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Data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
Constructing accurate, flexible, and efficient parametrizations is one of the great challenges in the numerical modelling of geophysical fluids. We consider here the simple yet paradigmatic case of a Lorenz 84 model forced by a Lorenz 63…
Solving the electronic Schr\"odinger equation for strongly correlated systems remains one of the grand challenges in quantum chemistry. Here we demonstrate that Transformer architectures can be adapted to capture the complex grammar of…
We apply a variational Ansatz based on neural networks to the problem of spin-$1/2$ fermions in a harmonic trap interacting through a short distance potential. We showed that standard machine learning techniques lead to a quick convergence…
Over the last decade, the Lattice Boltzmann method has found major scope for the simulation of a large spectrum of problems in soft matter, from multiphase and multi-component microfluidic flows, to foams, emulsions, colloidal flows, to…
We extend the self-consistent Ornstein-Zernike approximation (SCOZA), first formulated in the context of liquid-state theory, to the study of the random field Ising model. Within the replica formalism, we treat the quenched random field as…
Strongly correlated materials exhibit complex electronic phenomena that are challenging to capture with traditional theoretical methods, yet understanding these systems is crucial for discovering new quantum materials. Addressing the…
A phase-field model that allows for quantitative simulations of low-speed eutectic and peritectic solidification under typical experimental conditions is developed. Its cornerstone is a smooth free-energy functional, designed so that the…
The adhesive contact between elastic solids with randomly rough, self affine fractal surfaces is studied by molecular dynamics (MD) simulations. The interfacial binding energy obtained from the simulations of nominally flat and curved…
In modern computational materials science, deep learning has shown the capability to predict interatomic potentials, thereby supporting and accelerating conventional simulations. However, existing models typically sacrifice either accuracy…
We reconsider the structure-based route to coarse graining in which the coarse-grained model is defined in such a way to reproduce some distributions functions of the original system as accurately as possible. We consider standard…
Fluid models that approximate kinetic effects have received attention recently in the modelling of large scale plasmas such as planetary magnetospheres. In three-dimensional reconnection, both reconnection itself and current sheet…
Machine-learned interatomic potentials (MLIPs) are increasingly used to replace computationally demanding electronic-structure calculations to model matter at the atomic scale. The most commonly used model architectures are constrained to…
We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit…
We propose a Machine Learning (ML) non-Markovian closure modeling framework for accurate predictions of statistical responses of turbulent dynamical systems subjected to external forcings. One of the difficulties in this statistical closure…
We investigate the efficiency of the recently proposed Restricted Boltzmann Machine (RBM) representation of quantum many-body states to study both the static properties and quantum spin dynamics in the two-dimensional Heisenberg model on a…
The properties of constrained fluids have increasingly gained relevance for applications ranging from materials to biology. In this work, we propose a multiscale model using twin neural networks to investigate the properties of a fluid…
We analyze a linear 3D/3D fluid-structure interaction problem between a thin layer of a viscous fluid and a thin elastic plate-like structure with the aim of deriving a simplified reduced model. Based on suitable energy dissipation…
Interacting one-dimensional quantum systems play a pivotal role in physics. Exact solutions can be obtained for the homogeneous case using the Bethe ansatz and bosonisation techniques. However, these approaches are not applicable when…
We derive a microscopic theory for the structural dynamics in the vicinity of the glass transition for a liquid exposed to a one-dimensional periodic potential. The periodic potential breaks translational invariance, in particular, the…