Network-related problems in M2ACS

1. Network-related problems in M2ACS Mihai Anitescu

2. 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 challengewhile 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 PICTURE Team: Argonne National Lab (Lead), Pacific Northwest National Lab, Sandia National Lab, University of Wisconsin, University of Chicago

3. 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"

4. 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"

5. 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"

6. 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"