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CATEGORIES:Ph.D. Presentations
DESCRIPTION:Description: We consider the problem of directly controlling (i
.e.\, reshaping) stochastic uncertainties subject to continuous-time contro
lled nonlinear dynamics and fixed deadline constraints. This problem is kno
wn as the generalized Schrödinger bridge problem. Historically\, a version
of the problem originated in the works of Erwin Schrödinger in 1931-32\, an
d can be seen as the stochastic version of the optimal mass transport probl
em with prior nonlinear dynamics. From a control-theoretic viewpoint\, this
is an atypical stochastic optimal control problem--``atypical" because ins
tead of boundary conditions on a finite dimensional state space\, the probl
em involves endpoint boundary conditions on the space of joint state probab
ility density functions\, or probability measures in general. In recent yea
rs\, significant strides have been made in the control community to solve s
uch problems for some special classes of prior nonlinear dynamics including
control-affine gradient and mixed conservative-dissipative systems. Howeve
r\, the existing algorithms in the literature exploit special structures of
such prior nonlinear dynamics\, but in the absence of such structures\, no
general computational framework is available.In this work\, we propose to
leverage recent advances in machine learning\, specifically physics-informe
d neural networks (PINNs)\, to numerically solve generalized Schrödinger br
idge problems. We introduce a variant of the standard PINN to account for t
he endpoint joint distributional constraints via the Sinkhorn divergence th
at exploits the geometry on the space of probability measures. We explain h
ow this architecture can be implemented as differentiable layers. Our propo
sed framework allows numerically solving variants of Schrödinger bridge pro
blems for which no algorithms are available otherwise. This includes system
s with control non-affine as well as nonlinear non-autonomous (i.e.\, expli
cit time dependent) drifts and diffusions\, as well as situations where the
controlled dynamics may only be available in a data-driven manner (e.g.\,
in the form of neural networks).We demonstrate the efficacy of our computat
ional framework using two engineering case studies. The first case study in
volves optimally steering the stochastic angular velocity of a rotating rig
id body from a given statistics to another over a prescribed time horizon.
This is of interest\, for example\, in controlling the spin of a spacecraft
in the presence of stochastic uncertainties. The second case study involve
s controlled colloidal self-assembly for the purpose of advanced manufactur
ing of materials with desirable properties. In this case\, first principle
physics-based control-oriented models are difficult to obtain due to comple
x molecular dynamics\, quantum effects and thermal fluctuations. We show ho
w such colloidal self-assembly problems are amenable to generalized Schrödi
nger bridge formulation\, and solve the data-driven distribution steering p
roblems for such systems using our proposed framework. We provide detailed
numerical results and discuss the implementation details for the proposed c
omputational architecture and algorithms.\n\nEvent Host: Charlie Yan\, M.S.
Student\, Electrical Engineering\n\nAdvisor: Abhishek Halder
DTEND:20230518T170000Z
DTSTAMP:20231210T191530Z
DTSTART:20230518T160000Z
LOCATION:
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SUMMARY:MS Thesis Defense: C. Yan - Neural Schrödinger Bridge with Sinkhorn
Losses
UID:tag:localist.com\,2008:EventInstance_43174975384532
URL:https://calendar.ucsc.edu/event/ms_thesis_defense_c_yan_-_neural_schrod
inger_bridge_with_sinkhorn_losses
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