Dear all,
the next GSSI Math Colloquium will be held on Thursday June 17
at 5pm (please note **the time is 5pm instead of the
usual 3pm**).
The speaker is Lars Ruthotto, with a lecture connecting numerical
methods for differential equations and deep learning architectures.
More details below.
Lars Ruthotto is Associate Professor of Mathematics and Computer
Science at Emory University (Atlanta, USA).
Please feel free to distribute this announcement as you see fit.
Looking forward to seeing you all on Thursday!
Paolo Antonelli, Stefano Marchesani, Francesco Tudisco and Francesco
Viola
---------------------
Title:
Numerical Methods for Deep Learning motivated by Partial
Differential Equations
Abstract:
Understanding the world through data and computation has always
formed the core of scientific discovery. Amid many different
approaches, two common paradigms have emerged. On the one hand,
primarily data-driven approaches—such as deep neural networks—have
proven extremely successful in recent years. Their success is based
mainly on their ability to approximate complicated functions with
generic models when trained using vast amounts of data and enormous
computational resources. But despite many recent triumphs, deep
neural networks are difficult to analyze and thus remain mysterious.
Most importantly, they lack the robustness, explainability,
interpretability, efficiency, and fairness needed for high-stakes
decision-making. On the other hand, increasingly realistic
model-based approaches—typically derived from first principles and
formulated as partial differential equations (PDEs)—are now
available for various tasks. One can often calibrate these
models—which enable detailed theoretical studies, analysis, and
interpretation—with relatively few measurements, thus facilitating
their accurate predictions of phenomena.
In this talk, I will highlight recent advances and ongoing work to
understand and improve deep learning by using techniques from
partial differential equations. I will demonstrate how PDE
techniques can yield better insight into deep learning algorithms,
more robust networks, and more efficient numerical algorithms. I
will also expose some of the remaining computational and numerical
challenges in this area.
—
Francesco Tudisco
Assistant Professor
School of Mathematics
GSSI Gran Sasso Science Institute
Web: https://ftudisco.gitlab.io