Eun-Jin Kim

Coventry University | CU · Fluid and Complex Systems Research Centre

We propose a novel method for fast and accurate training of physics-informed neural networks (PINNs) to find solutions to boundary value problems (BVPs) and initial boundary value problems (IBVPs). By combining the methods of training deep neural networks (DNNs) and Extreme Learning Machines (ELMs), we develop a model which has the expressivity of...

Controlling the time evolution of a probability distribution that describes the dynamics of a given complex system is a challenging problem. Achieving success in this endeavour will benefit multiple practical scenarios, e.g., controlling mesoscopic systems. Here, we propose a control approach blending the model predictive control technique with ins...

DIII-D plasmas are compared for two upper divertor configurations: with the outer strike point on the Small Angle Slot (SAS) divertor target and with the outer strike point on the horizontal divertor target (HT). Scanning the vertical distance between the magnetic null point and the divertor target over a range 0.10 - 0.16 m is shown to increase th...

In this work, we explore information geometry theoretic measures for characterizing neural information processing from EEG signals simulated by stochastic nonlinear coupled oscillator models for both healthy subjects and Alzheimer’s disease (AD) patients with both eyes-closed and eyes-open conditions. In particular, we employ information rates to q...

Association football (commonly known as football or soccer) in the modern era places a greater emphasis on collaborating and working together as a team instead of relying solely on individual skills to strategize winning performances. The low-scoring and unpredictable nature of association football makes evaluating team performances challenging. Sp...

Abstract: Weinvestigatethestochasticdynamicsoftheprey–predatormodeloftheLow-to-High confinement mode (L-H) transition in magnetically confined fusion plasmas. By considering stochas- tic noise in the turbulence and zonal flows as well as constant and time-varying input power Q, we perform multiple stochastic simulations of over a million trajectori...

In this work, we explore information geometry theoretic approach to analyzing EEG signals simulated by stochastic nonlinear coupled oscillator models for both healthy subjects and Alzheimer’s Disease (AD) patients with both eyes-closed and eyes-open conditions. In particular, we employ information rates to quantify the time evolution of probability...

A stochastic, prey–predator model of the L–H transition in fusion plasma is investigated. The model concerns the regulation of turbulence by zonal and mean flow shear. Independent delta-correlated Gaussian stochastic noises are used to construct Langevin equations for the amplitudes of turbulence and zonal flow shear. We then find numerical solutio...

A geometrical method for assessing stochastic processes in plasma turbulence is investigated in this study. The thermodynamic length methodology allows using a Riemannian metric on the phase space; thus, distances between thermodynamic states can be computed. It constitutes a geometric methodology to understand stochastic processes involved in, e.g...

The first application of time-dependent probability density function (PDF) analysis to the L-H transition in fusion plasmas is presented. PDFs have been constructed using Doppler Backscattering data of fluctuation velocity, u⊥, and turbulence from the edge region of the DIII-D tokamak. This raw time-series data has been sliced into millisecond-long...

The physiological response of the cardio-vascular system (CVS) to physical activity is of great importance to those working in sporting research and has profound consequences for the health and well-being of people. Coronary vasodilation and the physiological mechanisms involved in exercise have frequently been the focus of numerical models for sim...

The quantification of causality is vital for understanding various important phenomena in nature and laboratories, such as brain networks, environmental dynamics, and pathologies. The two most widely used methods for measuring causality are Granger Causality (GC) and Transfer Entropy (TE), which rely on measuring the improvement in the prediction o...

We investigate the effects of different stochastic noises on the dynamics of the edge-localised modes (ELMs) in magnetically confined fusion plasmas by using a time-dependent PDF method, path-dependent information geometry (information rate, information length), and entropy-related measures (entropy production, mutual information). The oscillation...

As fractional-order models increasingly appear as an option to describe complex systems, they generate a demand for parameter estimation methods in the time and frequency domain. The extended Kalman filter (EKF) is a promising technique in the time domain, but it is sensitive to the initial conditions of the state and error covariance matrices. In...

In this work, we investigate the relation between the concept of 'information rate', an information geometric method for measuring the speed of the time evolution of the statistical states of a stochastic process, and stochastic thermodynamics quantities like entropy rate and entropy production. Then, we propose the application of entropy rate and...

In this work, we investigate the relation between the concept of ``information rate'', an information geometric method for measuring the speed of the time evolution of the statistical states of a stochastic process, and stochastic thermodynamics quantities like entropy rate and entropy production. Then, we propose the application of entropy rate an...

Numerical models of the cardiovascular system have largely focused on the function of the ventricles, with atrial function often neglected. Furthermore, the time-varying elastance method that prescribes the pressure-volume relationship rather than calculating it consistently is frequently used for the ventricles and atrium. This method has yet to b...

Magnetically confined plasmas are far from equilibrium and pose considerable challenges in statistical analysis. We discuss a non-perturbative statistical method, namely a time-dependent probability density function (PDF) approach that is potentially useful for analysing time-varying, large, or non-Gaussian fluctuations and bursty events associated...

The dithering H-mode phase, characterized by oscillations, is generally observed at input power values close to the L-H transition power threshold and low plasma collisionalities (low electron density and/or high plasma temperature). Measurements to characterize the dithering phase are presented for the low aspect ratio, high magnetic field tokamak...

The high confinement mode (H-mode) is the widely adopted standard operation scenario for the path to fusion in toroidal confinement devices. Since its discovery in 1982, the H-mode and access to the H-mode (the low to high and high to low transitions) remain two of the most actively researched areas in magnetically confined fusion programmes across...

Artificial neural networks (ANNs) are powerful tools capable of approximating any arbitrary mathematical function, but their interpretability remains limited, rendering them as black box models. To address this issue, numerous methods have been proposed to enhance the explainability and interpretability of ANNs. In this study, we introduce the appl...

A geometrical method is used for the analysis of stochastic processes in plasma turbulence. Distances between thermodynamic states can be computed according the thermodynamic length methodology which allows the use of a Riemannian metric on the phase space. A geometric methodology is suitable in order to understand stochastic processes involved in...

As a measure of sustainability, Fisher information is employed in the Gompertz growth model. The effect of different oscillatory modulations is examined on the system's evolution and Probability Density Function (PDF). For a sufficiently large frequency of periodic fluctuations occurring in both positive and negative feedbacks, the system maintains...

We introduce a novel framework for exploring the evolutionary consequences of phenotypic plasticity (adaptive and non-adaptive) integrating both genic and epigenetic effects on phenotype via stochastic differential equations and in-silico selection. In accordance with the most significant results derived from prior models, we demonstrate how plasti...

We investigate time-varying turbulence statistical properties of edge-localized modes (ELMs) in fusion plasmas. By utilizing a simplified stochastic model, we calculate a time-dependent probability density function and various entropy-related quantities such as entropy, entropy production, entropy flux, mutual information, and information flow and...

One of the short-coming challenges of power systems operation and planning is the difficulty to quantify the variability of power systems Kinetic Energy (KE) to unveil online additional information for the system operators’ decisions support. KE monitoring requires innovative methods to analyse the continuous fluctuations in the KE power’s systems....

Cardiac diseases and failure make up one of largest contributions to global mortality and significantly detriment the quality of life for millions of others. Disorders in the valves of the left ventricle are a prominent example of heart disease, with prolapse, regurgitation, and stenoses—the three main valve disorders. It is widely known that mitra...

Information Geometry is a useful tool to study and compare the solutions of a Stochastic Differential Equations (SDEs) for non-equilibrium systems. As an alternative method to solving the Fokker–Planck equation, we propose a new method to calculate time-dependent probability density functions (PDFs) and to study Information Geometry using Monte Car...

The noise-induced transport due to spatial symmetry-breaking is a key mechanism for the generation of a uni-directional motion by a Brownian motor. By utilising an asymmetric sawtooth periodic potential and three different types of periodic forcing G(t) (sinusoidal, square and sawtooth waves) with period T and amplitude A, we investigate the perfor...

Social discounting is a critical and contentious issue in evaluating the costs and benefits of climate policy, infrastructure projects, and other long-term public policies. In this paper, we look at the asymptotic statistical properties of the Weitzman (2001) gamma discounting in a dynamic stochastic continuous-time framework where individual disco...

Improving the mathematical model of the cardiovascular system is an important aspect of the control and design of ventricular assist devices. In this work, through numerical simulations, we analyse the usage of fractional-order operators as a way to improve the circulation model. More specifically, we show that the use of fractional-order derivativ...

In this work, a model reduction of a line robotic formation driven by simple PD-controllers is presented. The proposed mathematical model describes the control interactions between the agents which permits us to easily design a decentralised control strategy. To select the PD-controller gains for each agent, we employ a population-based algorithm t...

Information theory provides an interdisciplinary method to understand important phenomena in many research fields ranging from astrophysical and laboratory fluids/plasmas to biological systems. In particular, information geometric theory enables us to envision the evolution of non-equilibrium processes in terms of a (dimensionless) distance by quan...

An advantageous method for understanding complexity is information geometry theory. In particular, a dimensionless distance, called information length L, permits us to describe time-varying, non-equilibrium processes by measuring the total change in the information along the evolution path of a stochastic variable or the total number of statistical...

Information processing is common in complex systems, and information geometric theory provides a useful tool to elucidate the characteristics of non-equilibrium processes, such as rare, extreme events, from the perspective of geometry. In particular, their time-evolutions can be viewed by the rate (information rate) at which new information is reve...

Heart diseases are one of the leading causes of death worldwide, and a dysfunction of the cardiac electrical mechanisms is responsible for a significant portion of these deaths. One of these mechanisms, the mechano-electric feedback (MEF), is the electrical response of the heart to local mechanical changes in the environment. This electrical respon...

Exploration of the design and control of a formation of mobile robots in 1-dimension using a toy-model.

Detectionandmeasurementofabruptchangesinaprocesscanprovideuswithimportant tools for decision making in systems management. In particular, it can be utilised to predict the onset of a sudden event such as a rare, extreme event which causes the abrupt dynamical change in the system. Here, we investigate the prediction capability of information theory...

In this contribution, fractional‐order controllers of the type PDμ and PIλ are applied to a class of irrational transfer function models that appear in large‐scale systems, such as networks of mechanical/electrical elements and distributed parameter systems. More precisely, by considering the fractional‐order controller 𝑘𝑝+𝑘𝜂𝑠𝛼 in the Laplace domai...

When studying the behaviour of complex dynamical systems, a statistical formulation can provide useful insights. In particular, information geometry is a promising tool for this purpose. In this paper, we investigate the information length for n-dimensional linear autonomous stochastic processes, providing a basic theoretical framework that can be...

Forward and backward processes associated with the Low-to-High (L-H) transition in mag- netically confined fusion plasmas are investigated by using a time-dependent Probability Density Function (PDF) approach and information length diagnostics. Our model is based on the extension of the deterministic prey-predator-type model (Kim and Diamond, Phys....

The breakdown of cardiac self-organization leads to heart diseases and failure, the number one cause of death worldwide. Within the traditional time-varying elastance model, cardiac self organization and breakdown cannot be addressed due to its inability to incorporate the dynamics of various feedback mechanisms consistently. To face this challenge...

The breakdown of cardiac self-organization leads to heart diseases and failure, the number one cause of death worldwide. Within the traditional time-varying elastance model, cardiac self organization and breakdown cannot be addressed due to its inability to incorporate the dynamics of various feedback mechanisms consistently. To face this challenge...

We report a study of time-dependent probability density functions (PDFs) in the low-to-high confinement mode (L-H) transition by extending the previous prey-predator-type model [E. Kim and P. H. Diamond, Phys. Rev. Lett. 90, 185006 (2003).] to a stochastic model. We highlight the limited utility of mean value and variance in understanding the L-H t...

We report a first study of time-dependent Probability Density Functions (PDFs) in the Low-to- High confinement mode (L-H) transition by extending the previous prey-predator-type model (Kim & Diamond, Phys. Rev. Lett. 91, 185006, 2003) to a stochastic model. We highlight the limited utility of mean value and variance in understanding the L-H transit...

With improved measurement and modelling technology, variability has emerged as an essential feature in non-equilibrium processes. While traditionally, mean values and variance have been heavily used, they are not appropriate in describing extreme events where a significant deviation from mean values often occurs. Furthermore, stationary Probability...

The impact of adiabatic electrons on drift-wave turbulence, modeled by the Hasegawa–Wakatani equations, is studied using information length. Information length is a novel theoretical method for measuring distances between statistical states represented by different probability distribution functions (PDFs) along the path of a system and represents...

With improved measurement and modelling technology, variability has emerged as an essential feature in non-equilibrium processes. While traditionally, mean values and variance have been heavily used, they are not appropriate in describing extreme events where a significant deviation from mean values often occurs. Furthermore, stationary Probability...

The breakdown of cardiac self-organization leads to heart diseases and failure, the number one cause of death worldwide. The left ventricular pressure-volume relation plays a key role in the diagnosis and treatment of heart diseases. Lumped-parameter models combined with pressure-volume loop analysis are very effective in simulating clinical scenar...

Stochastic resonance is a subtle, yet powerful phenomenon in which a noise plays an interesting role of amplifying a signal instead of attenuating it. It has attracted a great attention with a vast number of applications in physics, chemistry, biology, etc. Popular measures to study stochastic resonance include signal-to-noise ratios, residence tim...

It is often the case when studying complex dynamical systems that a statistical formulation can provide the greatest insight into the underlying dynamics. When discussing the behavior of such a system which is evolving in time, it is useful to have the notion of a metric between two given states. A popular measure of information change in a system...

The impact of adiabatic electrons on drift-wave turbulence, modelled by the Hasegawa-Wakatani equations, is studied using information length. Information length is a novel theoretical method for measuring distances between statistical states represented by different probability distribution functions (PDFs) along the path of a system. Specifically,...

We explore the effect of different spatially periodic, deterministic forces on the information geometry of stochastic processes. The three forces considered are f 0 = sin(πx)/π and f ± = sin(πx)/π ± sin(2πx)/2π, with f − chosen to be particularly flat (locally cubic) at the equilibrium point x = 0, and f + particularly flat at the unstable fixed po...

We consider the classical double-well model of stochastic resonance, in which a particle in a potential V(x,t)=[−x ² ∕2+x ⁴ ∕4−Asin(ωt)x] is subject to an additional stochastic forcing that causes it to occasionally jump between the two wells at x≈±1. We present direct numerical solutions of the Fokker–Planck equation for the probability density fu...

There is overwhelming evidence, from laboratory experiments, observations, and computational studies, that coherent structures can cause intermittent transport, dramaticallyenhancing transport[...]

We investigate information geometry in a toy model of self-organised shear flows, where a bimodal PDF of x with two peaks signifying the formation of mean shear gradients is induced by a finite memory time of a stochastic forcing f . We calculate time-dependent probability density functions (PDFs) for different values of the correlation time and am...

We propose a new methodology to understand a stochastic process from the perspective of information geometry by investigating power-law scaling and fractals in the evolution of information. Specifically, we employ the Ornstein-Uhlenbeck process where an initial Probability Density Function (PDF) with a given width 0 and mean value y 0 relaxes into...

We propose a new methodology to understand a stochastic process from the perspective of information geometry by investigating power-law scaling and fractals in the evolution of information. Specifically, we employ the Ornstein-Uhlenbeck process where an initial probability density function (PDF) with a given width ϵ0 and mean value y0 relaxes into...

We report the time-evolution of Probability Density Functions (PDFs) in a toy model of self-organised shear flows, where the formation of shear flows is induced by a finite memory time of a stochastic forcing, manifested by the emergence of a bimodal PDF with the two peaks representing non-zero mean values of a shear flow. Using theoretical analyse...

Stochastic processes are ubiquitous in nature and laboratories, and play a major role across traditional disciplinary boundaries. These stochastic processes are described by different variables and are thus very system-specific. In order to elucidate underlying principles governing different phenomena, it is extremely valuable to utilise a mathemat...

We elucidate the effect of different deterministic nonlinear forces on geometric structure of stochastic processes by investigating the transient relaxation of initial PDFs of a stochastic variable x under forces proportional to -xn (n=3,5,7) and different strength D of δ-correlated stochastic noise. We identify the three main stages consisting of...

A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that the distance increases with the difference b...

A probabilistic description is essential for understanding the dynamics in many systems due to uncertainty or fluctuations. We show how to utilise time-dependent probability density functions to compute the information length , as a Lagrangian measure that counts the number of different states that a quantum system evolves through in time. Using ,...

A probabilistic description is essential for understanding growth processes in non-stationary states. In this paper, we compute time-dependent probability density functions (PDFs) in order to investigate stochastic logistic and Gompertz models, which are two of the most popular growth models. We consider different types of short-correlated multipli...

We report a non-perturbative study of the effects of shear flows on turbulence reduction in a decaying turbulence in two dimensions. By considering different initial power spectra and shear flows (zonal flows, combined zonal flows and streamers), we demonstrate how shear flows rapidly generate small scales, leading to a fast damping of turbulence a...

We report a non-perturbative study of the effect of different type of shear flows on the evolution of vorticity and particle density fluctuations in interchange turbulence. For the same shear strength, the transport of density is less reduced by streamers than by zonal flows, zonal flows leading to oscillation death. In the inviscid limit, vorticit...

Many systems in nature and laboratories are far from equilibrium and exhibit significant fluctuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time-dependent PDFs, becomes essential in understanding far-from-equilib...

Many systems in nature and laboratories are far from equilibrium and exhibit significant fluctuations , invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time-dependent PDFs, becomes essential in understanding far-from-equili...

Many systems in nature and laboratories are far from equilibrium and exhibit significant fluc- tuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time- dependent PDFs, becomes essential in understanding far-from-equi...

A probabilistic description is essential for understanding growth processes far from equilibrium. In this paper, we compute time-dependent Probability Density Functions (PDFs) in order to investigate stochastic logistic and Gompertz models, which are two of the most popular growth models. We consider different types of short-correlated internal (mu...

We propose a toy model for a cyclic order-disorder transition and introduce a geometric methodology to understand stochastic processes involved in transitions. Specifically, our model consists of a pair of forward and backward processes (FPs and BPs) for the emergence and disappearance of a structure in a stochastic environment. We calculate time-d...

A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium, given uncertainty inherent in the systems. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that t...

A probabilistic description is essential for understanding the dynamics of stochastic systems far from equilibrium, given uncertainty inherent in the systems. To compare different Probability Density Functions (PDFs), it is extremely useful to quantify the difference among different PDFs by assigning an appropriate metric to probability such that t...

We study magnetic Taylor-Couette flow in a system having nondimensional radii $r_i=1$ and $r_o=2$, and periodic in the axial direction with wavelengths $h\ge100$. The rotation ratio of the inner and outer cylinders is adjusted to be slightly in the Rayleigh-stable regime, where magnetic fields are required to destabilize the flow, in this case trig...

We investigate the effect of nonlinear interaction on the geometric structure of a non-equilibrium process. Specifically, by considering a driven-dissipative system where a stochastic variable x is damped either linearly (∝ x) or nonlinearly (∝ x 3 ) while driven by a white noise, we compute the time-dependent probability density functions (PDFs) d...

After their formation, stars slow down their rotation rates by the removal of angular momentum from their surfaces, e.g., via stellar winds. Explaining how this rotation of solar-type stars evolves in time is currently an interesting but difficult problem in astrophysics. Despite the complexity of the processes involved, a traditional model, where...

We report time-dependent Probability Density Functions (PDFs) for a nonlinear stochastic process with a cubic force by novel analytical and computational studies. Analytically, a transition probability is formulated by using a path integral and is computed by the saddle-point solution (instanton method) and a new nonlinear transformation of time. T...

We numerically solve the magnetic induction equation in a spherical shell geometry, with a kinematically prescribed axisymmetric flow that consists of a superposition of a small-scale helical flow and a large-scale shear flow. The small-scale flow is chosen to be a local analog of the classical Roberts cells, consisting of strongly helical vortex r...

This paper is an extension of the brief study by Sarah Douglas et al. [Phys. Plasmas 20 (2013) 114504] where in the study a sinusoidal perturbation of the heating power has been studied. In this paper a stepwise increase of the heating power and its influence on the L–H transition are studied. Using a function, Atanh(t/T) for the transition of inpu...

Information theory provides a useful tool to understand the evolution of complex nonlinear systems and their sustainability. In particular, Fisher Information (FI) has been evoked as a useful measure of sustainability and the variability of dynamical systems including self-organising systems. By utilising FI, we investigate the sustainability of th...

We show that music is represented by fluctuations away from the minimum path through statistical space. Our key idea is to envision music as the evolution of a non-equilibrium system and to construct probability distribution functions (PDFs) from musical instrument digital interface (MIDI) files of classical compositions. Classical music is then vi...

We investigate the geometric structure of a nonequilibrium process and its geodesic solutions. By employing an exactly solvable model of a driven dissipative system (generalized nonautonomous Ornstein-Uhlenbeck process), we compute the time-dependent probability density functions (PDFs) and investigate the evolution of this system in a statistical...

Since their formation, stars slow down their rotation rates by the removal of angular momentum from their surfaces, e.g. via stellar winds. Despite the complexity of the processes involved, a traditional model, where the removal of angular momentum loss by magnetic fields is prescribed, has provided a useful framework to understand observational re...

We numerically solve the magnetic induction equation in a spherical shell geometry, with a kinematically prescribed axisymmetric flow that consists of a superposition of a small-scale helical flow and a large-scale shear flow. The small-scale flow is chosen to be a local analog of the classical Roberts cells, consisting of strongly helical vortex r...