HIERARCHICAL MARKOV CHAIN MONTE CARLO METHODS FOR BAYESIAN INVERSE PROBLEMS

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Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...

Time-domain solutions of Maxwell’s equations in homogeneous and isotropic media are paramount to studying transient or broadband phenomena. However, analytical solutions are generally unavailable for practical applications, while numerical solutions are co ...

The goal of this work is to use anisotropic adaptive finite elements for the numerical simulation of aluminium electrolysis. The anisotropic adaptive criteria are based on a posteriori error estimates derived for simplified problems. First, we consider an ...

Molecular quantum dynamics simulations are essential for understanding many fundamental phenomena in physics and chemistry. They often require solving the time-dependent Schrödinger equation for molecular nuclei, which is challenging even for medium-sized ...

Geometric properties of lattice quantum gravity in two dimensions are studied numerically via Monte Carlo on Euclidean Dynamical Triangulations. A new computational method is proposed to simulate gravity coupled with fermions, which allows the study of int ...

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By juxtaposing ideas from fractal geometry and dynamical systems, Furstenberg proposed a series of conjectures in the late 1960's that explore the relationship between digit expansions with respect to multiplicatively independent bases. In this work, we in ...

A recent line of work in high-dimensional statistics working under the Gaussian mixture hypothesis has led to a number of results in the context of empirical risk minimization, Bayesian uncertainty quantification, separation of kernel methods and neural ne ...

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

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We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...

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This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

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Estimating the stress of reinforcing bars and its variations in service conditions can be useful to determine the reserve capacity of structures or to assess the risk of fatigue in the reinforcement. This paper investigates the use crack width measurements ...

HIERARCHICAL MARKOV CHAIN MONTE CARLO METHODS FOR BAYESIAN INVERSE PROBLEMS

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Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

From low-rank retractions to dynamical low-rank approximation and back

The time-domain Cartesian multipole expansion of electromagnetic fields

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

High-order geometric integrators for the variational Gaussian wavepacket dynamics and application to vibronic spectra at finite temperature

Hausdorff dimension of fermions on a random lattice

Pore size estimation in axon-mimicking microfibers with diffusion-relaxation MRI

Pseudo-Three-Dimensional Analytical Model of Linear Induction Motors for High-Speed Applications

Additive and geometric transversality of fractal sets in the integers

Universality laws for Gaussian mixtures in generalized linear models

Randomized flexible GMRES with deflated restarting

FENNECS: a novel particle-in-cell code for simulating the formation of magnetized non-neutral plasmas trapped by electrodes of complex geometries

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

Gibbs sampling the posterior of neural networks

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Reliable data-driven decision-making through optimal transport

Residual-based attention in physics-informed neural networks

Machine Learning for Modeling Stock Returns

Estimation of the bar stress based on crack width measurements in reinforced concrete structures