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Results: Short Term Forecasting of Chaos
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Machine Learning Analysis of Chaos and Vice Versa - Edward Ott, University of Maryland
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- 1 Intro
- 2 THE GENERAL MACHINE LEARNING (ML) SET UP FOR THIS TALK
- 3 illustrative Example: The Kuramoto-Sivashinsky (KS) Equation The KS equation is a spatiotemporally chaotic system
- 4 Results: Short Term Forecasting of Chaos
- 5 Has the long term dynamical behavior of the Kuramoto-Sivashinsky system truly been replicated? • If it has, even after the sensitive dependence implied by chaos causes prediction to fail, the ergodic…
- 6 Finding Ergodic Properties of a Dynamical System Purely from a Finite Time Series Data String
- 7 Some Tasks that Machine Learning of Ergodic Behavior Might Enable
- 8 Lyapunov exponents provide useful information • The expected duration of useful forecasts of a chaotic process can be estimated as the log of the amount of uncertainty in the specification of initial…
- 9 Lyapunov Exponents for the Example of the KS Equation
- 10 Our Modification of the Lyapunov Exponent Spectrum Remove Red: True KS system two zero
- 11 Why the ML System Does Not See the Galilean Symmetry Associated with the Galilean symmetry is a constant of motion of the KS equation
- 12 Question: Aside from possible corrections for symmetries, does the short term, closed loop forecasting machine learning system always successfully replicate the long term ergodic behavior of the chao…
- 13 EXAMPLE: THE KS EQUATION Prediction succeeds. Replication of long term
- 14 WHEN, HOW, AND WHY IS ERGODIC BEHAVIOR REPLICATED? WHEN, HOW, AND WHY CAN REPLICATION FAIL?
- 15 Outline of Lu et al. Let A denote the attractor of the unknown dynamical system from which the measurements are taken. Lu et al. show that training can ideally lead to the existence of an invariant s…
- 16 GENERALIZED SYNCHRONIZATION AND THE ECHO STATE PROPERTY OF THE OPEN-LOOP CONFIGURATION
