Random Dynamical System

Random dynamical systems, encompassing systems evolving under both deterministic and stochastic influences, are studied to understand their behavior and predict future states. Current research focuses on high-dimensional systems, employing techniques like spectral analysis to identify independent lower-dimensional subsystems and leveraging recurrent neural networks and physics-informed neural networks to model and simulate their trajectories, often incorporating generative adversarial networks for probabilistic forecasting. These advancements are crucial for improving the accuracy and efficiency of system identification, control, and prediction across diverse fields, including finance, biology, and engineering, particularly where dealing with noisy or incomplete data.

Papers

October 16, 2023

From Spectral Theorem to Statistical Independence with Application to System Identification
Muhammad Abdullah Naeem, Amir Khazraei, Miroslav Pajic
Application Proficiency Dynamical System System Identification Linear Transformation Stable Dynamical System Random Dynamical System

April 4, 2023

Learning and Concentration for High Dimensional Linear Gaussians: an Invariant Subspace Approach
Muhammad Abdullah Naeem
LeArning Abstract Gaussian Distribution Selective Focus Invariant Subspace Random Dynamical System Isotropic Gaussian Noise

January 31, 2023

Recurrences reveal shared causal drivers of complex time series
William Gilpin
Unobserved Variable Complex Time Series Random Dynamical System Recurrence Plot

December 7, 2022

Concentration Phenomenon for Random Dynamical Systems: An Operator Theoretic Approach
Muhammad Abdullah Naeem, Miroslav Pajic
State Space Markov Chain Concentration Bound Concentration Inequality Operator Theory Random Dynamical System Exponential Concentration Transition Operator

November 15, 2022

Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networks
Adrian N. Bishop
Recurrent Neural Network Deep Recurrent Neural Network Trajectory Corner Case Random Dynamical System

November 1, 2022

Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows
Raphaël Pellegrin, Blake Bullwinkel, Marios Mattheakis, Pavlos Protopapas
Neural Network Deep Learning Transfer Learning Physic Informed Neural Network Multi Head Fast Simulation Random Dynamical System Reactive Flow

May 25, 2022

Transportation-Inequalities, Lyapunov Stability and Sampling for Dynamical Systems on Continuous State Space
Muhammad Abdullah Naeem, Miroslav Pajic
Dynamical System Open Sampling Lyapunov Function State Space Concentration Inequality Random Dynamical System Exponential Concentration Transportation Equity

November 4, 2021

Generative Adversarial Network for Probabilistic Forecast of Random Dynamical System
Kyongmin Yeo, Zan Li, Wesley M. Gifford
Generative Adversarial Network GAN Model Probabilistic Forecast Random Dynamical System

Random Dynamical System

Papers

From Spectral Theorem to Statistical Independence with Application to System Identification

Learning and Concentration for High Dimensional Linear Gaussians: an Invariant Subspace Approach

Recurrences reveal shared causal drivers of complex time series

Concentration Phenomenon for Random Dynamical Systems: An Operator Theoretic Approach

Universal Time-Uniform Trajectory Approximation for Random Dynamical Systems with Recurrent Neural Networks

Transfer Learning with Physics-Informed Neural Networks for Efficient Simulation of Branched Flows

Transportation-Inequalities, Lyapunov Stability and Sampling for Dynamical Systems on Continuous State Space

Generative Adversarial Network for Probabilistic Forecast of Random Dynamical System