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ESAIM: Proceedings and Surveys
ISSN 2267-3059 · EDP Sciences · 462 articles in the index
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Multidimensional integration using machine learning and Monte Carlo methods for acoustic predictions
To predict underwater noise radiated by a ship, various numerical methods are available. In underwater acoustics, the most effective prediction methods consist in solving an acoustic analogy using an integral formulation. In this study, we propose a machine learning surrogate-based method, combined…
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Surrogate modeling of interactions in microbial communities through Physics-Informed Neural Networks*
Microorganisms form complex communities known as microbiota, influencing various aspects of host well-being. The Generalized Lotka-Volterra (GLV) model is commonly used to understand microorganism population dynamics, but its application to the microbiota faces challenges due to limited bacterial…
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Volume-preserving transformers for learning time series data with structure
Two of the many trends in neural network research of the past few years have been (i) the learning of dynamical systems, especially with recurrent neural networks such as long short-term memory networks (LSTMs) and (ii) the introduction of transformer neural networks for natural language processing…
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Generalizing the SINDy approach with nested neural networks
Symbolic Regression (SR) is a widely studied field of research that aims to infer symbolic expressions from data. A popular approach for SR is the Sparse Identification of Nonlinear Dynamical Systems (SINDy) framework, which uses sparse regression to identify governing equations from data. This…
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Comparison between tensor methods and neural networks in electronic structure calculations***
This article compares the tensor method density matrix renormalization group (DMRG) with two neural network based methods -namely FermiNet and PauliNet) for determining the ground state wavefunction of the many-body electronic Schrödinger problem. We provide numerical simulations illustrating the…
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Learning local Dirichlet-to-Neumann maps of nonlinear elliptic PDEs with rough coefficients*
Partial Differential Equations (PDEs) involving high-contrast and oscillating coefficients are common in scientific and industrial applications. Numerically approximating these PDEs is a challenging task, which can be addressed, for example, through Multi-scale Finite Element analysis. For linear…
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A dynamical neural Galerkin scheme for filtering problems
This paper considers the filtering problem which consists in reconstructing the state of a dynamical system with partial observations coming from sensor measurements, and the knowledge that the dynamics are governed by a physical PDE model with unknown parameters. We present a filtering algorithm…
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Predicting ultimate hydrogen production and residual volume during cyclic underground hydrogen storage in porous media using machine learning
Underground hydrogen storage (UHS) is a promising solution for balancing renewable energy supply by storing excess energy as molecular hydrogen (H2) for later use. Large-scale UHS in geological formations requires reservoir simulations of cyclic loading scenarios to optimize storage operations…
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Analysis and optimization of a liquid-vapor thermohydraulic model
This work presents a simplified model of compressible multiphase fluid flow in a heated porous medium. We first introduce the model and its numerical approximation using a linearized implicit finite volume scheme. We then propose a technique to accelerate the implicit scheme through a machine…
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Benchmarking PDE problems via machine learning for enhanced computational modeling
The rapid advancement of mathematical modeling and scientific computing has become instrumental in addressing complex challenges across diverse fields. This proposed project seeks to leverage the interdisciplinary platform provided by the CEMRACS (Centre d’Été Mathématique de Recherche Avancée en…
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Limit theorems: some recent results
The article presents a series of recent results in the field of limit theorems which allow to appreciate the richness of this theme. These results include: the study of the asymptotic behaviour of cumulative processes with applications to Hawkes processes; maximal inequalities and functional…
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Asynchronous layerwise deep learning with MCMC on low-power devices
We present a new architecture to learn a light neural network using an asynchronous layerwise bayesian optimization process deployed on low-power devices. The procedure is based on a sequence of five modules. In each module, an accept-reject algorithm allows to update real-valued - or binary -…
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Introduction aux équations aux dérivées partielles stochastiques
Le but de ces notes de cours est relativement simple, il s’agit de montrer comment aborder les équations aux dérivées partielles stochastiques en tant qu’objet infini-dimensionnel dérivant d’un système d’équations différentielles stochastiques en démarrant avec des notions simples sur la…
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A bi-directional low-Reynolds-number swimmer with passive elastic arms
It has been recently shown that it is possible to design simple artificial swimmers at low Reynolds number that possess only one degree of freedom and, nevertheless, can overcome Purcell’s celebrated scallop theorem. One of the few examples is given by Montino and DeSimone, Eur. Phys. J. E, vol…
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Investigation on the stability in a thick spray model
The aim of this work is to discuss linear stability and instability properties of a thick spray model. We linearize the equation and we give a criterion on the equilibrium to have linear instability. We also present numerical illustrations.
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Remarks on variable Lebesgue spaces and fractional Navier-Stokes equations
In this work we study the 3D Navier-Stokes equations, under the action of an external force and with the fractional Laplacian operator (−Δ)α in the diffusion term, from the point of view of variable Lebesgue spaces. Based on decay estimates of the fractional heat kernel we prove the existence and…
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Stability and instability of the quasilinear Gross-Pitaevskii dark solitons***
We study a quasilinear Schrödinger equation with nonzero conditions at infinity. In previous works, we obtained a continuous branch of traveling waves, given by dark solitons indexed by their speed. Neglecting the quasilinear term, one recovers the Gross-Pitaevskii equation, for which the branch of…
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Relative entropy for the numerical diffusive limit of the linear Jin-Xin system
This paper deals with the diffusive limit of the Jin and Xin model and its approximation by an asymptotic preserving finite volume scheme. At the continuous level, we determine a convergence rate to the diffusive limit by means of a relative entropy method. Considering a semi-discrete approximation…