Transcript Mihai Anitescu - Princeton EDGE Lab

Network-related problems in M2ACS
Mihai Anitescu
Multifaceted Mathematics for Complex Energy Systems (M2ACS)
Project Director: Mihai Anitescu, Argonne National Lab
Goals:
• Taking a holistic view, develop deep mathematical
understanding and effective algorithms at the
intersection of multiple math areas for problems
with multiple math facets (dynamics, graph theory,
integer/continous, probabilistic …) for CES
• We do integrative mathematics to support a DOE
grand challenge while advancing math itself.
PICTURE
Integrated Novel Mathematics Research:
• Predictive modeling
• Mathematics of decisions
• Scalable algorithms for optimization and
dynamic simulation
• Integrative frameworks (90/10 vs 10/90
Mission; we identify the math patterns that will
enable the CSE applications.
Long-Term DOE Impact:
• Development of new mathematics at the
intersection of multiple mathematical subdomains
• Addresses a broad class of math patterns from
complex energy systems, such as :
• Planning for power grid and related
infrastructure
• Analysis and design for renewable energy
integration
Team: Argonne National Lab (Lead), Pacific Northwest National Lab,
Sandia National Lab, University of Wisconsin, University of Chicago
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Leads to new challenges and math in and draws
expertise from
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Optimization
Probability/Stochastics/Statistics/Uncertainty Quantification
Dynamical Systems
Linear Algebra
Graph Theory
Data Analysis
Scalable Algorithms (Dynamics, Nonlinear Solvers, Optimization ...)
Domain-Specific Languages.
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One Challenge Class: Graph Theory
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Energy networks challenges
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Energy networks math challenges:
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Scalable dynamics and optimization solvers for network constraints
Models of network evolution
Emerging temporal and spatial network-scales.
Probabilistic model of network failure.
Synthetic networks to address privacy, competitiveness and incomplete data issues
Estimation and calibration of probabilistic network structure models.
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New fundamental graph theory opportunity?
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How do we concisely but comprehensively
for our goals parameterize graph
structure?
What are probabilistic models for graph
theory with “few parameters” that capture
the fundamentals of end-goal behaviors
(including evolution)?
What are graph metrics which are
“sufficient statistics” (both state and
topology) for our problems? –stats
mechanics analogy: the only “predictable
observables”
How do we know the resulting models are
consistent and sample from such models –
heterogeneous materials analogy?
Solution will likely involve: probability, data
analysis, optimization, graph theory,
dynamical systems
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(John Doyle’s ) Hourglass
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