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Gravitational-wave data analysis is rapidly absorbing techniques from deep learning, with a focus on convolutional networks and related methods that treat noisy time series as images. We pursue an alternative approach, in which waveforms…

We develop a novel deep learning approach for pricing European options in diffusion models, that can efficiently handle high-dimensional problems resulting from Markovian approximations of rough volatility models. The option pricing partial…

We are concerned with the reconstruction of inclusions in elastic bodies based on measurements from a laboratory experiment. In doing so, we solve the inverse problem of the time-harmonic elastic wave equation, in contrast to the stationary…

This work focuses on the numerical assessment of the accuracy of an adjoint-based gradient in the perspective of variational data assimilation and parameter identification in glaciology. Using noisy synthetic data, we quantify the ability…

In this work, we develop a modelling framework for granular flows based on the shallow water moment equations on inclined planes. Under the assumption of a polynomial expansion of the velocity field, the model extends the classical shallow…

Recent progress in robust statistical learning has mainly tackled convex problems, like mean estimation or linear regression, with non-convex challenges receiving less attention. Phase retrieval exemplifies such a non-convex problem,…

To compute the spatially distributed dielectric constant from the backscattering data, we study a coefficient inverse problem for a 1D hyperbolic equation. To solve the inverse problem, we establish a new version of Carleman estimate and…

We combine resolvent-mode decomposition with techniques from convex optimization to optimally approximate velocity spectra in a turbulent channel. The velocity is expressed as a weighted sum of resolvent modes that are dynamically…

We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…

We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…

It is by now well-known that one can recover a potential in the wave equation from the knowledge of the initial waves, the boundary data and the flux on a part of the boundary satisfying the Gamma-conditions of J.-L. Lions. We are…

We study the numerical behaviour of a particle method for gradient flows involving linear and nonlinear diffusion. This method relies on the discretisation of the energy via non-overlapping balls centred at the particles. The resulting…

Optimization with noisy gradients has become ubiquitous in statistics and machine learning. Reparameterization gradients, or gradient estimates computed via the "reparameterization trick," represent a class of noisy gradients often used in…

This work considers the reconstruction of a space-dependent potential from boundary observations in subdiffusion by a stable and robust recovery method. Specifically, we develop an algorithm to minimize the Kohn-Vogelius cost function,…

Direct numerical simulations are performed to investigate the combined effects of surface roughness and wall heat transfer on spatially developing compressible turbulent boundary layers at $Ma=2.5$. The roughness consists of transverse…

We perform full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid. We show that the instability development leads to chaotization and formation of wave turbulence. We study instability both of…

The behaviour of the turbulent Prandtl number ($Pr_t$) for buoyancy-affected flows near a vertical surface is investigated as an extension study of {Gibson \& Leslie, \emph{Int. Comm. Heat Mass Transfer}, Vol. 11, pp. 73-84 (1984)}. By…

We consider the problem of making nonparametric inference in a class of multi-dimensional diffusions in divergence form, from low-frequency data. Statistical analysis in this setting is notoriously challenging due to the intractability of…

We consider the inverse problem of estimating the spatially varying pulse wave velocity in blood vessels in the brain from dynamic MRI data, as it appears in the recently proposed imaging technique of Magnetic Resonance Advection Imaging…

Using weak wave turbulence theory analysis, we distinguish three main regimes for 2D stratified fluids in the dimensionless parameter space defined by the Froude number and the Reynolds number: discrete wave turbulence, weak wave…