arXiv subjects

Kyongmin Yeo

Publications and source records attributed to Kyongmin Yeo.

26 records · Page 2Linked to original sources

arXiv2019

Data-driven Reconstruction of Nonlinear Dynamics from Sparse Observation

We present a data-driven model to reconstruct nonlinear dynamics from a very sparse times series data, which relies on the strength of the echo state network (ESN) in learning nonlinear representation of data. With an assumption of the universal function approximation capability of ESN, it is shown that the reconstruction problem can be formulated as a fixed-point problem, in which the trajectory of the dynamical system is a fixed point of the ESN. An under-relaxed fixed-point iteration is proposed to reconstruct the nonlinear dynamics from a sparse observation. The proposed fixed-point ESN is tested against both univariate and multivariate chaotic dynamical systems by randomly removing up to 95% of the data. It is shown that the fixed-point ESN is able to reconstruct the complex dynamics from only 5 ~ 10% of the data. For a relatively simple non-chaotic dynamical system, the numerical experiments on a forced van der Pol oscillator show that it is possible to reconstruct the nonlinear dynamics from only 1~2% of the data.

cs.NE↗

arXiv2019

Short note on the behavior of recurrent neural network for noisy dynamical system

The behavior of recurrent neural network for the data-driven simulation of noisy dynamical systems is studied by training a set of Long Short-Term Memory Networks (LSTM) on the Mackey-Glass time series with a wide range of noise level. It is found that, as the training noise becomes larger, LSTM learns to depend more on its autonomous dynamics than the noisy input data. As a result, LSTM trained on noisy data becomes less susceptible to the perturbation in the data, but has a longer relaxation timescale. On the other hand, when trained on noiseless data, LSTM becomes extremely sensitive to a small perturbation, but is able to adjusts to the changes in the input data.

cs.NE↗

arXiv2018

Development of hp-inverse model by using generalized polynomial chaos

We present a hp-inverse model to estimate a smooth, non-negative source function from a limited number of observations for a two-dimensional linear source inversion problem. A standard least-square inverse model is formulated by using a set of Gaussian radial basis functions (GRBF) on a rectangular mesh system with a uniform grid space. Here, the choice of the mesh system is modeled as a random variable and the generalized polynomial chaos (gPC) expansion is used to represent the random mesh system. It is shown that the convolution of gPC and GRBF provides hierarchical basis functions for the linear source inverse model with the $hp$-refinement capability. We propose a mixed l_1 and l_2 regularization to exploit the hierarchical nature of the basis functions to find a sparse solution. The $hp$-inverse model has an advantage over the standard least-square inverse model when the number of data is limited. It is shown that the hp-inverse model provides a good estimate of the source function even when the number of unknown parameters ($m$) is much larger the number of data ($n$), e.g., m/n > 40.

physics.ao-ph↗

arXiv2018

Deep learning algorithm for data-driven simulation of noisy dynamical system

We present a deep learning model, DE-LSTM, for the simulation of a stochastic process with an underlying nonlinear dynamics. The deep learning model aims to approximate the probability density function of a stochastic process via numerical discretization and the underlying nonlinear dynamics is modeled by the Long Short-Term Memory (LSTM) network. It is shown that, when the numerical discretization is used, the function estimation problem can be solved by a multi-label classification problem. A penalized maximum log likelihood method is proposed to impose a smoothness condition in the prediction of the probability distribution. We show that the time evolution of the probability distribution can be computed by a high-dimensional integration of the transition probability of the LSTM internal states. A Monte Carlo algorithm to approximate the high-dimensional integration is outlined. The behavior of DE-LSTM is thoroughly investigated by using the Ornstein-Uhlenbeck process and noisy observations of nonlinear dynamical systems; Mackey-Glass time series and forced Van der Pol oscillator. It is shown that DE-LSTM makes a good prediction of the probability distribution without assuming any distributional properties of the stochastic process. For a multiple-step forecast of the Mackey-Glass time series, the prediction uncertainty, denoted by the 95\% confidence interval, first grows, then dynamically adjusts following the evolution of the system, while in the simulation of the forced Van der Pol oscillator, the prediction uncertainty does not grow in time even for a 3,000-step forecast.

physics.comp-ph↗

arXiv2017

Statistical Modeling for Spatio-Temporal Degradation Data

This paper investigates the modeling of an important class of degradation data, which are collected from a spatial domain over time; for example, the surface quality degradation. Like many existing time-dependent stochastic degradation models, a special random field is constructed for modeling the spatio-temporal degradation process. In particular, we express the degradation at any spatial location and time as an additive superposition of two stochastic components: a dynamic spatial degradation generation process, and a spatio-temporal degradation propagation process. Some unique challenges are addressed, including the spatial heterogeneity of the degradation process, the spatial propagation of degradation to neighboring areas, the anisotropic and space-time non-separable covariance structure often associated with a complex spatio-temporal degradation process, and the computational issue related to parameter estimation. When the spatial dependence is ignored, we show that the proposed spatio-temporal degradation model incorporates some existing pure time-dependent degradation processes as its special cases. We also show the connection, under special conditions, between the proposed model and general physical degradation processes which are often defined by stochastic partial differential equations. A numerical example is presented to illustrate the modeling approach and model validation.

stat.ME↗

arXiv2017

Model-free prediction of noisy chaotic time series by deep learning

We present a deep neural network for a model-free prediction of a chaotic dynamical system from noisy observations. The proposed deep learning model aims to predict the conditional probability distribution of a state variable. The Long Short-Term Memory network (LSTM) is employed to model the nonlinear dynamics and a softmax layer is used to approximate a probability distribution. The LSTM model is trained by minimizing a regularized cross-entropy function. The LSTM model is validated against delay-time chaotic dynamical systems, Mackey-Glass and Ikeda equations. It is shown that the present LSTM makes a good prediction of the nonlinear dynamics by effectively filtering out the noise. It is found that the prediction uncertainty of a multiple-step forecast of the LSTM model is not a monotonic function of time; the predicted standard deviation may increase or decrease dynamically in time.

cs.LG↗

arXiv2016

Collective dynamics in a binary mixture of hydrodynamically coupled micro-rotors

We study, numerically, the collective dynamics of self-rotating nonaligning particles by considering a monolayer of spheres driven by constant clockwise or counterclockwise torques. We show that hydrodynamic interactions alter the emergence of large-scale dynamical patterns compared to those observed in dry systems. In dilute suspensions, the flow stirred by the rotors induces clustering of opposite-spin rotors, while at higher densities same-spin rotors phase separate. Above a critical rotor density, dynamic hexagonal crystals form. Our findings underscore the importance of inclusion of the many-body, long-range hydrodynamic interactions in predicting the phase behavior of active particles.

cond-mat.soft↗

arXiv2016

Dynamics of inert spheres in active suspensions of micro-rotors

Inert particles suspended in active fluids of self-propelled particles are known to often exhibit enhanced diffusion and novel coherent structures. Here we numerically investigate the dynamical behavior and self-organization in a system consisting of passive and actively rotating spheres. The particles interact through direct collisions and the fluid flows generated as they move. In the absence of passive particles, three states emerge in a binary mixture of spinning spheres depending on particle fraction: a dilute gas-like state where the rotors move chaotically, a phase-separated state where like-rotors move in lanes or vortices, and a jammed state where crystals continuously assemble, melt and move (K. Yeo, E. Lushi, and P. M. Vlahovska, Phys. Rev. Lett. 114, 188301 (2015)). Passive particles added to the rotor suspension modify the system dynamics and pattern formation: while states identified in the pure active suspension still emerge, they occur at different densities and mixture proportions. The dynamical behavior of the inert particles is also non-trivially dependent on the system composition.

cond-mat.soft↗