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METHOD:PUBLISH
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X-ORIGINAL-URL:https://matematica.unipv.it/
X-WR-CALNAME:Dipartimento di Matematica UNIPV
X-WR-CALDESC:
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-PUBLISHED-TTL:PT1H
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BEGIN:VEVENT
CLASS:PUBLIC
DTSTART;TZID=Europe/Rome:20220322T150000
DTEND;TZID=Europe/Rome:20220322T160000
DTSTAMP:20220308T165300
UID:MEC-2d2c18c1aaeac9fcc028dd14f4c074ce@matematica.unipv.it
CREATED:20220308
LAST-MODIFIED:20220308
PRIORITY:5
TRANSP:OPAQUE
SUMMARY:Neural network and operator network approximations for elliptic PDEs
DESCRIPTION:Neural network and operator network approximations for elliptic PDEs\nCarlo Marcati (Università di Pavia)\nThe application of neural networks (NNs) to the numerical solution of PDEs has seen growing popularity in the last five years: NNs have been used as an ansatz space for the solutions, with different training approaches (PINNs, deep Ritz methods, etc.); they have also been used to infer discretization parameters and strategies. In this talk, I will focus on deep ReLU NN approximation theory. I will first show how NNs accurately approximate functions with isolated singularities, for example the solutions to elliptic problems in polygons and polyhedra, or eigenfunctions of problems with singular potentials that arise in quantum chemistry. I will then introduce operator networks, which approximate the solution operator of PDEs. I will, in particular, consider operator networks that, given a fixed right-hand side, map sets of diffusion-reaction coefficients into the space of solutions (coefficient-to-solution map). When the coefficients are smooth, the size of the networks can then be bounded with respect to the H^1 norm of the error, uniformly over the parameter set. The proofs of our approximation rates combine elliptic regularity, classical and recent results in numerical analysis, and tools from NN approximation theory.\n
URL:https://matematica.unipv.it/events/neural-network-and-operator-network-approximations-for-elliptic-pdes/
ORGANIZER;CN=Carlo Marcati (Università di Pavia):MAILTO:
CATEGORIES:Seminari di matematica applicata
LOCATION:Aula Beltrami
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