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Compared with traditional seismic noise attenuation algorithms that depend on signal models and their corresponding prior assumptions, removing noise with a deep neural network is trained based on a large training set, where the inputs are…

Because of the impact of extreme heat waves and heat domes on society and biodiversity, their study is a key challenge. We specifically study long-lasting extreme heat waves, which are among the most important for climate impacts. Physics…

In quantum mechanics, a norm squared wave function can be interpreted as the probability density that describes the likelihood of a particle to be measured in a given position or momentum. This statistical property is at the core of the…

We survey the mathematical foundations of geometric deep learning, focusing on group equivariant and gauge equivariant neural networks. We develop gauge equivariant convolutional neural networks on arbitrary manifolds $\mathcal{M}$ using…

Spectropolarimetric inversions are routinely used in the field of Solar Physics for the extraction of physical information from observations. The application to two-dimensional fields of view often requires the use of supercomputers with…

Various problems in computer vision and medical imaging can be cast as inverse problems. A frequent method for solving inverse problems is the variational approach, which amounts to minimizing an energy composed of a data fidelity term and…

Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all…

Feature representations, both hand-designed and learned ones, are often hard to analyze and interpret, even when they are extracted from visual data. We propose a new approach to study image representations by inverting them with an…

Nonlinear least squares data-fitting driven by physical process simulation is a classic and widely successful technique for the solution of inverse problems in science and engineering. Known as "Full Waveform Inversion" in application to…

Over the last years, deep learning methods have become an increasingly popular choice to solve tasks from the field of inverse problems. Many of these new data-driven methods have produced impressive results, although most only give point…

Inverse problems arise anywhere we have indirect measurement. As, in general they are ill-posed, to obtain satisfactory solutions for them needs prior knowledge. Classically, different regularization methods and Bayesian inference based…

We investigate the performance of fully convolutional networks to simulate the motion and interaction of surface waves in open and closed complex geometries. We focus on a U-Net architecture and analyse how well it generalises to geometric…

Traditional geological mapping, based on field observations and rock sample analysis, is inefficient for continuous spatial mapping of features like alteration zones. Deep learning models, such as convolutional neural networks (CNNs), have…

The linear inverse problem is fundamental to the development of various scientific areas. Innumerable attempts have been carried out to solve different variants of the linear inverse problem in different applications. Nowadays, the rapid…

Training deep neural networks results in strong learned representations that show good generalization capabilities. In most cases, training involves iterative modification of all weights inside the network via back-propagation. In Extreme…

We present a new, variational, fully nonlinear, probabilistic ambient noise tomography method, which estimates subsurface structure and quantifies the corresponding uncertainties directly in three dimensions (3D) from inter-receiver seismic…

Deep learning (DL) methods have emerged as a powerful tool for the inversion of geophysical data. When applied to field data, these models often struggle without additional fine-tuning of the network. This is because they are built on the…

Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency…

We explore the suitability of deep learning to capture the physics of subgrid-scale ideal magnetohydrodynamics turbulence of 2-D simulations of the magnetized Kelvin-Helmholtz instability. We produce simulations at different resolutions to…

Radio-Frequency (RF) imaging concerns the digital recreation of the surfaces of scene objects based on the scattered field at distributed receivers. To solve this difficult inverse scattering problems, data-driven methods are often employed…