by
Prof.Bernold Fiedler(Mathematics Institute, Free University of Berlin)
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Asia/Tokyo
Room 435, 437 Main Research Building
Room 435, 437 Main Research Building
Description
Dates: 15:30 p.m., October 4th (Thu.)
Place: Room 435, 437 Main Research Building
Lecturer: Prof. Bernold Fiedler (Mathematics Institute, Free University
of Berlin)
Title: Structured hybrid models and Hilbert’s thirteenth problem
Abstract:
When can a function of several variables be written as a finite composition of functions of fewer variables? This is the question of Hilbert’s problem XIII.
The answer by young V.I. Arnold in the form given by Kolmogorov says:
always, by functions of two variables, if we assume continuity. The
answer by Vitushkin says:
almost never, if we require differentiability. Modeling, for example in chemical engineering, frequently provides input-output relations
as compositions of input-output relations of smaller production units,
or ”reactors”.
The individual reactor mod- els, or functions, may be known (”white
box”) or unknown (”black box”). The hybrid model is the composition of such black- and white- box functions.
Let black boxes have at most d inputs – typically much less than the
total number of inputs to the composition network. Assuming sufficient, and at times prohibitive, differentiability we indicate how to uniquely identify all unknown ”black-box” functions in the network from only d-dimensional data on their composition.
This addresses the ”curse of dimension” in data analysis, and provides extrapolability.
Results are joint work with Stefan Liebscher, Andreas Schuppert, and
others. See also
http://dynamics.mi.fu-berlin.de/
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