Abstract : There has been a growing interest in exploiting machine learning to predict the behaviors of complex nonlinear dynamics. It is also of interest to clarify to what extent machine learning can be used to model and predict dynamical system structures that do not appear in training time series explicitly. In this mini-symposium, we will learn of new results on machine learning for dynamics and its applications to complex phenomena such as fluid and climate dynamics. Examples include the prediction of invariant sets $($fixed points, periodic points, strange attractors, and invariant manifolds$)$ and their stabilities, tipping point, and missing dynamics.
Organizer(s) : Masanobu Inubushi, Kengo Nakai, Hirofumi Notsu, Yoshitaka Saiki
[04040] Construction of differential equations from scalar chaotic time series
Format : Talk at Waseda University
Author(s) :
NATSUKI TSUTSUMI (Hitotsubashi University)
kengo nakai (Okayama University)
Yoshitaka Saiki (Hitotsubashi University)
Abstract : We propose a method of constructing a system of differential equations of chaotic behavior only from observable scalar time series. The method employs a regression using Gaussian radial basis functions together with polynomial terms. We apply it to several chaotic time series. The obtained model is assessed from the viewpoint of time series forecast, reconstruction of invariant sets, and invariant densities. Delay coordinate and a chaotic saddle have played a big role in the procedure.
[04709] Data-driven inference of Navier-Stokes turbulence from limited observations
Format : Talk at Waseda University
Author(s) :
Masanobu Inubushi (Tokyo University of Science)
Abstract : Inference of turbulent states governed by the Navier-Stokes equations is one of the challenging and crucial problems for applied mathematics and industrial applications because of the high dimensionality and nonlinearity of fluid dynamics. In this study, we propose a data-driven inference method of turbulent dynamics from limited observations, which is suitable for industrial applications, and discuss its performance from the viewpoint of dynamical system theory.
[03862] Long-lead prediction of Indian Summer Monsoon onset with reservoir computing
Format : Talk at Waseda University
Author(s) :
Takahito Mitsui (Technical University of Munich)
Niklas Boers (Technical University of Munich)
Abstract : Although the prediction of the Indian Summer Monsoon (ISM) onset is of crucial importance for water-resource management and agricultural planning on the Indian sub-continent, the long-term predictability, especially at seasonal time scales, is little explored. We propose a method based on reservoir computing that provides skilfull long-term forecasts of the ISM onset. Our study demonstrates that machine-learning-based approaches can be simultaneously helpful for both data-driven prediction and enhancing the process understanding of climate phenomena.
[03000] Learning Strange Attractors with Reservoir Systems
Format : Talk at Waseda University
Author(s) :
Allen Hart (University of Bath)
Abstract : This talk is based on a preprint by myself, Juan-Pablo Ortega, and Lyudmila Grigoryeva, which shows that the celebrated Takens Embedding Theorem is a particular case of a much more general statement according to which, randomly generated Echo State Networks (with linear activations) trained on generic observations of an invertible dynamical system carry in their wake an embedding of the phase space dynamics into the chosen Euclidean state space. This embedding coincides with a natural generalized synchronization that arises in this setup and that yields a topological conjugacy between the state-space dynamics driven by the generic observations of the dynamical system and the dynamical system itself. This result provides additional tools for the representation, learning, and analysis of chaotic attractors and sheds additional light on the reservoir computing phenomenon that appears in the context of recurrent neural networks.
[04147] Dynamical system properties of reservoir computing models
Format : Talk at Waseda University
Author(s) :
kengo nakai (Okayama University)
Miki U. Kobayashi ( Rissho University)
Yoshitaka Saiki (Hitotsubashi University)
Natsuki Tsutsumi (Tokyo University of Marine Science and Technology)
Abstract : It has been reported that reservoir computing is effective in the inference of time-series and some characteristics. We construct a model from training time-series of dynamical system with tangencies between stable and unstable manifolds or hetero-chaos, coexisting of invariant sets of different number of unstable dimensions. We confirm that these dynamical properties as well as fixed points and periodic orbits can be reconstructed by reservoir computing.
[02889] Predicting tipping point with machine learning
Format : Talk at Waseda University
Author(s) :
Ying-Cheng Lai (Arizona State University)
Abstract : Compared with the existing works on model-free prediction of chaotic systems, to predict a tipping point is significantly more challenging, because the training data are from the system when it is in a steady state. The speaker will describe the tipping-point mechanism, discuss how dynamical noise can be exploited in a machine learning scheme to predict the future occurrence of tipping points, and present benchmark examples as well as a real-world application.
[02921] Machine Learning for Predicting Missing Dynamics
Format : Talk at Waseda University
Author(s) :
Shixiao Willing Jiang (ShanghaiTech University)
Abstract : We present a framework for recovering missing dynamics using available data and machine learning techniques. The framework reformulates the prediction problem as a supervised learning problem to approximate a map that takes the memories of the resolved and identifiable unresolved variables to the missing components in the resolved dynamics. The map for this non-Markovian transition kernel is represented by appropriate RKHS or LSTM formulation. Supporting numerical results include the Lorenz system, the Kuramoto-Sivashinsky equation, etc.
[05374] Kernel Flows and Kernel Mode Decomposition for Learning Dynamical Systems from Data
Format : Talk at Waseda University
Author(s) :
Boumediene Hamzi (Caltech)
Abstract : Regressing the vector field of a dynamical system from a finite number of observed states is a natural way to learn surrogate models for such systems. We present variants of the method of Kernel Flows as simple approaches for learning the kernel that appear in the emulators we use in our work. First, we will talk about about the method of parametric and nonparametric kernel flows for learning chaotic dynamical systems. We’ll also talk about learning dynamical systems from irregularly-sampled time series as well as from partial observations. We will also introduce the method of Sparse Kernel Flows and apply it to learn 132 chaotic dynamical systems. Finally, we extend the method of Kernel Mode Decomposition to design kernels in view of detecting critical transitions in some fast-slow random dynamical systems.
This is joint work with Yang Lu, Xiuwen Sun, Houman Owhadi, Leo Paillet, Naiming Xie
[05420] Discovery of quasiperiodically driven dynamics using kernel methods
Format : Talk at Waseda University
Author(s) :
Suddhasattwa Das (Texas Tech University)
Shaurya Agarwal (University of Central Florida)
Shakib Mustavee (University of Central Florida)
Abstract : Quasiperiodically driven dynamical systems are nonlinear systems which are driven by some periodic source with multiple base-frequencies. Such systems abound in nature, and are present in data collected from sources such as astronomy and traffic data. Such dynamics decomposes into two components - the driving quasiperiodic source with generating frequencies; and the driven nonlinear dynamics. Analysis of the quasiperiodic part presents the same challenges as classical Harmonic analysis. On the other hand, the nonlinear part bears all the aspects of chaotic dynamics, and possibly carry stochastic perturbations. We present a kernel-based method which provides a robust means to learn both these components. It uses a combination of a kernel based Harmonic analysis and kernel based interpolation technique, to discover these two parts. The technique performs reliably in several real world systems, ranging from analyzing the human heart to traffic data.
Abstract : Reservoir computing (RC) is a machine learning framework that leverages a dynamical system as an information processor. This framework imposes a constraint on a system where the system must exhibit an identical response against an identical input sequence to work as a reproducible input processor; however, systems that violate the constraint can also process input. In this talk, we introduce a more general theoretical framework called generalized reservoir computing, covering the rest of irreproducible systems.
[05429] Reservoir computing with the Kuramoto model
Format : Talk at Waseda University
Author(s) :
Koichi Taniguchi (Tohoku University)
Abstract : The physical reservoir aims to achieve high-performance and low-cost machine learning by using real physical systems as reservoirs, but in general, there is no theoretical guideline for high-performance or optimality. In this talk, we discuss the reservoir computing with the Kuramoto model and the "edge of bifurcation" conjecture which means that its best performance is achieved by taking the model parameters just below the bifurcation point of the dynamical system.
[05431] Embedding bifurcation structures into a soft robotic actuator
Format : Talk at Waseda University
Author(s) :
Nozomi Akashi (Kyoto University)
Yasuo Kuniyoshi (The University of Tokyo)
Taketomo Jo (Bridgestone Corporation)
Mitsuhiro Nishida (Bridgestone Corporation)
Ryo Sakurai (Bridgestone Corporation)
Yasumichi Wakao (Bridgestone Corporation)
Kohei Nakajima (The University of Tokyo)
Abstract : We demonstrate that bifurcation structures can be embedded into a McKibben pneumatic artificial muscle, which is a common soft robotic actuator, through closed-loop control of physical reservoir computing. Our experiments reveal that both periodic and chaotic dynamics can be embedded into the artificial muscle by training only one side of these dynamics. Our results provide insight into reducing the amount and types of training data required for robot control through the utilization of bifurcation structures.
[05402] Physical reservoir computing using dynamics of biological neuronal network with modular structure
Format : Talk at Waseda University
Author(s) :
Takuma Sumi (Tohoku University)
Hideaki Yamamoto (Tohoku University)
Yuichi Katori (Future University of Hakodate)
Koki Ito (Tohoku University)
Shigeo Sato (Tohoku University)
Ayumi Hirano-Iwata (Tohoku University)
Abstract : Physical reservoir computing with biological neuronal network (BNN) has recently advanced the understanding of its computational principles. However, the BNN in conventional culture was randomly connected, generating non-physiological dynamics. Here, we employed micropatterning technology to fabricate BNNs with modular topology conserved evolutionarily in animal brains. We showed that the BNN reservoir exhibited higher classification when its network was functionally modular. Our findings provide insights into the link among non-random network connectivity, neuronal dynamics, and computing.
