State Vector Research Articles

Ensemble Based Estimation of Wet Refractivity Indices Using a Functional Model Approach

AbstractThe estimation of the wet refractivity indices is crucial for applications like weather predictions or improving the accuracy of real‐time positioning techniques. Traditionally, solving the inverse tomography problem to estimate these atmospheric parameters has been challenging due to its ill‐posed nature and high computational demands, necessitating additional constraints. To overcome these challenges, the data assimilation method is proposed here to integrate Global Navigation Satellite System (GNSS) observations into a background model. In this study, the Ensemble Kalman Filter (EnKF) was served as the assimilation core to reduce the computational load and to enable the epoch‐wise estimation of wet refractivity indices. The Global Pressure and Temperature 3 (GPT3w) model was utilized as the background, and wet refractivity indices at each epoch were transformed into B‐spline coefficients, representing state vector parameters. Subsequently, GNSS derived zenith wet delay (ZWD) values were integrated into the model using the EnKF method. The study's region encompassed the western parts of Europe and incorporated approximately 893 GNSS stations. Evaluation spanned from 1 January 2017 to 31 December 2017. The estimated wet refractivity indices from the proposed method were compared with observations from 16 existing radiosonde stations, radio occultation data, and ZWD values from the 47 selected GNSS test stations. Additionally, calculated ZWD values, resulting from the integration of wet refractivity indices, were compared to the ZWD values from 47 test stations in the study region. The numerical results demonstrated that the proposed method achieved a root mean square error value of approximately 2.6 ppm, which was nearly 49% and 18% lower than that of the considered empirical and numerical atmospheric models, respectively.

Do LSTM memory states reflect the relationships in reduced-complexity sandy shoreline models

Equilibrium-based models are a transparent method of modelling shoreline change, though often too simplistic to capture complex dynamics. Conversely, deep learning methodologies offer greater predictive power at the expense of transparency. In this research we scrutinize the internal workings of an LSTM shoreline model. A regression-based probe is used to show that cell state vectors, responsible for past-to-future information flow, autonomously generate equilibrium-like information akin to the physics-based equilibrium term of the ShoreFor model, Ωeq. The variation in probe skill throughout training is tracked to show that at 5 of 6 transects, the LSTM was able to meaningfully acquire equilibrium information (ΣΔR2 = 0.3–0.6). The results of this work offer evidence that an LSTM may model shoreline change with internal methods that are consistent with the current understanding of coastal shoreline dynamics. These physically meaningful representations emphasize the importance of co-evolution between machine learning and physics-based approaches moving forward.

Semi-supervised prediction method for time series based on Monte Carlo and time fusion feature attention

Accurate and reliable forecasting of time sequences is a challenging task in cyber–physical systems (CPS). Traditional time series prediction models struggle to provide accurate predictions for diverse types of time series data, especially with missing data due to variations in scale, types, and the complexity of real-world production environments. In this paper, we introduce a hybrid model named Temporal Feature Fusion Attention-based Monte Carlo Semi-supervised Long Short Term Memory (LSTM) network to address this issue. The model encodes the current state and historical information using a current time feature state vector. It then calculates the hidden feature vectors for the time series at different time points (past, present, and future), as well as for the current Monte Carlo filtering sequences. This approach leverages the correlation of time series features, transfers and fuses crucial historical features within the sequence with the optimized sequence feature information from the Monte Carlo algorithm. Our experiments confirm that with 10% of labeled data missing, our proposed method significantly improves the evaluation metric Mean Absolute Percentage Error (MAPE) by 17.827% compared to the baseline LSTM model. Moreover, our method surpasses other state-of-the-art methods across four distinct time series datasets, achieving the best prediction results.

Simulating photonic devices with noisy optical elements

Quantum computers are inherently affected by noise. While in the long term, error correction codes will account for noise at the cost of increasing physical qubits, in the near term, the performance of any quantum algorithm should be tested and simulated in the presence of noise. As noise acts on the hardware, the classical simulation of a quantum algorithm should not be agnostic on the platform used for the computation. In this paper, we apply the recently proposed noisy gates approach to efficiently simulate noisy optical circuits described in the dual rail framework. The evolution of the state vector is simulated directly, without requiring the mapping to the density matrix framework. Notably, we test the method on both the gate-based and measurement-based quantum computing models, showing that the approach is very versatile. We also evaluate the performance of a photonic variational quantum algorithm to solve the MAX-2-CUT problem. In particular we design and simulate an ansatz, which is resilient to photon losses up to p∼10−3 making it relevant for near-term applications. Published by the American Physical Society 2024

A reinforcement learning approach to solving very-short term train rescheduling problem for a single-track rail corridor

Railway operations are regularly affected by incidents such as disturbances and disruptions, which cause temporary operational restrictions to the trains in the network. Compared to real-time disturbances and disruptions, sometimes these incidents can be known at a short notice, e.g., 24–48 h beforehand, which is known as the Very-Short-Term-Planning in British rail operations. This paper presents a novel reinforcement learning based approach for rescheduling train services for in a single-track corridor with bi-directional traffic. As an important subfield of machine learning, reinforcement learning offers an alternate strategy for tackling the NP-hard train (re)scheduling problems and shows its advantages in balancing computational efficiency and solution quality. We propose a Q-learning approach with a tiered rewarding strategy and lightweight train representation in state vectors, which enables more efficient learning and knowledge sharing among homogeneous trains. Compared with an existing reinforcement learning approach, our proposed method can find better quality solutions due to its unique representation of state vectors and a novel tiered rewarding/punishing mechanism, overcoming certain disadvantages in existing approaches. Knowledge reusability is another advantage of the proposed approach, as prior knowledge obtained from training one instance can significantly enhance the performance of another, potentially more challenging, instance on the same corridor with substantially reduced computational time and effort on algorithm development. We also discuss the potential applications of the knowledge reusability feature inherent in reinforcement learning algorithms, which we believe will benefit the entire industry in addressing NP-hard problems through data-driven technologies.

Interval State Estimation of Systems with Metzler Polytopic Models

The paper deals with the design of interval observers for interval-defined strictly Metzler polytopic positive systems. The stability conditions for the proposed structure of the interval observer are formulated using linear matrix inequalities to ensure a positive estimate of the system state. The proposed method makes it possible to calculate time-varying lower and upper estimates of the state vector, assuming that the disturbance is bounded. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

Reachable set control of singular semi-Markov jump multi-agent systems with input delay via state decomposition method

This paper addresses the challenge of reachable set estimation in singular multi-agent systems with time-delay and semi-Markov switching topologies. The primary goal is to construct an ellipsoid that encompasses all states originating from the origin. Furthermore, criteria for reachable sets with reduced conservatism are developed. The singular multi-agent systems are reduced by the Laplace matrix, then the Lyapunov–Krasovskii functional is constructed by using decomposed state vector. In addition, the sufficient conditions for the reachable set of singular multi-agent systems bounded by ellipsoids are given by matrix theory and linear matrix inequality. Numerical examples show that our results is effective.

Efficient Quantum Circuit Simulation by Tensor Network Methods on Modern GPUs

Efficient simulation of quantum circuits has become indispensable with the rapid development of quantum hardware. The primary simulation methods are based on state vectors and tensor networks. As the number of qubits and quantum gates grows larger in current quantum devices, traditional state-vector based quantum circuit simulation methods prove inadequate due to the overwhelming size of the Hilbert space and extensive entanglement. Consequently, brutal force tensor network simulation algorithms become the only viable solution in such scenarios. The two main challenges faced in tensor network simulation algorithms are optimal contraction path finding and efficient execution on modern computing devices, with the latter determines the actual efficiency. In this study, we investigate the optimization of such tensor network simulations on modern GPUs and propose general optimization strategies from two aspects: computational efficiency and accuracy. Firstly, we propose to transform critical Einstein summation operations into GEMM operations, leveraging the specific features of tensor network simulations to amplify the efficiency of GPUs. Secondly, by analyzing the data characteristics of quantum circuits, we employ extended precision to ensure the accuracy of simulation results and mixed precision to fully exploit the potential of GPUs, resulting in faster and more precise simulations. Our numerical experiments demonstrate that our approach can achieve a 3.96x reduction in verification time for random quantum circuit samples in the 18-cycle case of Sycamore, with sustained performance exceeding 21 TFLOPS on one A100. This method can be easily extended to the 20-cycle case, maintaining the same performance, accelerating by 12.5x compared to the state-of-the-art CPU-based results and 4.48-6.78x compared to the state-of-the-art GPU-based results reported in the literature. Furthermore, the strategies presented in this article hold general applicability for accelerating problems that can be tackled by contracting tensor networks such as graphical models and combinatorial optimizations.

A Physics-Informed Auto-Learning Framework for Developing Stochastic Conceptual Models for ENSO Diversity

Abstract Understanding ENSO dynamics has tremendously improved over past decades. The ENSO diversity in spatial pattern, peak intensity, and temporal evolution is however still poorly represented in conceptual ENSO models. In this paper, a physics-informed auto-learning framework is applied to derive ENSO stochastic conceptual models with varying degrees of freedom. The framework is computationally efficient and easy to apply. Once the state vector of the target model is set, causal inference is exploited to build the right-hand side of the equations based on a mathematical function library. Fundamentally different from standard nonlinear regression, the auto-learning framework provides a parsimonious model by retaining only terms that improve the dynamical consistency with observations. It can also identify crucial latent variables and provide physical explanations. This methodology successfully reconstructs the equations of a realistic six-dimensional reference ENSO model based on the recharge oscillator theory from its data. A hierarchy of lower-dimensional models is derived and their representation of ENSO (including its diversity) systematically assessed. The minimum model that represents ENSO diversity is four-dimensional, with three interannual variables describing the western Pacific thermocline depth, the eastern and central Pacific sea surface temperatures (SSTs), and one intraseasonal variable for westerly wind events. Without the intraseasonal variable, the resulting three-dimensional model underestimates extreme events and is too regular. The limited number of weak nonlinearities in the model are essential in reproducing the observed extreme El Niño events and the observed nonlinear relationship between eastern and western Pacific SSTs.

Decimeter-Level Accuracy for Smartphone Real-Time Kinematic Positioning Implementing a Robust Kalman Filter Approach and Inertial Navigation System Infusion in Complex Urban Environments.

New smartphones provide real-time access to GNSS pseudorange, Doppler, or carrier-phase measurement data at 1 Hz. Simultaneously, they can receive corrections broadcast by GNSS reference stations to perform real-time kinematic (RTK) positioning. This study aims at the real-time positioning capabilities of smartphones using raw GNSS measurements as a conventional method and proposes an improvement to the positioning through the integration of Inertial Navigation System (INS) measurements. A U-Blox GNSS receiver, model ZED-F9R, was used as a benchmark for comparison. We propose an enhanced ambiguity resolution algorithm that integrates the traditional LAMBDA method with an adaptive thresholding mechanism based on real-time quality metrics. The RTK/INS fusion method integrates RTK and INS measurements using an extended Kalman filter (EKF), where the state vector x includes the position, velocity, orientation, and their respective biases. The innovation here is the inclusion of a real-time weighting scheme that adjusts the contribution of the RTK and INS measurements based on their current estimated accuracy. Also, we use the tightly coupled (TC) RTK/INS fusion framework. By leveraging INS data, the system can maintain accurate positioning even when the GNSS data are unreliable, allowing for the detection and exclusion of abnormal GNSS measurements. However, in complex urban areas such as Qazvin City in Iran, the fusion method achieved positioning accuracies of approximately 0.380 m and 0.415 m for the Xiaomi Mi 8 and Samsung Galaxy S21 Ultra smartphones, respectively. The subsequent detailed analysis across different urban streets emphasized the significance of choosing the right positioning method based on the environmental conditions. In most cases, RTK positioning outperformed Single-Point Positioning (SPP), offering decimeter-level precision, while the fusion method bridged the gap between the two, showcasing improved stability accuracy. The comparative performance between the Samsung Galaxy S21 Ultra and Xiaomi Mi 8 revealed minor differences, likely attributed to variations in the hardware design and software algorithms. The fusion method emerged as a valuable alternative when the RTK signals were unavailable or impractical. This demonstrates the potential of integrating RTK and INS measurements for enhanced real-time smartphone positioning, particularly in challenging urban environments.

Developed square-root cubature Kalman filter-based solution for improving power system state estimation with unknown inputs and non-Gaussian noise

Understanding the ever-changing dynamics of power systems is crucial, and dynamic state estimation (DSE) plays a vital role in achieving this. However, traditional nonlinear Kalman filters (NKFs) face limitations: lack of access to control inputs and presence of non-Gaussian noise in measurements, impacting their accuracy and robustness. This research introduces a novel robust DSE method that tackles these challenges head-on. For the first time in DSE, it leverages the predictive power of Holt-Winters Triple Exponential Smoothing to model the time-varying behavior of control inputs. This innovative approach allows for the simultaneous estimation of dynamic state variables such as the rotor angle and rotor speed changes, as well as transient voltages and control inputs like mechanical input torque and excitation voltage, even in the presence of non-Gaussian noise. Furthermore, the method employs modified projection statistics and a Cauchy function. This unique combination effectively bounds the influence of observation outliers while maintaining high statistical estimation efficiency. This innovative approach utilizes a square cubature Kalman filter (SCKF) for enhanced numerical stability. Extensive simulations under various anomalous conditions demonstrate the method's superior accuracy and efficiency in estimating the state vector. These results highlight its potential to significantly improve power system estimation and pave the way for real-time applications.

Terahertz Metasurfaces for Polarization Manipulation and Detection: Principles and Emerging Applications

AbstractTerahertz frequencies locating between microwave and infrared regions can record and process optical information for next‐generation information technology such as 6G communication. Metasurfaces, as emerging planar optical components built with micro‐ or nanostructures, enable precise control, and manipulation of electromagnetic waves from near fields to far fields. These subwavelength artificial structures can be engineered to exhibit specific polarization responses, thus holding significant potential for applications in polarization detection. In the terahertz (THz) region, polarization information is crucial for identifying and analyzing the properties of materials in the terahertz. In this review, we focus on recent advances in terahertz metasurfaces for polarization manipulation and detection, including principles and emerging applications. New polarization detection methods such as polarization state conversion, polarization‐selective absorption, polarization‐selective focusing, and vector beam construction are discussed. Finally, it is concluded with a few perspectives on emerging trends and existing challenges in the fields of terahertz polarization manipulation and detection.

Geometric optimal filtering for an articulated n‐trailer vehicle with unknown parameters

AbstractIn this article, we consider the equations of motion for an articulated ‐trailer vehicle with different masses and inertias in the presence of force and torque commands. We design a second‐order optimal filter to estimate the pose of the first vehicle and of the trailers exploiting the Lie group structure and the nonholonomic and hooking constraints. We consider the filtering problem from three different perspectives: in the first masses and inertias are time‐varying and perfectively known, in the second they are known only in the first part of the maneuver, but they are not updated over time. In the last case masses and inertias are considered within the state vector and therefore estimated by the filter. Depending on the needs in real‐life applications (e.g., whether the masses and inertias remain fixed or change during the maneuver and are unknown), the best‐performing filter can be used. The sensing system consists of a GPS‐like configuration (global positioning system) obtained by using an antenna attached to the leading car.

New disturbance observer-based speed estimator for induction motor

<p>This paper discusses a novel disturbance observer designed as an estimator to determine the rotor speed of an induction motor. This observer is a solution to obtain a simple structure with a small number of compact observer gains. Furthermore, the adaptation law is no longer required to estimate induction motor speed values. This is a machine model-based computation method that uses a stationary reference frame. The nonlinearity problem is solved using an additional state vector in the observer model, which is known as an extended state observer. This approach easily and systematically determines the observer gain by applying the linear quadratic regulator (LQR) method, thereby avoiding time-consuming trial errors. The proposed observer, which was presented in both continuous and discrete forms, was tested using a sensorless V/f- controlled induction motor. The simulation results show that the proposed observer can accurately estimate all states, namely, the rotor flux and stator current; therefore, the proposed estimator provides the speed and electromagnetic torque for a wide operational range of speeds and load torques. It was also shown that the proposed observer was robust to noise and uncertainty in induction motor parameters.</p>

Learning to drive as humans do: Reinforcement learning for autonomous navigation

This article introduces an approach aimed at enabling self-driving cars to emulate human-learned driving behavior. We propose a method where the navigation challenge of autonomous vehicles, from starting to ending positions, is framed as a series of decision-making problems encountered in various states negating the requirement for high-precision maps and routing systems. Utilizing high-quality images and sensor-derived state information, we design rewards to guide an agent’s movement from the initial to the final destination. The soft actor-critic algorithm is employed to learn the optimal policy from the interaction between the agent and the environment, informed by these states and rewards. In an innovative approach, we apply the variational autoencoder technique to extract latent vectors from high-quality images, reconstructing a new state space with vehicle state vectors. This method reduces hardware requirements and enhances training efficiency and task success rates. Simulation tests conducted in the CARLA simulator demonstrate the superiority of our method over others. It enhances the intelligence of autonomous vehicles without the need for intermediate processes such as target detection, while concurrently reducing the hardware footprint, even though it may not perform as well as the currently available mature techniques.

A latent space method with maximum entropy deep reinforcement learning for data assimilation

Data assimilation aims to calibrate the uncertain state or parameter vectors of a system by matching simulation results with observations, which is crucial for uncertainty quantification and optimization. Although traditional methods of data assimilation have shown promising results in practical applications, they need well-designed iteration rules (i.e., gradient, covariance, search strategies). Deep reinforcement learning (DRL) can solve data assimilation problems by trial and error, which does not require convoluted iteration rules. However, previous DRL methods cannot tackle high-dimensional data assimilation problems efficiently. In this work, we propose a latent space method with maximum entropy DRL for data assimilation to extend DRL to complicated systems with lots of parameters. Solutions can be found in a reduced space, through the interaction between the agent represented by artificial neural networks and the environment of numerical simulation. The proposed method contains two key points. First, to make the method applicable to high-dimensional problems, we construct a latent space method by integrating a dimensionality reduction method with the state, action, and reward settings for the agent. Second, a maximum entropy DRL algorithm, Soft Actor–Critic (SAC), was employed to efficiently explore the parameter space. The proposed method overcomes the limitation that previous DRL algorithms are only suitable for small-scale cases, and enables DRL to deal with medium-scale or even large-scale data assimilation problems. The performance of the proposed method was validated by comparison with a deep reinforcement learning algorithm and traditional data assimilation algorithms on 2D synthetic and 3D reservoir cases.

An integrated approach to Bayesian weight regulations and multitasking learning methods for generating emotion-based content in the metaverse

This paper introduces an integrated model designed to analyze topics and sentiments in textual data simultaneously, recognizing their interdependence. By tackling challenges such as data scarcity, missing information, and biased distributions, the proposed model effectively captures the dynamic interactions between topics and sentiments within complex datasets. The method combines the use of Convolutional Neural Networks (CNN) for detecting topic-related patterns with a revised Recurrent Neural Network (RNN) to trace the emotional flow within contexts, leveraging the strengths of sequential data processing. These components are integrated within a Bayesian probability framework, modeling the conditional probabilities of sentences expressing specific sentiments and documents being associated with particular topics. The combined feature and state vectors from the CNN and revised RNN within this Bayesian setup enable precise classification and prediction of topics and sentiments. Furthermore, this paper explores innovative research avenues, including sentiment analysis in 3D virtual reality environments and the development of new algorithms that reflect content creation techniques in the metaverse, offering dynamic system construction. This integrated approach not only enhances data-driven decision-making but also unlocks new possibilities for advanced multi-text analysis.

Observer-based output feedback control for switched T–S fuzzy systems with local nonlinear segments by using past output measurements

This paper researches the observer-based exponential stabilization problem for switched Takagi–Sugeno (T–S) fuzzy systems with unmeasurable premise variables and local nonlinearities. The local nonlinear parts that satisfy the incremental quadratic constraint exist in the systems and observers, which have the merit of being able to contain many common nonlinearities in a unified framework. Because the premise variables are not measurable, the performance of the observers in estimation is critical. Different from existing observer-based control strategies, the strategy of this paper not only depends on the current outputs of the systems but also relates to the past outputs of the systems which can provide a way to improve performance. In order to tackle the difficulties caused by introducing the past outputs and design a set of non-fragile fuzzy controllers to stabilize the systems, a new augmented state vector is constructed. Then, the conditions for designing the observer-based controller are derived by using auxiliary scalars, projection Lemma and S-procedure. Finally, the effectiveness of the control strategy obtained in this paper is proved by two examples.

Generalising quantum imaginary time evolution to solve linear partial differential equations

The quantum imaginary time evolution (QITE) methodology was developed to overcome a critical issue as regards non-unitarity in the implementation of imaginary time evolution on a quantum computer. QITE has since been used to approximate ground states of various physical systems. In this paper, we demonstrate a practical application of QITE as a quantum numerical solver for linear partial differential equations. Our algorithm takes inspiration from QITE in that the quantum state follows the same normalised trajectory in both algorithms. However, it is our QITE methodology’s ability to track the scale of the state vector over time that allows our algorithm to solve differential equations. We demonstrate our methodology with numerical simulations and use it to solve the heat equation in one and two dimensions using six and ten qubits, respectively.

Machine learning in viscoelastic fluids via energy-based kernel embedding

The ability to measure differences in collected data is of fundamental importance for quantitative science and machine learning, motivating the establishment of metrics grounded in physical principles. In this study, we focus on the development of such metrics for viscoelastic fluid flows governed by a large class of linear and nonlinear stress models. To do this, we introduce energy-compatible families of kernel functions corresponding to a given viscoelastic stress model. Each kernel implicitly embeds flowfield snapshots into a Reproducing Kernel Hilbert Space (RKHS) in which distances and angles are computed and whose squared norm equals the total mechanical energy. Additionally, we present a solution to the preimage problem for these kernels, enabling accurate reconstruction of flowfields from their RKHS representations. Through numerical experiments on an unsteady viscoelastic lid-driven cavity flow, we demonstrate the utility of energy-compatible kernels for extracting energetically-dominant coherent structures in viscoelastic flows across a range of Reynolds and Weissenberg numbers. Specifically, the features extracted by Kernel Principal Component Analysis (KPCA) of flowfield snapshots using energy-compatible kernel functions yield reconstructions with superior accuracy in terms of mechanical energy compared to conventional methods such as ordinary Principal Component Analysis (PCA) with naïvely-defined state vectors or KPCA with ad-hoc choices of kernel functions. Our findings underscore the importance of principled choices of metrics in both scientific and machine learning investigations of complex fluid systems.