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Collecting time series data spatially distributed in many locations is often important for analyzing climate change and its impacts on ecosystems. However, comprehensive spatial data collection is not always feasible, requiring us to predict climate variables at some locations. This study focuses on a prediction of climatic elements, specifically near-surface temperature and pressure, at a target location apart from a data observation point. Our approach uses two prediction methods: reservoir computing (RC), known as a machine learning framework with low computational requirements, and vector autoregression models (VAR), recognized as a statistical method for analyzing time series data. Our results show that the accuracy of the predictions degrades with the distance between the observation and target locations. We quantitatively estimate the distance in which effective predictions are possible. We also find that in the context of climate data, a geographical distance is associated with data correlation, and a strong data correlation significantly improves the prediction accuracy with RC. In particular, RC outperforms VAR in predicting highly correlated data within the predictive range. These findings suggest that machine learning-based methods can be used more effectively to predict climatic elements in remote locations by assessing the distance to them from the data observation point in advance. Our study on low-cost and accurate prediction of climate variables has significant value for climate change strategies.

Realizing smooth traffic flow is important for achieving carbon neutrality. Adaptive traffic signal control, which considers traffic conditions, has thus attracted attention. However, it is difficult to ensure optimal vehicle flow throughout a large city using existing control methods because of their heavy computational load. Here, we propose a control method called AMPIC (Adaptive Model Predictive Ising Controller) that guarantees both scalability and optimality. The proposed method employs model predictive control to solve an optimal control problem at each control interval with explicit consideration of a predictive model of vehicle flow. This optimal control problem is transformed into a combinatorial optimization problem with binary variables that is equivalent to the so-called Ising problem. This transformation allows us to use an Ising solver, which has been widely studied and is expected to have fast and efficient optimization performance. We performed numerical experiments using a microscopic traffic simulator for a realistic city road network. The results show that AMPIC enables faster vehicle cruising speed with less waiting time than that achieved by classical control methods, resulting in lower CO2 emissions. The model predictive approach with a long prediction horizon thus effectively improves control performance. Systematic parametric studies on model cities indicate that the proposed method realizes smoother traffic flows for large city road networks. Among Ising solvers, D-Wave's quantum annealing is shown to find near-optimal solutions at a reasonable computational cost., Comment: 18 pages, 8 figures

This study introduces an uncertainty-aware, mesh-free numerical method for solving Kolmogorov PDEs. In the proposed method, we use Gaussian process regression (GPR) to smoothly interpolate pointwise solutions that are obtained by Monte Carlo methods based on the Feynman-Kac formula. The proposed method has two main advantages: 1. uncertainty assessment, which is facilitated by the probabilistic nature of GPR, and 2. mesh-free computation, which allows efficient handling of high-dimensional PDEs. The quality of the solution is improved by adjusting the kernel function and incorporating noise information from the Monte Carlo samples into the GPR noise model. The performance of the method is rigorously analyzed based on a theoretical lower bound on the posterior variance, which serves as a measure of the error between the numerical and true solutions. Extensive tests on three representative PDEs demonstrate the high accuracy and robustness of the method compared to existing methods., Comment: 17 pages, 3 figures

We find the position-momentum decomposition of the quantum operators of the classic Meixner random variables. The position-momentum decomposition involves translation operators, which are used to give a new characterization of the Meixner random variables., Comment: 25 pages

The convergence properties of the upwind difference scheme for the Hamilton-Jacobi-Bellman (HJB) equation, which is a fundamental equation for optimal control theory, are investigated. We first perform a convergence analysis for the solution of the scheme, which eliminates ambiguities in the proofs of existing studies. We then prove the convergence of the spatial difference of the solution in the scheme by the correspondence between the HJB equations and the conservation laws. This result leads to a property of the objective function called epi-convergence, by which the convergence property of the input function is shown. The latter two results have not been addressed in existing studies. Numerical calculations support the obtained results., Comment: 21 pages, 8 figures

The use of quantum annealers in black-box optimization to obtain the desired properties of a product with a small number of trials has attracted attention. However, the application of this technique to engineering design problems is still limited. Here, we demonstrate the applicability of black-box optimization with a quantum annealer to the design of electric circuit systems, focusing on $\pi$-type noise filters as an example. We develop a framework that uses quantum annealing to find the optimal location of electrical components and conductor paths connecting the components, and confirm that the learning process appropriately works over a number of trials to efficiently search for a design with high performance. The results show the potential applicability of quantum annealing to design problems of electric circuit systems., Comment: 6 pages, 11 figures

We consider a Schelling-like segregation model, in which the behavior of individual agents is determined by a mixed individual and global utility. With a high ratio of global utility being incorporated, the agents are cooperative in order to realize a homogenized state, otherwise the agents are less cooperative, leading to an undesired Nash equilibrium with low utility. In the present study, we introduce a dynamically varying cooperation degree parameter to prevent the agents from falling into such a low-utility equilibrium state. More precisely, a large cooperation degree is assigned when the agents are in high-utility regions, whereas agents having low utility behave more individually. Simulation results show that homogenized phases with globally high utility are achieved with the present dynamical control, even for the case of a low mean value of cooperation degree. Since the cooperation degree represents the magnitude with which Pigouvian tax is enforced in the model of residential movement within a city, this result suggests the possibility of tax intervention to circumvent the undesired segregation of residents., Comment: 11 pages, 11 figures

Super-resolving the coarse outputs of global climate simulations, termed downscaling, is crucial in making political and social decisions on systems requiring long-term climate change projections. Existing fast super-resolution techniques, however, have yet to preserve the spatially correlated nature of climatological data, which is particularly important when we address systems with spatial expanse, such as the development of transportation infrastructure. Herein, we show an adversarial network-based machine learning enables us to correctly reconstruct the inter-regional spatial correlations in downscaling with high magnification of up to fifty while maintaining pixel-wise statistical consistency. Direct comparison with the measured meteorological data of temperature and precipitation distributions reveals that integrating climatologically important physical information improves the downscaling performance, which prompts us to call this approach $\pi$SRGAN (Physics Informed Super-Resolution Generative Adversarial Network). The proposed method has a potential application to the inter-regionally consistent assessment of the climate change impact. Additionally, we present the outcomes of another variant of the deep generative model-based downscaling approach in which the low-resolution precipitation field is substituted with the pressure field, referred to as $\psi$SRGAN (Precipitation Source Inaccessible SRGAN). Remarkably, this method demonstrates unexpectedly good downscaling performance for the precipitation field., Comment: 13+8 pages, 4+4 figures

In the framework of continued fraction expansions of Stieltjes transforms, we consider shifting of semicircular laws. The continuous part of the associated measure admits a density function which is the quotient of semicircular one by a polynomial. We study how this polynomial denominator determines shifted semicircular laws, with explicit descriptions in examples of shifting up to the level of step two., Comment: 32 pages

An iterative finite difference scheme for mean field games (MFGs) is proposed. The target MFGs are derived from control problems for multidimensional systems with advection terms. For such MFGs, linearization using the Cole-Hopf transformation and iterative computation using fictitious play are introduced. This leads to an implementation-friendly algorithm that iteratively solves explicit schemes. The convergence properties of the proposed scheme are mathematically proved by tracking the error of the variable through iterations. Numerical calculations show that the proposed method works stably for both one- and two-dimensional control problems., Comment: Manuscript accepted for publication in ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)

Automatic machine learning, or AutoML, holds the promise of truly democratizing the use of machine learning (ML), by substantially automating the work of data scientists. However, the huge combinatorial search space of candidate pipelines means that current AutoML techniques, generate sub-optimal pipelines, or none at all, especially on large, complex datasets. In this work we propose an AutoML technique SapientML, that can learn from a corpus of existing datasets and their human-written pipelines, and efficiently generate a high-quality pipeline for a predictive task on a new dataset. To combat the search space explosion of AutoML, SapientML employs a novel divide-and-conquer strategy realized as a three-stage program synthesis approach, that reasons on successively smaller search spaces. The first stage uses a machine-learned model to predict a set of plausible ML components to constitute a pipeline. In the second stage, this is then refined into a small pool of viable concrete pipelines using syntactic constraints derived from the corpus and the machine-learned model. Dynamically evaluating these few pipelines, in the third stage, provides the best solution. We instantiate SapientML as part of a fully automated tool-chain that creates a cleaned, labeled learning corpus by mining Kaggle, learns from it, and uses the learned models to then synthesize pipelines for new predictive tasks. We have created a training corpus of 1094 pipelines spanning 170 datasets, and evaluated SapientML on a set of 41 benchmark datasets, including 10 new, large, real-world datasets from Kaggle, and against 3 state-of-the-art AutoML tools and 2 baselines. Our evaluation shows that SapientML produces the best or comparable accuracy on 27 of the benchmarks while the second best tool fails to even produce a pipeline on 9 of the instances., Comment: Accepted to the Technical Track of ICSE 2022

This work is motivated by the pervasive use of method invocations in object-oriented (OO) programs, and indeed their prevalence in patches of OO-program bugs. We propose a generate-and-validate repair technique, called ELIXIR designed to be able to generate such patches. ELIXIR aggressively uses method calls, on par with local variables, fields, or constants, to construct more expressive repair-expressions, that go into synthesizing patches. The ensuing enlargement of the repair space, on account of the wider use of method calls, is effectively tackled by using a machine-learnt model to rank concrete repairs. The machine-learnt model relies on four features derived from the program context, i.e., the code surrounding the potential repair location, and the bug report. We implement ELIXIR and evaluate it on two datasets, the popular Defects4J dataset and a new dataset Bugs.jar created by us, and against 2 baseline versions of our technique, and 5 other techniques representing the state of the art in program repair. Our evaluation shows that ELIXIR is able to increase the number of correctly repaired bugs in Defects4J by 85% (from 14 to 26) and by 57% in Bugs.jar (from 14 to 22), while also significantly out-performing other state-of-the-art repair techniques including ACS, HD-Repair, NOPOL, PAR, and jGenProg.

The rectification of electro-osmotic flows is important in micro/nano fluidics applications such as micro-pumps and energy conversion devices. Here, we propose a simple electro-osmotic diode in which colloidal particles are contained between two parallel membranes with different pore densities. While the flow in the forward direction just pushes the colloidal particles toward the high-pore-density membrane, the backward flow is blocked by the particles near the low-pore-density membrane, which clog the pores. Nonequilibrium molecular dynamics simulations show a strong nonlinear dependence on the electric field for both the electric current and electro-osmotic flow, indicating diode characteristics. A mathematical model to reproduce the electro-osmotic diode behavior is constructed, introducing an effective pore diameter as a model for pores clogged by the colloidal particles. Good agreement is obtained between the proposed model with estimated parameter values and the results of direct molecular dynamics simulations. The proposed electro-osmotic diode has potential application in downsized microfluidic pumps, e.g., the pump induced under AC electric fields., Comment: Accepted for publication in Physical Review Research

Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of multiscale dynamics, we propose a reservoir computing (RC) model with diverse timescales by using a recurrent network of heterogeneous leaky integrator (LI) neurons. We evaluate computational performance of the proposed model in two time series prediction tasks related to four chaotic fast-slow dynamical systems. In a one-step-ahead prediction task where input data are provided only from the fast subsystem, we show that the proposed model yields better performance than the standard RC model with identical LI neurons. Our analysis reveals that the timescale required for producing each component of target multiscale dynamics is appropriately and flexibly selected from the reservoir dynamics by model training. In a long-term prediction task, we demonstrate that a closed-loop version of the proposed model can achieve longer-term predictions compared to the counterpart with identical LI neurons depending on the hyperparameter setting., Comment: 7 pages, 6 figures, supplemental material (10 pages)

Swarm robot systems, which consist of many cooperating mobile robots, have attracted attention for their environmental adaptability and fault tolerance advantages. One of the most important tasks for such systems is coverage control, in which robots autonomously deploy to approximate a given spatial distribution. In this study, we formulate a coverage control paradigm using the concept of optimal transport and propose a novel control technique, which we have termed the optimal transport-based coverage control (OTCC) method. The proposed OTCC, derived via the gradient flow of the cost function in the Kantorovich dual problem, is shown to covers a widely used existing control method as a special case. We also perform a Lyapunov stability analysis of the controlled system, and provide numerical calculations to show that the OTCC reproduces target distributions with better performance than the existing control method., Comment: This paper has been accepted for IEEE Control Systems Letters

When controlling multi-agent systems, the trade-off between performance and scalability is a major challenge. Here, we address this difficulty by using mean field games (MFGs), which is a framework that deduces the macroscopic dynamics describing the density profile of agents from their microscopic dynamics. To effectively use the MFG, we propose a model predictive MFG (MP-MFG), which estimates the agent population density profile with using kernel density estimation and manages the input generation with model predictive control. The proposed MP-MFG generates control inputs by monitoring the agent population at each time step, and thus achieves higher robustness than the conventional MFG. Numerical results show that the MP-MFG outperforms the MFG when the agent model has modeling errors or the number of agents in the system is small., Comment: This paper has been accepted for 2021 IEEE International Conference on Systems, Man, and Cybernetics (IEEE SMC2021)

The spread of intelligent transportation systems in urban cities has caused heavy computational loads, requiring a novel architecture for managing large-scale traffic. In this study, we develop a method for globally controlling traffic signals arranged on a square lattice by means of a quantum annealing machine, namely the D-Wave quantum annealer. We first formulate a signal optimization problem that minimizes the imbalance of traffic flows in two orthogonal directions. Then we reformulate this problem as an Ising Hamiltonian, which is fully compatible with quantum annealers. The new control method is compared with a conventional local control method for a large 50-by-50 city, and the results exhibit the superiority of our global control method in suppressing traffic imbalance over wide parameter ranges. Furthermore, the solutions to the global control method obtained with the quantum annealing machine are better than those obtained with conventional simulated annealing. In addition, we prove analytically that the local and the global control methods converge at the limit where cars have equal probabilities for turning and going straight. These results are verified with numerical experiments., Comment: This is a pre-print of an article published in Scientific Reports. The final authenticated version is available online at: https://doi.org/10.1038/s41598-021-82740-0

Designing efficient traffic lanes for pedestrians is a critical aspect of urban planning as walking remains the most common form of mobility among the increasingly diverse methods of transportation. Herein, we investigate pedestrian counter flows in a straight corridor, in which two groups of people are walking in opposite directions. We demonstrate, using a molecular dynamics approach applying the social force model, that a simple array of obstacles improves flow rates by producing flow separations even in crowded situations. We also report on a developed model describing the separation behavior that regards an array of obstacles as a membrane and induces spontaneous separation of pedestrians groups. When appropriately designed, those obstacles are fully capable of controlling the filtering direction so that pedestrians tend to keep moving to their left (or right) spontaneously. These results have the potential to provide useful guidelines for industrial designs aimed at improving ubiquitous human mobility., Comment: Manuscript accepted for publication in Europhysics Letters

The D-Wave quantum annealer has emerged as a novel computational architecture that is attracting significant interest, but there have been only a few practical algorithms exploiting the power of quantum annealers. Here we present a model predictive control (MPC) algorithm using a quantum annealer for a system allowing a finite number of input values. Such an MPC problem is classified as a non-deterministic polynomial-time-hard combinatorial problem, and thus real-time sequential optimization is difficult to obtain with conventional computational systems. We circumvent this difficulty by converting the original MPC problem into a quadratic unconstrained binary optimization problem, which is then solved by the D-Wave quantum annealer. Two practical applications, namely stabilization of a spring-mass-damper system and dynamic audio quantization, are demonstrated. For both, the D-Wave method exhibits better performance than the classical simulated annealing method. Our results suggest new applications of quantum annealers in the direction of dynamic control problems., Comment: 11 pages, 4 figures, manuscript accepted in Scientific Reports

Electro- and diffusio- phoresis of particles correspond respectively to the transport of particles under electric field and solute concentration gradients. Such interfacial transport phenomena take their origin in a diffuse layer close to the particle surface, and the motion of the particle is force-free. In the case of electrophoresis, it is further expected that the stress acting on the moving particle vanishes locally as a consequence of local electroneutrality. But the argument does not apply to diffusiophoresis, which takes its origin in solute concentration gradients. In this paper we investigate further the local and global force balance on a particle undergoing diffusiophoresis. We calculate the local tension applied on the particle surface and show that, counter-intuitively, the local force on the particle does not vanish for diffusiophoresis, in spite of the global force being zero as expected. Incidentally, our description allows to clarify the osmotic balance in diffusiophoresis, which has been a source of debates in the recent years. We explore various cases, including hard and soft interactions, as well as porous particles, and provide analytic predictions for the local force balance in these various systems. The existence of local stresses may induce deformation of soft particles undergoing diffusiophoresis, hence suggesting applications in terms of particle separation based on capillary diffusiophoresis.

We present a numerical scheme for simulating the dynamics of Brownian particles suspended in a fluid. The motion of the particles is tracked by the Langevin equation, whereas the host fluid flow is analyzed by using the lattice Boltzmann method. The friction force between a particle and the fluid is evaluated correctly based on the velocity difference at the position of the particle. The coupling method accurately reproduces the long-time tail observed in the velocity auto-correlation function. We also show that the fluctuation-dissipation relation holds between the relaxation of a single particle and the velocity autocorrelation function of fluctuating particles., Comment: 5 pages, 3 figures

We report a numerical study of the diffusiophoresis of short polymers using non-equilibrium molecular dynamics simulations. More precisely, we consider polymer chains in a fluid containing a solute which has a concentration gradient, and examine the variation of the induced diffusiophoretic velocity of the polymer chains as the interaction between the monomer and the solute is varied. We find that there is a non-monotonic relation between the diffusiophoretic mobility and the strength of the monomer-solute interaction. In addition we find a weak dependence of the mobility on the length of the polymer chain, which shows clear difference from the diffusiophoresis of a solid particle. Interestingly, the hydrodynamic flow through the polymer is much less screened than for pressure driven flows.

We introduce the free analogue of the classical beta prime distribution by the multiplicative free convolution of the free Poisson and the reciprocal of free Poisson distributions, and related free analogues of the classical $F$, $T$, and beta distributions. We show the rationales of our free analogues via the score functions and the potentials. We calculate the moments of the free beta prime distribution explicitly in combinatorial by using non-crossing linked partitions, and demonstrate that the free beta prime distribution belongs to the class of the free negative binomials in the free Meixner family., Comment: 36 pages

In this paper, we explore osmotic transport by means of molecular dynamics (MD) simulations. We first consider osmosis through a membrane, and investigate the reflection coefficient of an imperfectly semi-permeable membrane, in the dilute and high concentration regimes. We then explore the diffusion-osmotic flow of a solute-solvent fluid adjacent to a solid surface, driven by a chemical potential gradient parallel to the surface. We propose a novel non-equilibrium MD (NEMD) methodology to simulate diffusion-osmosis, by imposing an external force on every particle, which properly mimics the chemical potential gradient on the solute in spite of the periodic boundary conditions. This NEMD method is validated theoretically on the basis of linear-response theory by matching the mobility with their Green-Kubo expressions. Finally, we apply the framework to more realistic systems, namely a water-ethanol mixture in contact with a silica or a graphene surface., Comment: Accepted for publication in the Journal of Chemical Physics

In this paper, we explore various forms of osmotic transport in the regime of high solute concentration. We consider both the osmosis across membranes and diffusio-osmosis at solid interfaces, driven by solute concentration gradients. We follow a mechanical point of view of osmotic transport, which allows us to gain much insight into the local mechanical balance underlying osmosis. We demonstrate in particular how the general expression of the osmotic pressure for mixtures, as obtained classically from the thermodynamic framework, emerges from the mechanical balance controlling non-equilibrium transport under solute gradients. Expressions for the rejection coefficient of osmosis and the diffusio-osmotic mobilities are accordingly obtained. These results generalize existing ones in the dilute solute regime to mixtures with arbitrary concentrations., Comment: Accepted for publication in the Journal of Chemical Physics

We demonstrate, on the basis of molecular dynamics simulations, the possibility of an efficient water-ethanol separation using nanoporous carbon membranes, namely carbon nanotube membranes, nanoporous graphene sheets, and multilayer graphene membranes. While these carbon membranes are in general permeable to both pure liquids, they exhibit a counter-intuitive "self-semi-permeability" to water in the presence of water-ethanol mixtures. This originates in a preferred ethanol adsorption in nanoconfinement that prevents water molecules from entering the carbon nanopores. An osmotic pressure is accordingly expressed across the carbon membranes for the water-ethanol mixture, which agrees with the classic van't Hoff type expression. This suggests a robust and versatile membrane-based separation, built on a pressure-driven reverse-osmosis process across these carbon-based membranes. In particular, the recent development of large-scale 'graphene-oxide' like membranes then opens an avenue for a versatile and efficient ethanol dehydration using this separation process, with possible application for bio-ethanol fabrication., Comment: Accepted for publication in the Journal of Chemical Physics

In this paper we investigate the hydrodynamic permeance of water through graphene-based membranes, inspired by recent experimental findings on graphene-oxide membranes. We consider the flow across multiple graphene layers having nanoslits in a staggered alignment, with an inter-layer distance ranging from sub- nanometer to a few nanometers. We compare results for the permeability obtained by means of molecular dynamics simulations to continuum predictions obtained by using the lattice Boltzmann calculations and hydrodynamic modelization. This highlights that, in spite of extreme confinement, the permeability across the graphene-based membrane is quantitatively predicted on the basis of a continuum expression, taking properly into account entrance and slippage effects of the confined water flow. Our predictions refute the breakdown of hydrodynamics at small scales in these membrane systems. They constitute a benchmark to which we compare published experimental data., Comment: Published in the Journal of Chemical Physics

The electro-osmotic flow through a channel between two undulated surfaces induced by an external electric field is investigated. The gap of the channel is very small and comparable to the thickness of the electrical double layers. A lattice Boltzmann simulation is carried out on the model consisting of the Poisson equation for electrical potential, the Nernst--Planck equation for ion concentration, and the Navier--Stokes {\color{black}equations} for flows of the electrolyte solution. An analytical model that predicts the flow rate is also derived under the assumption that the channel width is very small compared with the characteristic length of the variation along the channel. The analytical results are compared with the numerical results obtained by using the lattice Boltzmann method. In the case of a constant surface charge density along the channel, the variation of the channel width reduces the electro-osmotic flow, and the flow rate is smaller than that of a straight channel. In the case of a surface charge density distributed in homogeneously, one-way flow occurs even under the restriction of a zero net surface charge along the channel., Comment: 10 pages, 7 figures