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On the Interplay Between Deep Learning and Dynamical Systems
Deep Learning Dynamical Systems 北大
2023/6/16
The explosion of spatiotemporal data in the physical world requires new deep learning tools to model complex dynamical systems.
Workshop on Stochastic Dynamical Systems and Ergodicity
Workshop Stochastic Dynamical Systems and Ergodicity
2017/7/5
The objective of the workshop is to bring together researchers in stochastic dynamical systems, ergodic theory, SPDEs, BSDEs, nonlinear expectations and stochastic controls to interact aiming to stimu...
三亚国际数学论坛：International Conference on Singularity Theory and Dynamical Systems
三亚国际数学论坛 International Conference Singularity Theory and Dynamical Systems
2017/7/3
The aim of the symposium is to bring together specialists of various do- mains of singularity theory and mathematical foundation of complex systems representing very classical aspects of the Fields. W...
International Conference on Statistical Properties of Nonequilibrium Dynamical Systems
certain general types of stochastic deterministic dynamical systems
2016/7/18
The International Conference on Statistical Properties of Nonequilibrium Dynamical Systems will be held in the South University of Science and Technology of China (SUSTC) in Shenzhen, China, from July...
Nonlinear Stochastic Perturbations of Dynamical Systems and Quasi-linear Parabolic PDE’s with a Small Parameter
Quasi linear parabolic equations parameters quasi linear initial boundary value
2015/9/28
In this paper we describe the asymptotic behavior, in the exponential time scale, of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time beh...
Metastability for Non-Linear Random Perturbations of Dynamical Systems
Quasi linear parabolic equation the small parameter the second order items
2015/9/28
In this paper we describe the long time behavior of solutions to quasi-linear parabolic equations with a small parameter at the second order term and the long time behavior of the corresponding di@...
A Compactification of H′ enon Mappings in C2 as Dynamical Systems
H′ enon Mappings C2 as Dynamical Systems
2015/8/26
A Compactification of H′ enon Mappings in C2 as Dynamical Systems.
Towards a Global Theory of Singularly Perturbed Dynamical Systems
Perturbed Dynamical System Theory
2015/8/25
Dynamical systems with multiple time scales arise naturally in many domains.
Models of neural systems provide the principal motivation for this
paper. Most of the previous mathematical analysis of q...
A class of Lyapunov functionals for analyzing hybrid dynamical systems
Lyapunov functionals the hybrid system function hysteresis nonlinear system lyapunov functionals
2015/8/11
In this paper, we introduce a new class of Lyapunov functionals for analyzing hybrid dynamical systems. This class can be thought of as a generalization of the Lyapunov functional introduced by Yakubo...
Polynomial level-set methods for nonlinear dynamical systems analysis
dynamical systems analysis level-set methods
2015/6/19
In this paper, we present a method for computing the domain of attraction for non-linear dynamical systems. We propose a level-set method where sets are represented as sublevel sets of polynomials. Th...
Pathwise Stationar y Solutions and Random Per iodic Solutions of Random Dynamical Systems (SPDEs, Random Maps)
Pathwise Stationar y Solutions Random Per
2015/4/3
here are two fundamental concepts in deter ministic dynamical systems: fixed
point (equilibr ium point) and per iodic solutions. For stochastic dynamical systems, they correspond to fundamental ideas...
First-order SODE: OU processdX+aX(t)dt= dW(t)
Three options:a >0, a= 0, a <0.
First-order SPDE:du= au
xx dt+dW(t, x)
One option:a >0(Infinite-dimensional stable OU process.)
Second-order SODE:X¨ ...
Lyapunov Exponents for Infinite Dimensional Random Dynamical Systems in a Banach Space
Random Dynamical Systems Lyapunov Exponents
2015/4/3
Metric Dynamical System
Let be a probability space.
Let be a metric dynamical system:
(i)
(ii)
(iii) preserves th...
“Superparamagnetic limit”: As magnetic devices become smaller
and smaller, the time for thermal activated switching might
become too short (shorter than desired data retention time).
Stochastic Quantification of Missing Mechanisms in Dynamical Systems
ynamical Systems Missing Mechanisms
2015/4/3
Due to lack of knowledge:
Missing mechanisms (ignored “too small" or “too fast" or
“unimportant" processes)
Unresolved scales (not represented in models)
Model uncertainties