ALLOWAP: ALgorithms for Large-scale
Optimization
of WAve Propagation Problems
波動現象中若干大型優化問題的運算方
法
PROJET
ANR-19-CE46-0013-01. 2020-2024
Abstract
The goal of this project is to design and develop
large-scale parallel algorithms for dealing with optimization
problems
involving wave phenomena. Such problems arise in many
practical applications:
two examples are in seismic inversion, where one tries to
deduce the geology of
rock formations that best fits the available seismic data, and
in wave
localization, which can be used to improve the efficiency of
wireless charging
devices. To make the optimization tractable, parallel
computers must be used to
cope with the large amounts of data and intensive computation
inherent to these
problems. In the last decade, parallel-in-time methods have
made enormous
progress: for parabolic problems, a near-optimal scaling with
respect to the
number of processors has been achieved (scalability). For wave
propagation,
there has been no such success.
To achieve our
goal of developing innovative,
space-time parallel methods for solving such optimization
problems, we will
consider three interrelated aspects. The first aspect is the
direct simulation
of wave-type systems, which must be done repeatedly over the
course of the
optimization. The second aspect is the optimization over
bounded time horizons,
which is at the heart of both data assimilation and wave
localization problems.
Here, our approach is to split the full optimality system into
many subsystems
in time and in space, and to use transmission conditions to
ensure consistency
with the global solution. We will then exploit the control
structure and use
the discrete Hilbert Uniqueness Method to derive optimal
transmission
conditions. Approximating these conditions by local,
easy-to-implement
conditions will then lead to highly efficient methods. The
third aspect
concerns the assimilation of infinite streams of data, where
one cannot benefit
from adjoint techniques. We will tackle this problem by
combining parallel
simulation with observer approaches, so that the time
integration benefits from
the space-time parallel methods mentioned above. Our methods
will be used to
tackle two concrete problems, namely wave localization in
complex geometries
and data assimilation in geophysical and environmental
systems.