Scalable methods for optimal control of systems governed by PDEs with random coefficient fields

53 Pages·2017·7.8 MB·English

Scalable methods for optimal control of systems
governed by PDEs with random coefficient fields
Alen Alexanderian,1 Peng Chen,2 Omar Ghattas,2
No´emi Petra3 Georg Stadler,4 Umberto Villa2
1DepartmentofMathematics
NorthCarolinaStateUniversity
2InstituteforComputationalEngineeringandSciences
TheUniversityofTexasatAustin
3SchoolofNaturalSciences
UniversityofCalifornia,Merced
3CourantInstituteofMathematicalSciences
NewYorkUniversity
April20,2017
ICESBabuˇskaForum
TheUniversityofTexasatAustin
Bayesianinversion
Experimentaldatay
πpost(m|y)∝πlike(y|m)π0(m)
Designofexperiments
(cid:90)
mξin Ψ(cid:2)πpost(m|y;ξ)(cid:3)π(y)dy
ξ:experimentaldesign
Ψ:designobjective/criterion
Optimalcontrol/design
underuncertainty
(cid:90)
e.g.min q(z,m)µ(dm)
z
From data to decisions under uncertainty
Uncertainparameterm
MathematicalModel
(m,u) = f
A
QuantityofInterest(QoI)
q(m)
OmarGhattas (ICES,UTAustin) Optimalcontrolunderuncertainty Mar24,2017 2/41
Designofexperiments
(cid:90)
mξin Ψ(cid:2)πpost(m|y;ξ)(cid:3)π(y)dy
ξ:experimentaldesign
Ψ:designobjective/criterion
Optimalcontrol/design
underuncertainty
(cid:90)
e.g.min q(z,m)µ(dm)
z
From data to decisions under uncertainty
Uncertainparameterm
prior
Bayesianinversion
Experimentaldatay
posterior πpost(m|y)∝πlike(y|m)π0(m)
πlike(y|m)=πnoise(Bu−y)
MathematicalModel
(m,u) = f
A
QuantityofInterest(QoI)
q(m)
OmarGhattas (ICES,UTAustin) Optimalcontrolunderuncertainty Mar24,2017 2/41
Optimalcontrol/design
underuncertainty
(cid:90)
e.g.min q(z,m)µ(dm)
z
From data to decisions under uncertainty
Uncertainparameterm
prior
Bayesianinversion
Experimentaldatay
posterior πpost(m|y)∝πlike(y|m)π0(m)
πlike(y|m)=πnoise(Bu−y)
experiments
MathematicalModel
(m,u) = f
A
QuantityofInterest(QoI) Designofexperiments
q(m) mξin(cid:90) Ψ(cid:2)πpost(m|y;ξ)(cid:3)π(y)dy
ξ:experimentaldesign
Ψ:designobjective/criterion
OmarGhattas (ICES,UTAustin) Optimalcontrolunderuncertainty Mar24,2017 2/41
From data to decisions under uncertainty
Uncertainparameterm
prior
Bayesianinversion
Experimentaldatay
posterior πpost(m|y)∝πlike(y|m)π0(m)
πlike(y|m)=πnoise(Bu−y)
experiments
MathematicalModel
(m,u) = f(;z)
zA:=controlfunc·tion
QuantityofInterest(QoI) Designofexperiments
q(z,m) mξin(cid:90) Ψ(cid:2)πpost(m|y;ξ)(cid:3)π(y)dy
ξ:experimentaldesign
Ψ:designobjective/criterion
Optimalcontrol/design
underuncertainty
(cid:90)
e.g.min q(z,m)µ(dm)
z
OmarGhattas (ICES,UTAustin) Optimalcontrolunderuncertainty Mar24,2017 2/41
Example: Groundwater contaminant remediation
Source: ReedMaxwell,CSM
OmarGhattas (ICES,UTAustin) Optimalcontrolunderuncertainty Mar24,2017 3/41
Example: Groundwater contaminant remediation
Inverse problem
Infer (uncertain) soil permeability from (uncertain) measurements of pressure
head at wells and from a (uncertain) model of subsurface flow and transport
Prediction (or forward) problem
Predict (uncertain) evolution of contaminant concentration at municipal wells
from(uncertain)permeabilityand(uncertain)subsurfaceflow/transportmodel
Optimal experimental design problem
Where should new observation wells be placed so that permeability is inferred
with the least uncertainty?
Optimal design problem
Where should new remediation wells be placed so that (uncertain)
contaminant concentrations at municipal wells are minimized?
Optimal control problem
What should the rates of extraction/injection at remediation wells be so that
(uncertain) contaminant concentrations at municipal wells are minimized?
OmarGhattas (ICES,UTAustin) Optimalcontrolunderuncertainty Mar24,2017 4/41
Applications of inverse problems in CCGO
Antarctic ice sheet flow (+ ocean dynamics)
Joint with Patrick Heimbach, Tom Hughes, Tobin Isaac (Georgia Tech),
Tom O’Leary-Roseberry, Noemi Petra (UC-Merced), Georg Stadler (NYU),
Umberto Villa, Alice Zhu
Globalandregionalseismicinversion,jointseismic–EMinversion,inversescattering
Joint with Hossein Aghakhani, Nick Alger, Tan Bui, Ben Crestel, David Keyes
(KAUST), George Turkiyyah (KAUST), Georg Stadler (NYU), Umberto Villa
Global mantle convection
Joint with Mike Gurnis (Caltech), Johann Rudi, Georg Stadler (NYU)
Poroelastic subsurface flow inversion and management of induced seismicity
Joint with Amal Alghamdi, Marc Hesse, Georg Stadler (NYU), Umberto Villa,
Karen Willcox (MIT)
Turbulent combustion: inference and control
Joint with George Biros, Peng Chen, Matthias Heinkenschloss (Rice),
Myoungkyu Lee, Bob Moser, Todd Oliver, Chris Simmons, David Sondak,
Andrew Stuart (Caltech), Umberto Villa, Karen Willcox (MIT)
Reservoir inversion
Joint with George Biros, Tan Bui, Clint Dawson, Sam Estes, John Lee,
Umberto Villa
Soft tissue biomechanical inversion
Joshua Chen, Michael Sacks, Umberto Villa
OmarGhattas (ICES,UTAustin) Optimalcontrolunderuncertainty Mar24,2017 5/41
Forward and inverse global mantle convection modeling
OmarGhattas (ICES,UTAustin) Optimalcontrolunderuncertainty Mar24,2017 6/41
Scalable solver (2015 Gordon Bell Prize)
OmarGhattas (ICES,UTAustin) Optimalcontrolunderuncertainty Mar24,2017 7/41