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Machine learning for fast and reliable solution of time-dependent differential equations

Publications associées (30)

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In the rapidly evolving landscape of machine learning research, neural networks stand out with their ever-expanding number of parameters and reliance on increasingly large datasets. The financial cost and computational resources required for the training p ...

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Transformer models such as GPT generate human-like language and are predictive of human brain responses to language. Here, using functional-MRI-measured brain responses to 1,000 diverse sentences, we first show that a GPT-based encoding model can predict t ...

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A Combination Technique for Optimal Control Problems Constrained by Random PDEs

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We present a combination technique based on mixed differences of both spatial approximations and quadrature formulae for the stochastic variables to solve efficiently a class of optimal control problems (OCPs) constrained by random partial differential equ ...

2024

Global existence for perturbations of the 2D stochastic Navier-Stokes equations with space-time white noise

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We prove global in time well-posedness for perturbations of the 2D stochastic Navier-Stokes equations partial derivative( t)u + u center dot del u = Delta u - del p + sigma + xi, u(0, center dot ) = u(0),div (u) = 0, driven by additive space-time white noi ...

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Academic Press Inc Elsevier Science2024

Reliable data-driven decision-making through optimal transport

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Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks th ...

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Extracting maximal information from experimental data requires access to the likelihood function, which however is never directly available for complex experiments like those performed at high energy colliders. Theoretical predictions are obtained in this ...

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Topics in statistical physics of high-dimensional machine learning

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In the past few years, Machine Learning (ML) techniques have ushered in a paradigm shift, allowing the harnessing of ever more abundant sources of data to automate complex tasks. The technical workhorse behind these important breakthroughs arguably lies in ...

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Machine learning (ML) enables artificial intelligent (AI) agents to learn autonomously from data obtained from their environment to perform tasks. Modern ML systems have proven to be extremely effective, reaching or even exceeding human intelligence. Altho ...

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

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This paper presents the new 2D electrostatic particle -in -cell code FENNECS developed to study the formation of magnetized non -neutral plasmas in geometries with azimuthal symmetry. This code has been developed in the domain of gyrotron electron gun desi ...

2024