Naoya Takeishi

Naoya Takeishi, Yoshinobu Kawahara, Takehisa Yairi

The analysis of nonlinear dynamical systems based on the Koopman operator is attracting attention in various applications. Dynamic mode decomposition (DMD) is a data-driven algorithm for Koopman spectral analysis, and several variants with a wide range of applications have been proposed. However, popular implementations of DMD suffer from observation noise on random dynamical systems and generate an inaccurate estimation of the spectra of the stochastic Koopman operator. In this paper, we propose subspace DMD as an algorithm for the Koopman analysis of random dynamical systems with observation noise. Subspace DMD first computes the orthogonal projection of future snapshots to the space of past snapshots and then estimates the spectra of a linear model, and its output converges to the spectra of the stochastic Koopman operator under standard assumptions. We investigate the empirical performance of subspace DMD with several dynamical systems and show its utility for the Koopman analysis of random dynamical systems.

Naoya Takeishi, Alexandros Kalousis

The combination of deep neural nets and theory-driven models, which we call deep grey-box modeling, can be inherently interpretable to some extent thanks to the theory backbone. Deep grey-box models are usually learned with a regularized risk minimization to prevent a theory-driven part from being overwritten and ignored by a deep neural net. However, an estimation of the theory-driven part obtained by uncritically optimizing a regularizer can hardly be trustworthy when we are not sure what regularizer is suitable for the given data, which may harm the interpretability. Toward a trustworthy estimation of the theory-driven part, we should analyze regularizers' behavior to compare different candidates and to justify a specific choice. In this paper, we present a framework that enables us to analyze a regularizer's behavior empirically with a slight change in the neural net's architecture and the training objective.

Maciej Falkiewicz, Naoya Takeishi, Imahn Shekhzadeh et al.

Bayesian inference allows expressing the uncertainty of posterior belief under a probabilistic model given prior information and the likelihood of the evidence. Predominantly, the likelihood function is only implicitly established by a simulator posing the need for simulation-based inference (SBI). However, the existing algorithms can yield overconfident posteriors (Hermans *et al.*, 2022) defeating the whole purpose of credibility if the uncertainty quantification is inaccurate. We propose to include a calibration term directly into the training objective of the neural model in selected amortized SBI techniques. By introducing a relaxation of the classical formulation of calibration error we enable end-to-end backpropagation. The proposed method is not tied to any particular neural model and brings moderate computational overhead compared to the profits it introduces. It is directly applicable to existing computational pipelines allowing reliable black-box posterior inference. We empirically show on six benchmark problems that the proposed method achieves competitive or better results in terms of coverage and expected posterior density than the previously existing approaches.

Keisuke Fujii, Koh Takeuchi, Atsushi Kuribayashi et al.

Evaluation of intervention in a multiagent system, e.g., when humans should intervene in autonomous driving systems and when a player should pass to teammates for a good shot, is challenging in various engineering and scientific fields. Estimating the individual treatment effect (ITE) using counterfactual long-term prediction is practical to evaluate such interventions. However, most of the conventional frameworks did not consider the time-varying complex structure of multiagent relationships and covariate counterfactual prediction. This may lead to erroneous assessments of ITE and difficulty in interpretation. Here we propose an interpretable, counterfactual recurrent network in multiagent systems to estimate the effect of the intervention. Our model leverages graph variational recurrent neural networks and theory-based computation with domain knowledge for the ITE estimation framework based on long-term prediction of multiagent covariates and outcomes, which can confirm the circumstances under which the intervention is effective. On simulated models of an automated vehicle and biological agents with time-varying confounders, we show that our methods achieved lower estimation errors in counterfactual covariates and the most effective treatment timing than the baselines. Furthermore, using real basketball data, our methods performed realistic counterfactual predictions and evaluated the counterfactual passes in shot scenarios.

João A. Cândido Ramos, Lionel Blondé, Naoya Takeishi et al.

In this paper, we introduce MAAD, a novel, sample-efficient on-policy algorithm for Imitation Learning from Observations. MAAD utilizes a surrogate reward signal, which can be derived from various sources such as adversarial games, trajectory matching objectives, or optimal transport criteria. To compensate for the non-availability of expert actions, we rely on an inverse dynamics model that infers plausible actions distribution given the expert's state-state transitions; we regularize the imitator's policy by aligning it to the inferred action distribution. MAAD leads to significantly improved sample efficiency and stability. We demonstrate its effectiveness in a number of MuJoCo environments, both int the OpenAI Gym and the DeepMind Control Suite. We show that it requires considerable fewer interactions to achieve expert performance, outperforming current state-of-the-art on-policy methods. Remarkably, MAAD often stands out as the sole method capable of attaining expert performance levels, underscoring its simplicity and efficacy.

Kaito Goto, Naoya Takeishi, Takehisa Yairi

Converting betting odds into accurate outcome probabilities is a fundamental challenge in order to use betting odds as a benchmark for sports forecasting and market efficiency analysis. In this study, we propose two methods to overcome the limitations of existing conversion methods. Firstly, we propose an odds-only method to convert betting odds to probabilities without using historical data for model fitting. While existing odds-only methods, such as Multiplicative, Shin, and Power exist, they do not adjust for biases or relationships we found in our betting odds dataset, which consists of 90014 football matches across five different bookmakers. To overcome these limitations, our proposed Odds-Only-Equal-Profitability-Confidence (OO-EPC) method aligns with the bookmakers' pricing objectives of having equal confidence in profitability for each outcome. We provide empirical evidence from our betting odds dataset that, for the majority of bookmakers, our proposed OO-EPC method outperforms the existing odds-only methods. Beyond controlled experiments, we applied the OO-EPC method under real-world uncertainty by using it for six iterations of an annual basketball outcome forecasting competition. Secondly, we propose a generalised linear model that utilises historical data for model fitting and then converts betting odds to probabilities. Existing generalised linear models attempt to capture relationships that the Efficient Market Hypothesis already captures. To overcome this shortcoming, our proposed Favourite-Longshot-Bias-Adjusted Generalised Linear Model (FL-GLM) fits just one parameter to capture the favourite-longshot bias, providing a more interpretable alternative. We provide empirical evidence from historical football matches where, for all bookmakers, our proposed FL-GLM outperforms the existing multinomial and logistic generalised linear models.

Henrik Krauss, Johann Licher, Naoya Takeishi et al.

This work addresses open-loop control of a soft continuum robot (SCR) from video-learned latent dynamics. Visual Oscillator Networks (VONs) from previous work are used, that provide mechanistically interpretable 2D oscillator latents through an attention broadcast decoder (ABCD). Open-loop, single-shooting optimal control is performed in latent space to track image-specified waypoints without camera feedback. An interactive SCR live simulator enables design of static, dynamic, and extrapolated targets and maps them to model-specific latent waypoints. On a two-segment pneumatic SCR, Koopman, MLP, and oscillator dynamics, each with and without ABCD, are evaluated on setpoint and dynamic trajectories. ABCD-based models consistently reduce image-space tracking error. The VON and ABCD-based Koopman models attains the lowest MSEs. Using an ablation study, we demonstrate that several architecture choices and training settings contribute to the open-loop control performance. Simulation stress tests further confirm static holding, stable extrapolated equilibria, and plausible relaxation to the rest state. To the best of our knowledge, this is the first demonstration that interpretable, video-learned latent dynamics enable reliable long-horizon open-loop control of an SCR.

Xingyu Song, Yuan Mei, Naoya Takeishi

Modern generative models can be understood as probability transport from a simple base distribution to a target data distribution. Deterministic transport models offer tractable velocity-field parameterizations, whereas stochastic generative models capture richer density evolution through drift and diffusion. Yet when stochastic dynamics are described through deterministic velocity fields, the effects of drift and diffusion are often compressed into a single effective field, obscuring the distinct roles of deterministic evolution and stochastic fluctuation. In this work, we show that the deterministic field \(b_t\) of a stochastic generative process admits a natural transport--osmotic decomposition that separates deterministic transport from stochastic, diffusion-induced effects: \(b_t = u_t + d_t\), where \(u_t\) governs marginal probability transport and \(d_t\) captures an osmotic effect induced by diffusion and determined by the marginal score. Based on this decomposition, we propose Bridge Matching, a flow-based framework for learning decomposed generative dynamics through both marginal and conditional formulations. In generative modeling experiments, we recombine the learned components as \(b_t = u_t + λ_d d_t\), showing that the proposed decomposition enables interpretable and controllable sampling by adjusting the osmotic contribution in probability transport.

Yuan Mei, Xingyu Song, Xiaowen Song et al.

Neural surrogate models for physical simulations are trained on discretized samples of continuous domains, where the induced empirical measure leads to uneven supervision, biasing optimization and causing spatial inconsistencies in physical fidelity. To mitigate this measure-induced bias, we propose M$^3$ (Multi-scale Morton Measure), a scalable framework that balances training measures by partitioning space according to physical variation and allocating supervision across multiple scales. Applied to three industrial-scale datasets with diverse discretizations, M$^3$ consistently improves predictions in the continuous physical domain, achieving up to 4.7$\times$ lower error in large-scale volumetric cases. These gains persist under aggressive subsampling (160M $\rightarrow$ 16M $\rightarrow$ 1.6M points), where M$^3$-trained models outperform those trained on higher-resolution data, reducing physics-weighted relative $L_2$ error by 3--4$\times$ and the corresponding MSE by up to 13$\times$. These results highlight data distribution as a key factor in operator learning and position M$^3$ as a scalable, data-efficient approach for physically consistent modeling.

Leander Thiele, Adrian E. Bayer, Naoya Takeishi

The simulation cost for cosmological simulation-based inference can be decreased by combining simulation sets of varying fidelity. We propose an approach to such multi-fidelity inference based on feature matching and knowledge distillation. Our method results in improved posterior quality, particularly for small simulation budgets and difficult inference problems.

Naoya Takeishi

Hybrid modeling, the combination of machine learning models and scientific mathematical models, enables flexible and robust data-driven prediction with partial interpretability. However, effectively the scientific models may be ignored in prediction due to the flexibility of the machine learning model, making the idea of hybrid modeling pointless. Typically some regularization is applied to hybrid model learning to avoid such a failure case, but the formulation of the regularizer strongly depends on model architectures and domain knowledge. In this paper, we propose to focus on the flatness of loss minima in learning hybrid models, aiming to make the model as simple as possible. We employ the idea of sharpness-aware minimization and adapt it to the hybrid modeling setting. Numerical experiments show that the SAM-based method works well across different choices of models and datasets.

Henrik Krauss, Johann Licher, Naoya Takeishi et al.

Data-driven learning of soft continuum robot (SCR) dynamics from high-dimensional observations offers flexibility but often lacks physical interpretability, while model-based approaches require prior knowledge and can be computationally expensive. We bridge this gap by introducing (1) the Attention Broadcast Decoder (ABCD), a plug-and-play module for autoencoder-based latent dynamics learning that generates pixel-accurate attention maps localizing each latent dimension's contribution while filtering static backgrounds. (2) By coupling these attention maps to 2D oscillator networks, we enable direct on-image visualization of learned dynamics (masses, stiffness, and forces) without prior knowledge. We validate our approach on single- and double-segment SCRs, demonstrating that ABCD-based models significantly improve multi-step prediction accuracy: 5.7x error reduction for Koopman operators and 3.5x for oscillator networks on the two-segment robot. The learned oscillator network autonomously discovers a chain structure of oscillators. Unlike standard methods, ABCD models enable smooth latent space extrapolation beyond training data. This fully data-driven approach yields compact, physically interpretable models suitable for control applications.

Keisuke Fujii, Kazushi Tsutsui, Yu Teshima et al.

Simulators of animal movements play a valuable role in studying behavior. Advances in imitation learning for robotics have expanded possibilities for reproducing human and animal movements. A key challenge for realistic multi-animal simulation in biology is bridging the gap between unknown real-world transition models and their simulated counterparts. Because locomotion dynamics are seldom known, relying solely on mathematical models is insufficient; constructing a simulator that both reproduces real trajectories and supports reward-driven optimization remains an open problem. We introduce a data-driven simulator for multi-animal behavior based on deep reinforcement learning and counterfactual simulation. We address the ill-posed nature of the problem caused by high degrees of freedom in locomotion by estimating movement variables of an incomplete transition model as actions within an RL framework. We also employ a distance-based pseudo-reward to align and compare states between cyber and physical spaces. Validated on artificial agents, flies, newts, and silkmoth, our approach achieves higher reproducibility of species-specific behaviors and improved reward acquisition compared with standard imitation and RL methods. Moreover, it enables counterfactual behavior prediction in novel experimental settings and supports multi-individual modeling for flexible what-if trajectory generation, suggesting its potential to simulate and elucidate complex multi-animal behaviors.

Haruki Settai, Naoya Takeishi, Takehisa Yairi

For continuous systems modeled by dynamical equations such as ODEs and SDEs, Bellman's Principle of Optimality takes the form of the Hamilton-Jacobi-Bellman (HJB) equation, which provides the theoretical target of reinforcement learning (RL). Although recent advances in RL successfully leverage this formulation, the existing methods typically assume the underlying dynamics are known a priori because they need explicit access to the coefficient functions of dynamical equations to update the value function following the HJB equation. We address this inherent limitation of HJB-based RL; we propose a model-free approach still targeting the HJB equation and propose the corresponding temporal difference method. We establish exponential convergence of the idealized continuous-time dynamics and empirically demonstrate its potential advantages over transition-kernel-based formulations. The proposed formulation paves the way toward bridging stochastic control and model-free reinforcement learning.

Maciej Falkiewicz, Naoya Takeishi, Alexandros Kalousis

We propose a novel deep generative model, the Kolmogorov-Smirnov Generative Adversarial Network (KSGAN). Unlike existing approaches, KSGAN formulates the learning process as a minimization of the Kolmogorov-Smirnov (KS) distance, generalized to handle multivariate distributions. This distance is calculated using the quantile function, which acts as the critic in the adversarial training process. We formally demonstrate that minimizing the KS distance leads to the trained approximate distribution aligning with the target distribution. We propose an efficient implementation and evaluate its effectiveness through experiments. The results show that KSGAN performs on par with existing adversarial methods, exhibiting stability during training, resistance to mode dropping and collapse, and tolerance to variations in hyperparameter settings. Additionally, we review the literature on the Generalized KS test and discuss the connections between KSGAN and existing adversarial generative models.

Keisuke Fujii, Kazushi Tsutsui, Atom Scott et al.

Modeling of real-world biological multi-agents is a fundamental problem in various scientific and engineering fields. Reinforcement learning (RL) is a powerful framework to generate flexible and diverse behaviors in cyberspace; however, when modeling real-world biological multi-agents, there is a domain gap between behaviors in the source (i.e., real-world data) and the target (i.e., cyberspace for RL), and the source environment parameters are usually unknown. In this paper, we propose a method for adaptive action supervision in RL from real-world demonstrations in multi-agent scenarios. We adopt an approach that combines RL and supervised learning by selecting actions of demonstrations in RL based on the minimum distance of dynamic time warping for utilizing the information of the unknown source dynamics. This approach can be easily applied to many existing neural network architectures and provide us with an RL model balanced between reproducibility as imitation and generalization ability to obtain rewards in cyberspace. In the experiments, using chase-and-escape and football tasks with the different dynamics between the unknown source and target environments, we show that our approach achieved a balance between the reproducibility and the generalization ability compared with the baselines. In particular, we used the tracking data of professional football players as expert demonstrations in football and show successful performances despite the larger gap between behaviors in the source and target environments than the chase-and-escape task.

Naoya Ozaki, Kanta Yanagida, Takuya Chikazawa et al.

Asteroid exploration has been attracting more attention in recent years. Nevertheless, we have just visited tens of asteroids while we have discovered more than one million bodies. As our current observation and knowledge should be biased, it is essential to explore multiple asteroids directly to better understand the remains of planetary building materials. One of the mission design solutions is utilizing asteroid flyby cycler trajectories with multiple Earth gravity assists. An asteroid flyby cycler trajectory design problem is a subclass of global trajectory optimization problems with multiple flybys, involving a trajectory optimization problem for a given flyby sequence and a combinatorial optimization problem to decide the sequence of the flybys. As the number of flyby bodies grows, the computation time of this optimization problem expands maliciously. This paper presents a new method to design asteroid flyby cycler trajectories utilizing a surrogate model constructed by deep neural networks approximating trajectory optimization results. Since one of the bottlenecks of machine learning approaches is the computation time to generate massive trajectory databases, we propose an efficient database generation strategy by introducing pseudo-asteroids satisfying the Karush-Kuhn-Tucker conditions. The numerical result applied to JAXA's DESTINY+ mission shows that the proposed method is practically applicable to space mission design and can significantly reduce the computational time for searching asteroid flyby sequences.

Keisuke Fujii, Naoya Takeishi, Kazushi Tsutsui et al.

Extracting the interaction rules of biological agents from movement sequences pose challenges in various domains. Granger causality is a practical framework for analyzing the interactions from observed time-series data; however, this framework ignores the structures and assumptions of the generative process in animal behaviors, which may lead to interpretational problems and sometimes erroneous assessments of causality. In this paper, we propose a new framework for learning Granger causality from multi-animal trajectories via augmented theory-based behavioral models with interpretable data-driven models. We adopt an approach for augmenting incomplete multi-agent behavioral models described by time-varying dynamical systems with neural networks. For efficient and interpretable learning, our model leverages theory-based architectures separating navigation and motion processes, and the theory-guided regularization for reliable behavioral modeling. This can provide interpretable signs of Granger-causal effects over time, i.e., when specific others cause the approach or separation. In experiments using synthetic datasets, our method achieved better performance than various baselines. We then analyzed multi-animal datasets of mice, flies, birds, and bats, which verified our method and obtained novel biological insights.

Naoya Takeishi, Alexandros Kalousis

Integrating physics models within machine learning models holds considerable promise toward learning robust models with improved interpretability and abilities to extrapolate. In this work, we focus on the integration of incomplete physics models into deep generative models. In particular, we introduce an architecture of variational autoencoders (VAEs) in which a part of the latent space is grounded by physics. A key technical challenge is to strike a balance between the incomplete physics and trainable components such as neural networks for ensuring that the physics part is used in a meaningful manner. To this end, we propose a regularized learning method that controls the effect of the trainable components and preserves the semantics of the physics-based latent variables as intended. We not only demonstrate generative performance improvements over a set of synthetic and real-world datasets, but we also show that we learn robust models that can consistently extrapolate beyond the training distribution in a meaningful manner. Moreover, we show that we can control the generative process in an interpretable manner.

Naoya Takeishi, Keisuke Fujii, Koh Takeuchi et al.

Extracting coherent patterns is one of the standard approaches towards understanding spatio-temporal data. Dynamic mode decomposition (DMD) is a powerful tool for extracting coherent patterns, but the original DMD and most of its variants do not consider label information, which is often available as side information of spatio-temporal data. In this work, we propose a new method for extracting distinctive coherent patterns from labeled spatio-temporal data collections, such that they contribute to major differences in a labeled set of dynamics. We achieve such pattern extraction by incorporating discriminant analysis into DMD. To this end, we define a kernel function on subspaces spanned by sets of dynamic modes and develop an objective to take both reconstruction goodness as DMD and class-separation goodness as discriminant analysis into account. We illustrate our method using a synthetic dataset and several real-world datasets. The proposed method can be a useful tool for exploratory data analysis for understanding spatio-temporal data.

Keisuke Fujii, Naoya Takeishi, Yoshinobu Kawahara et al.

Extracting the rules of real-world multi-agent behaviors is a current challenge in various scientific and engineering fields. Biological agents independently have limited observation and mechanical constraints; however, most of the conventional data-driven models ignore such assumptions, resulting in lack of biological plausibility and model interpretability for behavioral analyses. Here we propose sequential generative models with partial observation and mechanical constraints in a decentralized manner, which can model agents' cognition and body dynamics, and predict biologically plausible behaviors. We formulate this as a decentralized multi-agent imitation-learning problem, leveraging binary partial observation and decentralized policy models based on hierarchical variational recurrent neural networks with physical and biomechanical penalties. Using real-world basketball and soccer datasets, we show the effectiveness of our method in terms of the constraint violations, long-term trajectory prediction, and partial observation. Our approach can be used as a multi-agent simulator to generate realistic trajectories using real-world data.

Naoya Takeishi, Yoshinobu Kawahara

Invariance and stability are essential notions in dynamical systems study, and thus it is of great interest to learn a dynamics model with a stable invariant set. However, existing methods can only handle the stability of an equilibrium. In this paper, we propose a method to ensure that a dynamics model has a stable invariant set of general classes such as limit cycles and line attractors. We start with the approach by Manek and Kolter (2019), where they use a learnable Lyapunov function to make a model stable with regard to an equilibrium. We generalize it for general sets by introducing projection onto them. To resolve the difficulty of specifying a to-be stable invariant set analytically, we propose defining such a set as a primitive shape (e.g., sphere) in a latent space and learning the transformation between the original and latent spaces. It enables us to compute the projection easily, and at the same time, we can maintain the model's flexibility using various invertible neural networks for the transformation. We present experimental results that show the validity of the proposed method and the usefulness for long-term prediction.

Naoya Takeishi, Yoshinobu Kawahara

In anomaly detection, the degree of irregularity is often summarized as a real-valued anomaly score. We address the problem of attributing such anomaly scores to input features for interpreting the results of anomaly detection. We particularly investigate the use of the Shapley value for attributing anomaly scores of semi-supervised detection methods. We propose a characteristic function specifically designed for attributing anomaly scores. The idea is to approximate the absence of some features by locally minimizing the anomaly score with regard to the to-be-absent features. We examine the applicability of the proposed characteristic function and other general approaches for interpreting anomaly scores on multiple datasets and multiple anomaly detection methods. The results indicate the potential utility of the attribution methods including the proposed one.

Naoya Takeishi

We present a method to compute the Shapley values of reconstruction errors of principal component analysis (PCA), which is particularly useful in explaining the results of anomaly detection based on PCA. Because features are usually correlated when PCA-based anomaly detection is applied, care must be taken in computing a value function for the Shapley values. We utilize the probabilistic view of PCA, particularly its conditional distribution, to exactly compute a value function for the Shapely values. We also present numerical examples, which imply that the Shapley values are advantageous for explaining detected anomalies than raw reconstruction errors of each feature.

Keisuke Fujii, Naoya Takeishi, Motokazu Hojo et al.

Understanding biological network dynamics is a fundamental issue in various scientific and engineering fields. Network theory is capable of revealing the relationship between elements and their propagation; however, for complex collective motions, the network properties often transiently and complexly change. A fundamental question addressed here pertains to the classification of collective motion network based on physically-interpretable dynamical properties. Here we apply a data-driven spectral analysis called graph dynamic mode decomposition, which obtains the dynamical properties for collective motion classification. Using a ballgame as an example, we classified the strategic collective motions in different global behaviours and discovered that, in addition to the physical properties, the contextual node information was critical for classification. Furthermore, we discovered the label-specific stronger spectra in the relationship among the nearest agents, providing physical and semantic interpretations. Our approach contributes to the understanding of principles of biological complex network dynamics from the perspective of nonlinear dynamical systems.

Naoya Takeishi, Yoshinobu Kawahara

Prior domain knowledge can greatly help to learn generative models. However, it is often too costly to hard-code prior knowledge as a specific model architecture, so we often have to use general-purpose models. In this paper, we propose a method to incorporate prior knowledge of feature relations into the learning of general-purpose generative models. To this end, we formulate a regularizer that makes the marginals of a generative model to follow prescribed relative dependence of features. It can be incorporated into off-the-shelf learning methods of many generative models, including variational autoencoders and generative adversarial networks, as its gradients can be computed using standard backpropagation techniques. We show the effectiveness of the proposed method with experiments on multiple types of datasets and generative models.

Naoya Takeishi, Kosuke Akimoto

Exploiting the appropriate inductive bias based on the knowledge of data is essential for achieving good performance in statistical machine learning. In practice, however, the domain knowledge of interest often provides information on the relationship of data attributes only distantly, which hinders direct utilization of such domain knowledge in popular regularization methods. In this paper, we propose the knowledge-based distant regularization framework, in which we utilize the distant information encoded in a knowledge graph for regularization of probabilistic model estimation. In particular, we propose to impose prior distributions on model parameters specified by knowledge graph embeddings. As an instance of the proposed framework, we present the factor analysis model with the knowledge-based distant regularization. We show the results of preliminary experiments on the improvement of the generalization capability of such model.

Rem Hida, Naoya Takeishi, Takehisa Yairi et al.

For extracting meaningful topics from texts, their structures should be considered properly. In this paper, we aim to analyze structured time-series documents such as a collection of news articles and a series of scientific papers, wherein topics evolve along time depending on multiple topics in the past and are also related to each other at each time. To this end, we propose a dynamic and static topic model, which simultaneously considers the dynamic structures of the temporal topic evolution and the static structures of the topic hierarchy at each time. We show the results of experiments on collections of scientific papers, in which the proposed method outperformed conventional models. Moreover, we show an example of extracted topic structures, which we found helpful for analyzing research activities.

Chun Fui Liew, Danielle DeLatte, Naoya Takeishi et al.

In recent years, research and development in aerial robotics (i.e., unmanned aerial vehicles, UAVs) has been growing at an unprecedented speed, and there is a need to summarize the background, latest developments, and trends of UAV research. Along with a general overview on the definition, types, categories, and topics of UAV, this work describes a systematic way to identify 1,318 high-quality UAV papers from more than thirty thousand that have been appeared in the top journals and conferences. On top of that, we provide a bird's-eye view of UAV research since 2001 by summarizing various statistical information, such as the year, type, and topic distribution of the UAV papers. We make our survey list public and believe that the list can not only help researchers identify, study, and compare their work, but is also useful for understanding research trends in the field. From our survey results, we find there are many types of UAV, and to the best of our knowledge, no literature has attempted to summarize all types in one place. With our survey list, we explain the types within our survey and outline the recent progress of each. We believe this summary can enhance readers' understanding on the UAVs and inspire researchers to propose new methods and new applications.

Naoya Takeishi, Yoshinobu Kawahara, Takehisa Yairi

Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often need to prepare nonlinear observables manually according to the underlying dynamics, which is not always possible since we may not have any a priori knowledge about them. In this paper, we propose a fully data-driven method for Koopman spectral analysis based on the principle of learning Koopman invariant subspaces from observed data. To this end, we propose minimization of the residual sum of squares of linear least-squares regression to estimate a set of functions that transforms data into a form in which the linear regression fits well. We introduce an implementation with neural networks and evaluate performance empirically using nonlinear dynamical systems and applications.