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BEGIN:VEVENT
UID:20201025T041348CET-3606mL9zHU@ical.php
DTSTAMP:20201025T031048Z
CLASS:PUBLIC
DESCRIPTION:Abstract: In this talk I will try to provide a very quick intr
oduction from\n generic artificial neural networks (ANN) to their applicat
ion to numerically solving PDE. This less of a research talk\, and more li
ke a tutorial and practical in nature.\n In the first part\, I will descri
be a simple model of feed-forward artificial neural network\, starting fro
m the biologically motivated individual perceptron as its core unit. If te
chnology permits\, I will include a MATLAB demonstration for some simple r
egression and classification problems\, and mention the universal represen
tation theorem.\nIn the intermission\, I will provide a superficial overvi
ew of more specific/complicated network architectures that are currently b
eing employed\, such as convolutional NN\, recurrent NN\, auto-encoder net
works\, generative adversarial networks (GAN). I will also hint at the dif
ference between supervised and unsupervised (or\n self-supervised) trainin
g\, as well as talk about a menu of activation functions and network regul
arizers.\n In the second part\, we will focus on a relatively recent appro
ach to use 'Deep learning' to numerically tackle (certain) PDE. We will sp
ecifically look at the core ideas in the 2018 paper on 'Deep Galerkin Meth
ods' [1]. There\, we construct an ANN to represent the unknown function u:
for arbitrary input values x\, the network will evaluate to\n an approxim
ation of u(x). This DGM network will be trained using a loss\n function de
fined based on the PDE terms\, and converge to the solution of\n the PDE.
Again\, if technology permits\, I will provide a live demo of a (few) simp
le examples.\n\n [1] Sirignano and Spiliopoulos\, 'DGM: A deep learning al
gorithm for\n solving partial differential equations'\, Journal of Computa
tional\n Physics 375 (2018):1339-1364.
DTSTART:20200917T150000
DTEND:20200917T160000
LOCATION:Webex Meeting number: 120 556 7048 Password: applied
SUMMARY:Deep learning and PDE: a quick and practical introduction
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