Project Grant 2229011

COLLABORATIVE RESEARCH: AMPS: RARE EVENTS IN POWER SYSTEMS: NOVEL MATHEMATICS, STATISTICS AND ALGORITHMS. -THE PROJECT GOAL IS TO BUILD A COMPREHENSIVE THEORETICAL AND ALGORITHMIC FRAMEWORK OF AI/ML FOR DETECTION, TRACKING, FORECASTING AND MITIGATION OF EXTREME AND RARE BUT CONSEQUENTIAL EVENTS IN POWER SYSTEMS. THE OVERWHELMING MAJORITY OF CONVENTIONAL APPLICATIONS OF AI/ML INVOLVE LEARNING THE `MIDDLE' OF THE DISTRIBUTION. APPLICATIONS HAVE BECOME MOSTLY ROUTINE EXERCISES IN `INTERPOLATION' IN BOTH INDUSTRY AND ACADEMIA, THANKS TO THE DEEP LEARNING (DL) BREAKTHROUGH. BASED ON COPIOUS AMOUNTS OF `TYPICAL' INFORMATION, A GENERIC DL TASK FOCUSES ON DESIGNING ALGORITHMS WHICH EXTRACT AND BUILD FEATURES WHICH REPRESENT THE MOST COMMON CHARACTERISTICS OF THE MASSIVE SCIENTIFIC DATA. THE DIFFERENCE BETWEEN THIS CONVENTIONAL DL SITUATION AND DL FOR EXTREME EVENTS IS THAT, IN THE LATTER SETTING, THE TASK IS ONE OF EXTRAPOLATION. MOREOVER, MASSIVE SCIENTIFIC DATA, BENEFICIAL IN NORMAL REGIMES, BECOMES A CURSE FOR EXTRAPOLATION WHICH FOCUSES ON EXTRACTING RARE BUT SIGNIFICANT EVENTS -- THE BLACK SWANS -- WHICH ARE, LIKE A NEEDLE IN A HAYSTACK, NOTORIOUSLY DIFFICULT TO DETECT AND TRACK, AND THEN USE TO MAKE RELIABLE FORECASTS AND POSSIBLE MITIGATIONS AS EVENTS DEVELOP. IN OTHER WORDS, BASED ON VERY LIMITED INFORMATION, THE RESEARCH OBJECTIVE IS TO EXTRACT REGULARITY PATTERNS, WHICH CAN PERSIST OVER LONG SPATIAL AND TEMPORAL SCALES, THAT THEN LEAD TO POTENTIAL RARE EXTREMES. THE PI WILL STUDY MODELS THAT RELATE TO SUCH AS THE EXTREME HEAT OF THE SUMMER OF 2020 OR THE EXTREME COLD IN TEXAS IN THE SPRING OF 2021; POWER SYSTEM BLACKOUTS, LIKE THE 2004 EAST COAST BLACKOUT. THE METHODS WILL HAVE EVEN BROADER APPLICABILITY, FOR EXAMPLE, IF PREDICTION AND DETECTION OF FAILURES IN OTHER PHYSICAL AND CYBER NETWORKS. PI WILL INVESTIGATE SPECIFIC OBJECTIVES IN THREE AREAS: (A) PHYSICS-INFORMED STATISTICAL MODELING FOR POWER SYSTEMS, (B) COMPUTATIONAL METHODS OF INFERENCE FOR EXTREMES IN POWER SYSTEMS, AND (C) LEARNING AND QUANTIFICATION OF ERRORS IN THE MODELS. THEY WILL APPLY THE METHODOLOGY DEVELOPED WITHIN THE NOVEL FRAMEWORK TO INCLUDING EARLY DETECTION OF RARE BUT DEVASTATING CASCADING FAILURES IN POWER SYSTEMS. THE MATHEMATICAL/THEORETICAL CORE OF THE METHODOLOGY WILL CONSIST IN INTEGRATION OF POWER-SYSTEM-SPECIFIC CONSTRAINTS INTO THE GENERAL EXTREME VALUE THEORY (EVT). THIS INTEGRATION WILL BE ACHIEVED VIA SYNTHESIS OF EVT WITH THE COMPLEMENTARY APPROACHES FROM THE PHYSICS INFORMED MACHINE LEARNING, PROBABILISTIC GRAPHICAL MODELS AND OPTIMAL TRANSPORT THEORY. ON THE COMPUTATIONAL SIDE, PI WILL UTILIZE EVT TO DEVELOP EFFICIENT MODEL CALIBRATION, INFERENCE AND LEARNING ALGORITHMS FOR LARGE-SCALE STOCHASTIC SYSTEMS, DESCRIBED VIA PROPERLY PARAMETERIZED NON-LINEAR REAL OR COMPLEX-VALUED ALGEBRAIC AND DIFFERENTIAL EQUATIONS WITH RANDOM STOCHASTIC INPUT. MOREOVER, THEIR COUPLED THEORETICAL AND COMPUTATIONAL EFFORTS WILL BE USEFUL IN A BROADER CONTEXT FOR EXTENDING THE RARE EVENT CONTROL AND PREVENTION METHODOLOGY TO OTHER SYSTEMS AND APPLICATIONS OF NATIONAL IMPORTANCE. THIS AWARD REFLECTS NSF'S STATUTORY MISSION AND HAS BEEN DEEMED WORTHY OF SUPPORT THROUGH EVALUATION USING THE FOUNDATION'S INTELLECTUAL MERIT AND BROADER IMPACTS REVIEW CRITERIA.