Network-related problems in M2ACS Mihai Anitescu

Multifaceted Mathematics for Complex Energy Systems ( M2ACS) Project Director: Mihai Anitescu, Argonne National Lab 2 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. 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 sub- domains 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 PICTURE

Leads to new challenges and math in and draws expertise from  Optimization  Probability/Stochastics/Statistics/Uncertainty Quantification  Dynamical Systems  Linear Algebra  Graph Theory  Data Analysis  Scalable Algorithms (Dynamics, Nonlinear Solvers, Optimization...)  Domain-Specific Languages. Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All" 3

One Challenge Class: Graph Theory Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All"4

Energy networks challenges  Energy networks math challenges: –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. –…… Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All" 5

New fundamental graph theory opportunity?  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  (John Doyle’s ) Hourglass Go to ”Insert (View) | Header and Footer" to add your organization, sponsor, meeting name here; then, click "Apply to All"6