spectral Estimators for High-Dimensional Matrix Inference

Critical degeneracy in a nonlinear hyperbolic equation can produce atypical instability

High order geometric methods with splines: fast solution with explicit time-stepping for Maxwell equations

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Non-intrusive data-driven reduced-order modeling for time-dependent parametrized problems

Self-sustained dynamics and forced resonant oscillations in flows: cross-junction jets and sloshing liquids

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Data-Driven Control and Optimization under Noisy and Uncertain Conditions

Dynamical Low-Rank Approximation for Stochastic Differential Equations

Results on Sparse Integer Programming and Geometric Independent Sets

A mathematical theory for mass lumping and its generalization with applications to isogeometric analysis

HP - A code for the calculation of Hubbard parameters using density-functional perturbation theory

Leveraging topology, geometry, and symmetries for efficient Machine Learning

Reduced basis methods for numerical room acoustic simulations with parametrized boundaries

Fast global spectral methods for three-dimensional partial differential equations

TimeEvolver: A program for time evolution with improved error bound

Mesh d-refinement: a data-based computational framework to account for complex material response

Filtered data and eigenfunction estimators for statistical inference of multiscale and interacting diffusion processes

Optimal radial basis for density-based atomic representations