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NeuralPDE: Automating Physics-Informed Neural Networks (PINNs) with Error Approximations
[article]
2021
arXiv
pre-print
Preserved Fulltext
Physics-informed neural networks (PINNs) are an increasingly powerful way to solve partial differential equations, generate digital twins, and create neural surrogates of physical models. In this manuscript we detail the inner workings of NeuralPDE.jl and show how a formulation structured around numerical quadrature gives rise to new loss functions which allow for adaptivity towards bounded error tolerances. We describe the various ways one can use the tool, detailing mathematical techniques
arXiv:2107.09443v1
fatcat:22zfxicti5ed3msl6lcbzmynga
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... e using extended loss functions for parameter estimation and operator discovery, to help potential users adopt these PINN-based techniques into their workflow. We showcase how NeuralPDE uses a purely symbolic formulation so that all of the underlying training code is generated from an abstract formulation, and show how to make use of GPUs and solve systems of PDEs. Afterwards we give a detailed performance analysis which showcases the trade-off between training techniques on a large set of PDEs. We end by focusing on a complex multiphysics example, the Doyle-Fuller-Newman (DFN) Model, and showcase how this PDE can be formulated and solved with NeuralPDE. Together this manuscript is meant to be a detailed and approachable technical report to help potential users of the technique quickly get a sense of the real-world performance trade-offs and use cases of the PINN techniques.
Firstborn of Venice: Vicenza in the Early Renaissance State
1991
American Historical Review
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Battista Pagliarino labeled all 271 of his worthy families nobili, even those "of low condition." ...
Venetian disapproval led to temporary suspension of the horse race, but in 1460 the communal deputy Valerio Loschi revived and endowed the race "so that the whole day shall be festive." 21 Vicentines ...
doi:10.2307/2164129
fatcat:uvr62tll7rhaznbalolzbv6mqq
4 Si veda, tra l'altro, Mary McIntosh,-The homosexual role‖
2006
Sexual interactions
unpublished
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Storia della sessualità e studi LGBTIQ in una prospettiva interdisciplinare 31 Paolo Valerio, Fabiana Santamaria, Bambini e adolescenti intersessuali: quali dilemmi? ...
Questo è affrontato nel testo a cura di Paolo Valerio e Roberto Vitelli, Sesso e genere. Uno sguardo tra storia e nuove prospettive (Vitelli, Valerio, 2012) . ...
Uno sguardo tra storia e nuove prospettive (Vitelli, Valerio, 2012) . ...
fatcat:l4p2565jmzdpbg3t5tiitbxanu
GIORNALE LIGUSTICO DI ARCHEOLOGIA, STORIA E LETTERATURA FONDATO E DIRETTO A N N O N O N O LUCHETTO GATTILUSIO
unpublished
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Un altro atto di Guglielmo Pagliarino, del 26 aprile 1268, con tiene una quitanza generale rilasciata da esso Luchetto e dal fratei suo Giacomino a favore di Enrico Passio; ed è impor tante per ciò, che ...
Maona nuova gli confermo 1' appalto nel 1364· Alla di
lui morte, seguita nel 1381, 1' appalto venne concesso pei dieci
anni, e poscia nel 1391 rinnovato per un altro decennio, al
borghese Raffaello Valerio ...
fatcat:fi2ayb6nx5gobcavz6ylidsi44