DATA-DRIVEN DYNAMICAL SYSTEMS, STOCHASTIC MODELING AND PREDICTION

Prerequisites & course information

Requisites: ( MATH 320 , 340 , 341 , 345 , or 375 ) and ( STAT/MATH 309 , 431 , STAT 311 , or MATH 531 ) and ( MATH 322 , 341 , 375 , 421 , or 467 ), graduate/professional standing, or declared in Mathematics VISP (undergraduate or graduate) Course Designation: Core GenEd - Natural Science & Wellness Breadth - Natural Science Level - Advanced L&S Credit - L&S Liberal Arts and Science Grad 50% - Counts toward 50% graduate coursework requirement Repeatable for Credit: No Last Taught: Spring 2026 Learning Outcomes: 1. Conduct numerical simulations of stochastic dynamical systems and implement data assimilation methods. Audience: Both Grad & Undergrad 2. Analyze data from a stochastic dynamical system and characterize the system's properties in terms of its statistics, such as mean, variance, and autocorrelation function. Audience: Both Grad & Undergrad 3. Calculate analytical formulas for the solutions of discrete-time stochastic processes and stochastic differential equations. Audience: Both Grad & Undergrad 4. Recall and state the basic properties of Brownian motion and the Wiener process. Audience: Both Grad & Undergrad 5. Illustrate the basic properties of Brownian motion and the Wiener process using numerical simulations. Audience: Both Grad & Undergrad 6. Estimate the parameters of a dynamical system using simulated data. Audience: Both Grad & Undergrad 7. Predict the future evolution of a dynamical system using analytical formulas and numerical simulations. Audience: Both Grad & Undergrad 8. Assess the accuracy of a prediction in terms of different definitions of error and uncertainty. Audience: Both Grad & Undergrad 9. Identify applications of course content in areas of modern research. Audience: Graduate Learning Outcomes: 1. Conduct numerical simulations of stochastic dynamical systems and implement data assimilation methods. Audience: Both Grad & Undergrad 2. Analyze data from a stochastic dynamical system and characterize the system's properties in terms of its statistics, such as mean, variance, and autocorrelation function. Audience: Both Grad & Undergrad 3. Calculate analytical formulas for the solutions of discrete-time stochastic processes and stochastic differential equations. Audience: Both Grad & Undergrad 4. Recall and state the basic properties of Brownian motion and the Wiener process. Audience: Both Grad & Undergrad 5. Illustrate the basic properties of Brownian motion and the Wiener process using numerical simulations. Audience: Both Grad & Undergrad 6. Estimate the parameters of a dynamical system using simulated data. Audience: Both Grad & Undergrad 7. Predict the future evolution of a dynamical system using analytical formulas and numerical simulations. Audience: Both Grad & Undergrad 8. Assess the accuracy of a prediction in terms of different definitions of error and uncertainty. Audience: Both Grad & Undergrad 9. Identify applications of course content in areas of modern research. Audience: Graduate