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ECE 5694 - Nonlinearity & Predictability in the Real-World (3)

Course Description

Analysis of the impact nonlinearity and structural model error have on simulation-based predictability, detection, control, uncertainty quantification (UQ) and insight into actual systems whose dynamics are best described by nonlinear models. “All models are wrong;” presentation of methods for detecting how/when they fail. Introduction to a geometric view of dynamics, language and limitations of nonlinear dynamics and chaos. Resource allocation in the design and construction of nonlinear prediction/automated decision systems. The role of model-based probability(s) in real time monitoring, decision-making and policy/regulatory guidance. Comparison, evaluation and deep-combination of competing probabilistic engines. Implications for UQ in applications including guidance, AI,automated machinery, disaster risk reduction and sports.

Why take this course?

Today more than ever students in engineering and the sciences need to grasp the concepts, mathematical foundations, computational realities, challenges and open problems posed by nonlinearity and structural model error. This course will demonstrate uniquely (by quantitative examples from a wide variety of fields) the impacts of these issues both in model formulation and tuning, and in forecast interpretation and predictability. Probabilistic prediction experiments both on numerical simulations and on actual real-world systems provide students distinctive, valuable research skills to recognize, demonstrate and where possible cope with these issues in the future. Subtleties of linear algebra, experimental design and the nature of high-dimensional spaces sometimes underdeveloped in introductory courses are confronted. Projects provide a “feeling of risk” engagement with statistical methods that is not provided elsewhere. Students benefit from the opportunity to see how “hot topic” methods fail (which can include their own research interest) and ideally to see these failures before they manifest in practice.

Learning Objectives

  • Compute the descriptive statistics and information measures which quantify the predictability of nonlinear dynamical systems.
  • Formulate their personal probability forecasts in real time for a variety of events including hurricane formation and NFL home-team wins.
  • Estimate the time-scales on which these descriptive statistics are relevant in application, skillful in real-time, while discriminating between common causes of model failure and quantifying the decay of predictability and UQ in practice.
  • Evaluate the skill of competing forecast engines and discuss their expected skill in combination.
  • Translate model-based simulation and background information into probabilistic forecast distributions, then quantify, interpret and communicate their efficacy in decision support, either automated or with a human in the loop.
  • Analyze the strengths and weaknesses of model-based probabilistic decision support, and critique the role of such information in monitoring, guidance, and automated decision-making including AI and machine learning.