Swarm intelligence (SI) algorithms have been studied in solving real-world optimization problems called black-box optimization problems. Typical features of SI algorithms are: (1) being a population-based metaheuristics; (2) using fitness values of a given objective function; and (3) having very simple search rules which search agents follow. As such, SI algorithms have been applied to various black-box optimization problems. Particle swarm optimization is one of powerful SI algorithms, in which a swarm consists of plural particles as solution candidates. Particles directly fly a search space and share their own information each other, and thus PSO can find good quality of solutions. However, a PSO swarm is easily stuck in solving optimization problems whose search space is high-dimensional and complicated. In order to solve such problems, large numbers of particles and reference frame invariance are needed for PSO algorithms. Herein, we suggest a piecewise-linear particle swarm optimizer (PPSO) which is a deterministic PSO. PPSO has two simple search modes switched to another mode dynamically, whose search dynamics are complex. As such, PPSO algorithm can be implemented on hardware with low hardware costs because PPSO algorithm must not require many random number generators. In addition, PPSO algorithm can find a good quality of solution in solving complex optimization problems. We studied search performances of PPSO compared to PSO algorithms and provide theoretical analysis of reference frame invariance for PPSO. In order to verify search performances and theoretical analysis, we performed numerical simulations.

This paper summarizes the open panel discussions at the special session (SS) held on December 8th, 2021, entitled “Designing the human-centric IoT society: Cooperative industry-academic strategies for creative future connection” in the 2021 Nonlinear Science Workshop (NLSW2021). The SS was jointly organized by Tohoku Forum for Creativity(TFC) and the NOLTA society. Before the SS, an online advance questionnaire survey was conducted using Google Forms. After three introductory talks, 52 participants from academic and industry fields discussed, and shared their idea in the open panel for the future IoT society to enhance human well-being.

A network model with temporal difference (TD) learning and reservoir computing (RC) has been proposed to control autonomous robots. RC is a framework for constructing a recurrent neural network that processes complex time series with less computational cost. TD learning is a framework of reinforcement learning, which realizes that an agent takes actions in an environment to maximize the cumulative reward. The control model using TD learning with RC realize the optimization of agent's action based on the sensory signal that is a continuous-valued time-varying signal. The model uses online reinforcement learning to train the connection weights between the reservoir and the output layer to represent the action value. In the present study, we evaluate the model with a task requiring short-term memory and clarify the reservoir's role in memorizing task-relevant sensory information. We show that the reservoir in the RC-based TD learning model enhances the performance in the memory-required task. The choice of parameter values that specify the reservoir dynamics is critical to ensure performance in the task.

In this study, we have developed the method to obtain the homoclinic bifurcation parameter of an arbitrary targeted fixed point in the logistic map T_r. We have considered the geometrical structure of T_r around x =0.5 and derived the core condition of the bifurcation occurrence. As the result of numerical experiment, we have calculated the exact bifurcation parameter of the fixed point of T_r^ℓ with ℓ≦256. We have also discussed the Feigenbaum constants found in the bifurcation parameter and the fixed point coordinate sequences. This fact implies the local stability of the fixed point and global structure around it are in association via the constants.

In this study, we have focused on the two-to-one maps and developed the numerical method to calculate the unstable periodic points (UPPs), based on the theory of the symbolic dynamical system. The core technique of the method is the definition of a non-deterministic map G. From the experimental result of three typical maps: logistic map, tent map, and Bernoulli map, we have confirmed the proposed method works very well within the defined errors. Our method has the following advantages: the method converges rapidly as the period of the target UPP is larger; we can choose the target UPP regardless of its cause (any bifurcation is not a matter); we can find the UPPs that are always unstable in the given parameter range. The convergence of the method is guaranteed by two standpoints: the corresponding symbolic dynamical system, and the asymptotic stability of UPP of G. Hereby, the error of the convergence is scalable according to the numeric precision of the software.

The purpose of this study is to visualize nonlinear relationships which are quite ambiguous in the conventional correlation diagram. We firstly applied the LightGBM as a machine learning model to increase the modeling ability, and secondly applied the SHAP analysis to evaluate the contribution of explanatory variables to the objective variable. Finally, we visualize the contribution to identify nonlinear relationships, which can be used for practical marketing problems. As an example, we demonstrated that our visualization can work well to express the nonlinear relationships hidden in capital flows of Japanese mutual funds, and can see investors psychology based on the behavioral economics from the given results.

Two classical Ising machine schemes, the Oscillator Ising Machine (OIM) and the Bistable Latch Ising Machine (BLIM), have been shown to feature global Lyapunov functions, i.e., continuous “energy-like” functions whose local minima are naturally found by the physics of these schemes. We show that the Coherent Ising Machine (CIM), an optical scheme that predated OIM and BLIM, also has a global Lyapunov function that approximates the Ising Hamiltonian at stable equilibrium points. Our result sharpens understanding of CIM operation, revealing that its mechanism for breaking out of local minima is a purely probabilistic classical one, similar to Gibbs sampling.

Since participation in blockchain mining requires a lot of computational power and consumes a large amount of electricity, which leads to a significant level of carbon emissions, governments of some nations frame the policy about blockchain mining, such as cracking down on or imposing an additional tax for mining. We propose a dynamical model of miners' decision-making under the imposition of both an income and a green tax. We show that the mining reward affects the qualitative change of the behaviors of miners depending on the income tax rate and that both a saddle-node bifurcation and a transcritical bifurcation occur in the model.

This paper presents differential evolution with perturbation (DEP) for continuous function optimization. Differential evolution is a simple and efficient algorithm. Perturbation is the phenomenon that the motion by the contribution of the main force is disturbed by the influence subsidiary power. In order to show the effectiveness of the proposed algorithm, we compare it to existing algorithms by CEC2017 datasets.

The purpose of this study is to separate the intrinsic equity value and the mispricing caused by irrational investor sentiments from the actual stock price. We applied machine learning approach to improve traditional valuation models like the DDM, the RIM, and the OVM and to detect nonlinear and nonstationary dynamics hidden in financial growth of corporate companies. However, because the intrinsic equity value is completely unobservable, we confirmed the validity of our approach by stock portfolio simulations based on the value and growth strategy from the viewpoint of market efficiency.

In supervised learning, annotation is hard work because training data must be labeled and a lot of training data is needed. Therefore, we propose a novel label estimation method based on Fisher criterion to estimate label of unlabeled data from a small amount of labeled data. Fisher criterion maximizes between-class variance and minimizes within-class variance. Since the Fisher criterion is only used for linearly separable data, we apply our proposed method to linearly inseparable data. We demonstrate that the proposed method is effective in estimating the labels of linearly inseparable data.

Reservoir computing is a machine learning model that is widely used for time series tasks due to its advantages of low cost and fast learning. However, conventional reservoir computing often do not achieve the memory capacity and nonlinearity required for the task. To solve this problem, we proposed hysteresis reservoir computing which conventional reservoir neurons are replaced by hysteresis neurons. The model generates various output sequences by changing their parameters. In addition, it has the potential to memorize time series because it presents complex periodic solutions. In this paper, we confirm the dynamics generated by changing the hysteresis reservoir computing parameters. The experimental results show that changing the parameters improves the learning ability and can represent specific series of data. This indicates an important dynamics in terms of memory capacity and the ability to represent.

In this paper, we propose a novel progressive image transmission framework based on spatio-temporal image decomposition and synthesis by the SD-CNN. In our method, we redesign the baseline SD-CNN and the weighted sum is introduced in the accumulator. This innovation enables lossless or near-lossless progressive image transmission. Experimental results in various test images support that the image reconstruction performance of the SD-CNN has dramatically improved by our method.

Quasi-Newton (QN) methods have shown to be effective in training neural networks. However, the computation and the storage of the approximated Hessian in large-scale applications is still a problem. The Memory-less QN (MLQN) was introduced as a method that did not require the storage of the matrix. This paper describes the effectiveness of the momentum term for the accelerated MLQN method through computer simulations on function approximation and classification problems.

For an indefinite length spectrogram sequence of phonemes, we experimentally verified two methods of obtaining speaker embedding by transforming it to fixed length: adding padding and time stretching. We confirmed that both methods can maintain the extraction performance. We also confirm that the fixed frame length does not affect the results.

In this paper, we aim to clarify the computational complexity of artificial neural networks. We investigate the computational complexity of hysteresis neural networks (HNN) for solving constraint satisfaction problems. We confirm that the amount of computation is proportional to the logarithm of the size of the problem.

In order to realize a barrier free society, it is important to realize sign language recognition on smartphones. Several methods have been proposed for fingersplling recognition, which is the basis of sign language recognition. In this paper, we propose a simple still fingerspelling recognition system. The system apply the two dimensional hand point information obtained by MediaPipe. The obtained information is identified by a linear SVM. The proposed system requires only a smaller amount of input data than the previous ones, and the processing is realized by SVM which requires a small amount of computation. Although the proposed system requires only a small amount of computation, it achieves extremely recognition accuracy for still fingerspellings.

Doubly nested mixed-mode oscillations (MMOs) have been observed in a driven classical Bonhoeffer-van der Pol oscillator. However, the bifurcation phenomena surrounding doubly nested MMOs have not yet been clarified. In this study, we investigated the bifurcation phenomena of doubly nested MMOs. A one-parameter bifurcation diagram and phase planes were used to confirm the circuit behavior around the bifurcation points. First-return maps were then used to show the effects of bifurcation phenomena on sequences of doubly nested MMOs. The composite first-return map qualitatively explains the bifurcation mechanism that causes doubly nested MMOs.

The dimension of data influences the clustering method used for pattern recognition. Dimension reduction method, therefore, has a significant impact on clustering performance. This study compares discriminant analysis (DA) and Laplacian eigenmaps (LE), two supervised and unsupervised dimension reduction methods, from the standpoint of the degree of separation. This comparison revealed that LE suffers from a loss of accuracy due to the lack of an averaging operation. Therefore, we propose a new dimensionality reduction method, discriminant LE (DLE), which eliminates the shortcomings of LE. DLE is a straightforward approximation of DA using the similarity. We also propose recursive similarity processing method to reduce pseudoclusters. Finally, we also conclude that DLE is more useful than LE for clustering and that recursive similarity processing improves the performance of DLE.

A cyclic chaotic neural network reservoir (CNNR) circuit is implemented on a stacked three-dimensional (3D) cyclic neural network integrated circuit (IC) system, which was originally designed and fabricated for a deep feedforward neural network. We create a circuit emulator for a neuron chip used in the 3D integrated system according to the measurement results obtained from the chip. We preliminary evaluate the performance of the cyclic CNNR circuit for a waveform classification task using the emulator.

This paper describes the parallelization of Nested Layer Particle Swarm Optimization (NLPSO) to improve the computation time for bifurcation point detection. While NLPSO allows for the search for bifurcation points with less prior knowledge than the previously used Newton's approach, a reduction in computation time is necessary. Parallelization with CUDA made bifurcation point identification with NLPSO up to 24× faster in our experiments.

To realize massive IoT environments, we proposed Asynchronous Pulse Code Multiple Access (APCMA). APCMA encodes information as intervals between pulses. The sparse signal of APCMA allows a large number of devices to share the limited radio resources. In this paper, we evaluate APCMA with a variety of setting and find that code division of two and duty cycle of 0.01 % can provide 10000 devices with the per-device throughput of about 3.46 bps with 99 % precision. It also is shown that APCMA outperfoms LoRaWAN and CDMA.

Stochastic Computing (SC)[2] is a probability-based computing method, which enables the performance of various operations with a small number of logic gates (i.e., low power) in exchange for high accuracy. Using SC for edge artificial intelligence (AI) integrated circuits can help circumvent the limitations inherent in the power and area required for edge AI.

In this study, a three-layered Neural Network (NN) is presented with an online learning function that introduces pseudo-activation, pseudo-subtraction, and imperfect addition into the SC framework. This method may expand the options for edge AI integrated circuits using SC.

In block encryption algorithms, random permutations are often employed for nonlinear transformation called a substitution box (S-box). Because an S-box is the only nonlinear portion of a block cipher, it accounts for most of implementation costs. For decryption, the circuit implementation of the corresponding inverse permutation is also required. To reduce the circuit size of the inverse permutation, we derive a method to generate inverse permutations based on the compositions of permutations. The effectiveness of the proposed method in terms of the complexity of Boolean functions is demonstrated through its application to the S-box used in PRESENT and to the optimum S-boxes.

Reducing the number of connections in hardware artificial neural networks, as compared with their software counterparts, can result in a drastic reduction in costs, because the reduction translates into utilizing fewer devices. This paper presents the demonstration of a method, by using simulations, to halve the amount of weights in a network while minimizing the accuracy loss. Additionally, the appropriate considerations for translating these simulation results to hardware networks are also detailed.

Word co-occurrence networks (WCNs) are a major tool used to analyze languages quantitatively. In a WCN, the vertices are words (morphemes), and the edges connect n consecutive words in a sentence on the basis of the n-gram. Most studies use WCNs transformed at n=2. In this study, we investigated the changes in the structural features of WCNs when n increases using four types of documents for eight languages. We found that WCNs with n≧ 3 reflect features of the languages that do not appear when n = 2 and that some structural features evaluated by network measures depend on the text data.

This study investigates the real-time computation of a large-scaled spiking neural network using graphic processing units. A randomly coupled network comprising several hundred thousand spiking neurons was computed in real-time. We also developed an entorhinal-hippocampal neural network consisting of approximately 50,000 spiking neurons and implemented a mechanism to form place cells in the hippocampal network through the entorhinal cortex based on the direction of motion and velocity of a mobile robot. In an experiment using a real mobile robot, we confirmed that place cells were formed in the hippocampus while the robot moved through a square open field.

In bicycle sharing systems (BSSs), developing effective strategies for rebalancing bicycles in real BSS require building realistic benchmark instances from the actual usage history of rented and returned bicycles. Thus, in this study, we analyzed real BSSs in Boston; Washington, D.C.; New York; and Chicago. First, we investigated whether excess and lack of bicycles were generated for the four BSSs and found that excess and lack of bicycles existed for all BSSs. Next, to determine the temporal patterns of rented and returned BSSs bicycles, we treated the usage history data of rental and return timings as a point process. To analyze the point process data, we used a raster plot, the coefficient of variation (C_V) and the local variation (L_V) of the inter-event-intervals (IEIs) for the rental and return timings. The results of L_V suggested that the statistical characteristics of the temporal patterns of events of rented and returned bicycles among the four BSSs were similar for both weekdays and weekends, and for daytime (8:00-20:59) and all day (24h). The results also suggested that the statistical characteristics of the temporal patterns of events of rented and returned bicycles in New York follow the Poisson process and those in the other cities (Boston, Washington, D.C., and Chicago) did not necessary follow the Poisson process.

First-order methods such as SGD and Adam are popularly used in training Neural networks. On the other hand, second-order methods have shown to have better performance and faster convergence despite their high computational cost by incorporating the curvature information. While second-order methods determine the step size by line search approaches, first-order methods achieve efficient learning by devising a way to adjust the step size. In this paper, we propose a new learning algorithm for training neural networks by combining first-order and second-order methods. We investigate the effectiveness of our proposed method when combined with popular first-order methods - SGD, Adagrad, and Adam, through experiments using image classification problems.

In the field of neuroscience, it is widely acknowledged that neurons exhibit periodic, quasi-periodic, and chaotic responses to periodic inputs. In this study, we evaluated the responses of the Izhikevich neuron model stimulated by sinusoidal inputs. First, we analyzed the dynamical behavior of the Izhikevich neuron model to the sinusoidal inputs in the state space and found two types of responses: periodic and non-periodic. Next, we obtained the domains of the periodic and non-periodic responses on the frequency-amplitude plane of the sinusoidal inputs by evaluating the diversity index of the inter-spike intervals. Finally, we analyzed the responses of the Izhikevich neuron model using the stroboscopic plot. Consequently, we clarified that a periodic response is a limit cycle and an irregular response is a torus, which implies that the irregular responses of the Izhikevich neuron model stimulated by sinusoidal inputs are quasi-periodic responses.

Reservoir computing (RC) is possible using physical systems. We have previously proposed an RC for ideal atomic switches. When temporal current fluctuations (noise) from the measurement of actual atomic switches are introduced into the proposed RC, performance degrades significantly. To address this issue, we propose novel methods for increasing the operating current range and observing the atomic switch several times to determine the average noise. Consequently, the memory capacity of the RC model increased, despite the presence of noise. To improve the precision of RC, we investigated the capacity and showed that changing the time constant of atomic switches results in an improvement.

Recently, there has been considerable research on nonvolatile analog devices for artificial intelligence (AI); however, it focuses on all-coupled neural networks. In contrast, polymer wire-type synaptic devices, which can be expected to be arbitrarily wired similar to a biological neural network, have already been proposed and demonstrated. In this study, we model a polymer wire synaptic device based on the results of previous research, and demonstrate an example of applying simple perceptron (AI) to the model. The results of our study show that it is possible to predict effective methods of using polymer wire synaptic elements in AI.

State space reconstruction using time-delay coordinate systems is the most effective and significant technique for analyzing complex time series generated by nonlinear dynamical systems. In this study, we investigated the relationships between reconstruction parameters and the similarity of the structural properties of original and reconstructed attractors. In particular, we investigated the similarities between inter-point distance distributions on original and reconstructed attractors, while varying the reconstruction parameters for reconstructing a dynamical system using a time-delay coordinate system. The results show that the product of the reconstruction dimension and the time-delay should be constant to obtain high similarity.

In this paper, a novel hardware-efficient auditory neuron model whose nonlinear dynamics is described by an ergodic cellular automaton is proposed. It is shown that the proposed model can reproduce first pitch-shift effect, which is one of the nonlinear sound processing functions observed in the biological auditory system. The proposed model and an ordinary differential equation (ODE) model based on generic threshold-plus-reinjection dynamics are implemented on field-programmable gate arrays (FPGAs) and it is demonstrated that the proposed model employs fewer circuit elements for FPGA implementation and consumes lower power than the ODE model.

Reservoir computing (RC) has attracted attention and has been used in many applications because of its low training cost. Multiple studies using RC for image recognition have been proposed, and some have achieved accuracy rates of greater than 99% on the MNIST dataset. For the Fashion-MNIST and CIFAR-10 datasets, however, they have not yet achieved high accuracy. This study proposes a novel convolutional neural network based on RC that can be optimized by ridge regression rather than back-propagation. The reservoir-based network has multiple reservoirs with various leak rates to extract features with various spatial frequencies from the inputs. The experimental results show that the performance of the proposed model achieves higher accuracy rates in the mentioned datasets compared with those of other reservoir-based image recognition approaches.

This paper studies dimensionality reduction of parameters in a piecewise linear model of boost converter with PV input. The circuit is subject to a bi-objective optimization problem: the first objective evaluates extracting input power and the second objective evaluates circuit dynamics stability. A trade off exists between the two objectives and is represented by a Pareto front. An approximation of the Pareto front is a criterion for the dimensionality reduction. Performing precise numerical experiment, a simple dimensionality reduction from two-dimensional parameter space into a one-dimensional parameter subspace is achieved.

This paper proposes a mode-in-state contribution factor for a class of nonlinear dynamical systems by utilizing spectral properties of the Koopman operator and sensitivity analysis. Using eigenfunctions of the Koopman operator for a target nonlinear system, we show that the relative contribution between modes and state variables can be quantified beyond a linear regime, where the nonlinearity of the system is taken into consideration. The proposed contribution factor is applied to the numerical analysis of large-signal simulations for an interconnected AC/multi-terminal DC power system.

Although cells in different tissues of the human body share the same genome, their functions are different from each other because of tissue-specific gene expression. In this study, we investigated the cause of the differences in gene expression patterns in each tissue. We used gene regulatory networks (GRNs) constructed from genomic experimental data that are available in recent years. We investigated the frequency of the occurrence of subgraphs consisting of three vertices (SG3s) in GRNs and found that some SG3s may contribute to the emergence of tissue-specific genes.

Estimating circadian rhythm disturbance is important for differentiating between mental illness and healthy states. Electroencephalogram (EEG) allows brain activity detection directly; however, the recorded signal combines neural activity across multiple time scales, which has been previously quantified using the multiscale entropy (MSE) analysis. We investigated whether MSE analysis of EEG data can detect circadian rhythms. Our results demonstrated increased brain activity complexity in the temporal scale in the daytime; moreover, these changes were more accurately detected by MSE than conventional power analysis. Our method can be applied for EEG-based analysis of circadian rhythms in clinical and healthcare fields.

Reinforcement learning is promising as a machine learning paradigm in edge computing. However, its high computational cost poses a challenge when implementing in devices with limited circuit resources and power consumption. In this study, we investigated the relationship between the bit-length of floating-point operations and the learning performance of the reinforcement learning algorithm. In the case of the FrozenLake maze problem, we found that the learning performance of 8-bit floating-point arithmetic decreased, while that of 16-bit floating-point arithmetic was comparable to that of 64-bit CPU arithmetic. Our results provide a practical guideline for designing a dedicated reinforcement learning hardware with minimum circuit resources and power consumption.

In this paper, phase-locking phenomena in two coupled cellular automaton (CA) phase oscillators for applying to central pattern generators (CPGs) are theoretically analyzed. The two CA phase oscillators are asynchronously coupled and referred to as the ergodically coupled CA phase oscillators since transition moments of discrete states are described by an irrational rotation. The theoretical analysis reveals stable fixed points that guarantee phase-locking in the ergodically coupled CA phase oscillators. It is then shown that the ergodically coupled CA phase oscillators are more suitable for applying to CPGs than the synchronously coupled CA phase oscillators in terms of phase-locking phenomena.

In the conventional implementations for solving bifurcation problems, Jacobian matrix and its partial derivatives regarding the given problem should be provided manually. This process is not so easy, thus it often induces human errors like computation failures, typing error, especially if the system is higher order. In this paper, we develop a preprocessor that gives Jacobian matrix and partial derivatives symbolically by using SymPy packages on the Python platform. Possibilities about the inclusion of errors are minimized by symbolic derivations and reducing loop structures. It imposes a user only on putting an expression of the equation into a JSON format file. We demonstrate bifurcation calculations for discrete neuron dynamical systems. The system includes an exponential function, which makes the calculation of derivatives complicated, but we show that it can be implemented simply by using symbolic differentiation.

The human brain performs intelligent behavior with its hierarchical neural structure. In the past years, the relationship among different brain areas and their roles have been widely studied. In particular, functional connectivity has been used to discuss mechanisms that perform information processing in the brain. Alternatively, computational models have also been used to reveal the mechanisms. Reservoir computing is one of the models that simulate the dynamical process of the brain. The purpose of this paper is to apply the functional connectivity analysis to the reservoir computing model. This approach will contribute to comparing the computational model with the neurophysiological study.

This paper describes a novel algorithm of set-based comprehensive learning and particle swarm optimization with memory for discrete optimization problem. Our algorithm is an approach of searching for the best position in a set by referring to the current position when updating the solution. In order to show the validity of our algorithm, we examine numerical experiments compared to existing algorithms.

With respect to the next frontier of neuromorphic sensing, we propose a parameter tuning method based on mutual information criteria for MEMS-based reservoir computing. It is required for MEMS reservoirs to tune the balance of the linear and nonlinear characteristics and to control their dynamical behaviors depending on driving forces, such as chaos and hysteresis. We focus on a pre-training method for machine learning called the intrinsic plasticity (IP) learning, and apply it to controlling the dynamical behaviors of MEMS reservoirs. First, we demonstrate simulation results for chaos suppression. Next, we applied our IP learning to parameter tuning of the MEMS-based reservoir Finally, we show that our approach can improve prediction accuracy in nonlinear transformation tasks.

This paper proposes a wireless power transfer (WPT) system using the load-independent inverse class-E oscillator. The proposed system realizes autonomous operation without using external driving circuits. Therefore, it is easier to design the power-transmission inverter at high frequencies, in particular. Moreover, the proposed WPT system has load-independent characteristics. It maintains constant output voltage and zero current switching (ZCS) of the MOSFET without applying any controls for load variations. We conducted the circuit analysis and the experimental verifications for the proposed system. In the experiment, the proposed system achieved 76.5% power-delivery efficiency with 20 W output power and 1 MHz operating frequency at the rated state.

To investigate the role of the nonlinearity of input interactions in the neural network, we examined the influence of acetylcholine as a top-down input on the interaction between bottom-up inputs in dentate granule cells in the hippocampus. The results showed that nonlinearity in the interaction between bottom-up inputs was modulated by the top-down input and was related to inhibitory cells. Our findings suggest that nonlinearity in the interaction of inputs plays a key role in coincidence detection, which is regulated by the top-down input. This indicates a crucial role for nonlinearity in the neurodynamics of the hippocampal local network.

This paper considers the identification problem of network structures for networked dynamical systems. We define the network structure as a coupling function describing the network connectivity and the nonlinear data exchange functions in the network, and attempt to identify the coupling function from potentially noisy measurement data. We develop an identification method of network structures applicable even to network systems consisting of nonlinear systems and nonlinear coupling functions by using the Koopman operator theory. First, we design observable functions as basis functions of a functional space, and determine the Koopman operators associated with the dynamics of the network. Then, the coupling function is identified as a projection on the span of the observables. Also, we make use of the sparse identification techniques to reduce requirements on data amounts and improve robustness with respect to measurement noise. Numerical examples show that the proposed method is applicable to a wide range of nonlinear systems, including chaotic systems with nonlinear coupling functions, and yields better performance than some existing methods. Identification results for two different nonlinear network systems with nonlinear coupling functions show the usefulness of the proposed method.