[Amath-seminars] Boeing Colloquium Thursday, Nov. 2

[Amin Rahman]

Dear Amath and Friends,

Our next Boeing Colloquium, presented by Professor Houman Owhadi of Caltech
University (https://www.cms.caltech.edu/people/owhadi), will be held next
Thursday, Nov. 2, 2023, 4 – 5 p.m. in Smith Hall 205.

Title: Computational Hypergraph Discovery, a framework for connecting the
dots

Abstract: Function approximation can be categorized into three levels of
complexity. Type 1: Approximate an unknown function given  (possibly noisy)
input/output data. Type 2: Consider a collection of variables and functions
indexed by the nodes and hyperedges of a hypergraph (a generalization of a
graph in which edges can connect more than two vertices). Assume some of
the functions to be unknown. Given multiple samples from subsets of the
variables of the hypergraph (satisfying the functional dependencies imposed
by its structure), approximate all the unobserved variables and unknown
functions of the hypergraph. Type 3: Expanding on Type 2, if the hypergraph
structure itself is unknown, use partial observations (of subsets of the
variables of the hypergraph) to uncover its structure (the hyperedges and
potentially missing vertices) and then approximate its unknown functions
and unobserved variables. Numerical approximation, Supervised Learning, and
Operator Learning can all be formulated as type 1 problems (with functional
inputs/outputs spaces). Type 2 problems include solving and learning
(possibly stochastic) ordinary or partial differential equations, Deep
Learning, dimension reduction, reduced-ordered modeling, system
identification, closure modeling, etc. The scope of Type 3 problems extends
well beyond Type 2 problems and includes applications involving
model/equation/network discovery and reasoning with raw data. While most
problems in Computational Sciences and Engineering (CSE) and Scientific
Machine Learning (SciML) can be framed as Type 1 and Type 2 challenges,
many problems in science can only be categorized as Type 3 problems.
Despite their prevalence, these Type 3 challenges have been largely
overlooked due to their inherent complexity. Although Gaussian Process (GP)
methods are sometimes perceived as a well-founded but old technology
limited to curve fitting (Type 1 problems), a generalization of these
methods holds the key to developing an interpretable framework for solving
Type 2 and Type 3 problems inheriting the simple and transparent
theoretical and computational guarantees of kernel/optimal recovery
methods. This will be the topic of our presentation.


Best regards,
Amin

-- 
Aminur (Amin) Rahman (He/him/his)
Acting Instructor (postdoc)
Department of Applied Mathematics
http://faculty.washington.edu/arahman2
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