[Dottorcomp] Fwd: Seminar Series on Scientific Machine Learning

[Luca Franco Pavarino]

With pleasure we announce the online seminar series on Scientific Learning
organized by the PhD school FoMICS-DADSi at USI Lugano/Switzerland.

The first seminar will be given on 19 May at 5:00 pm (UTC+2:00 Zurich time)
by Prof. Paris Perdikaris (Department of Mechanical Engineering and Applied
Mechanics, University of Pennsylvania).

The seminar will consist of a lecture plus a scientific talk.

Topic of the lecture:  Making neural networks physics-informed
Topic of the scientific talk: Learning the solution operator of parametric
partial differential equations with physics-informed DeepONets.

The event will be virtual. To register, please contact nestom a usi.ch<mailto:
nestom a usi.ch>.
Further details can be found at
https://fomics.usi.ch/index.php/workshops/15-ics/306-pinn


Part A: Lecture
Making neural networks physics-informed
Leveraging advances in automatic differentiation, physics-informed neural
networks are introducing a new paradigm in tackling forward and inverse
problems in computational mechanics. Under this emerging paradigm, unknown
quantities of interest are typically parametrized by deep neural networks,
and a multi-task learning problem is posed with the dual goal of fitting
observational data and approximately satisfying a given physical law,
mathematically expressed via systems of partial differential equations
(PDEs). PINNs have demonstrated remarkable flexibility across diverse
applications, but, despite some empirical success, a concrete mathematical
understanding of the mechanisms that render such constrained neural network
models effective is still lacking. In fact, more often than not, PINNs are
notoriously hard to train, especially for forward problems exhibiting
high-frequency or multi-scale behavior. In this talk we will discuss the
basic principles of making neural networks physics informed with an
emphasis on the caveats one should be aware of and how those can be
addressed in practice.

Part B: Seminar
Learning the solution operator of parametric partial differential equations
with physics-informed DeepONets
Deep operator networks (DeepONets) are receiving increased  attention
thanks to their demonstrated capability to approximate  nonlinear operators
between infinite-dimensional Banach spaces. However, despite their
remarkable early promise, they typically require large training data-sets
consisting of paired input-output observations which may be expensive to
obtain, while their predictions may not be consistent with the underlying
physical principles that generated the observed data. In this work,  we
propose a novel model class coined as physics-informed DeepONets,  which
introduces an effective regularization mechanism for biasing the outputs of
DeepOnet models towards ensuring physical consistency. This is accomplished
by leveraging automatic differentiation to impose the underlying physical
laws via soft penalty constraints during model training. We demonstrate
that this simple, yet remarkably effective extension can not only yield a
significant improvement in the predictive accuracy of DeepOnets, but also
greatly reduce the need for large training data-sets. To this end, a
remarkable observation is that physics-informed DeepONets are capable of
solving parametric partial differential equations (PDEs) without any paired
input-output observations, except for a set of given initial or boundary
conditions. We illustrate the effectiveness of the proposed framework
through a series of comprehensive numerical studies across various types of
PDEs.  Strikingly, a trained physics informed DeepOnet model can predict
the solution of O(1000)  time-dependent PDEs in a fraction of a second --
up to three orders of magnitude faster compared to a conventional PDE
solver.




––––––––––––––––––––––––––––––––––
Prof. Dr. Rolf Krause

Chair for Advanced Scientific Computing
Group High Performance Methods for Numerical Simulation  in Science,
Medicine and Engineering

Euler Institute

Center for Computational Medicine in Cardiology

https://www.euler.usi.ch<https://www.euler.usi.ch/>


Università della Svizzera italiana

East Campus - Sector D
Office D5.15
Via la Santa 1
6962 Lugano-Viganello, Switzerland
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