Random Initial State Research Articles

Reverse Quantum Annealing Assisted by Forward Annealing

Quantum annealers conventionally use forward annealing to generate heuristic solutions. Reverse annealing can potentially generate better solutions but necessitates an appropriate initial state. Ways to find such states are generally unknown or highly problem dependent, offer limited success, and severely restrict the scope of reverse annealing. We use a general method that improves the overall solution quality and quantity by feeding reverse annealing with low-quality solutions obtained from forward annealing. An experimental demonstration of solving the graph coloring problem using the D-Wave quantum annealers shows that our method is able to convert invalid solutions obtained from forward annealing to at least one valid solution obtained after assisted reverse annealing for 57% of 459 random Erdos–Rényi graphs. Our method significantly outperforms random initial states, obtains more unique solutions on average, and widens the applicability of reverse annealing. Although the average number of valid solutions obtained drops exponentially with the problem size, a scaling analysis for the graph coloring problem shows that our method effectively extends the computational reach of conventional forward annealing using reverse annealing.

Tensor approximation of functional differential equations.

Functional differential equations(FDEs) play a fundamental role in many areas of mathematical physics, including fluid dynamics (Hopf characteristic functional equation), quantum field theory (Schwinger-Dyson equations), and statistical physics. Despite their significance, computing solutions to FDEs remains a longstanding challenge in mathematical physics. In this paper we address this challenge by introducing approximation theory and high-performance computational algorithms designed for solving FDEs on tensor manifolds. Our approach involves approximating FDEs using high-dimensional partial differential equations(PDEs), and then solving such high-dimensional PDEs on a low-rank tensor manifold leveraging high-performance (parallel) tensor algorithms. The effectiveness of the proposed approach is demonstrated through its application to the Burgers-Hopf FDE, which governs the characteristic functional of the stochastic solution to the Burgers equationevolving from a random initial state.

Robust iterative learning control for discrete-time systems with random initial state shifts

This paper presents the sufficient conditions of the stability for discrete-time systems with random initial state shifts when applying iterative learning control. Different sufficient conditions have been developed for systems with different characteristics to ensure boundedness of tracking errors and convergence of the learning process under random initial condition. First, the relationship between the initial shifts of two adjacent iterations is addressed with the help of the transition matrix. And the different analysis models are established for each type of systems: one-dimensional matrix analysis model and 2-D Roesser model. Second, the new and sufficient conditions are established for the proposed learning control law to ensure systems convergence by matrix theory and two-dimensional system theory. Third, solving the linear matrix inequality (LMI) yields the control gains. Finally, digital simulations illustrate the effectiveness and sufficiency of the presented conditions.

Adaptive neural network iterative learning control of long-stroke hybrid robots with initial errors and full state constraints

Research on initial errors and constraint restrictions is one of the main research directions in the field of control of uncertain robotic systems. An adaptive iterative learning control (AILC) method based on radial basis function (RBF) neural network is proposed to address the trajectory tracking problem of the long-stroke hybrid robot system with random initial errors and full state constraints. The RBF neural network is used to approximate the unknown nonlinear terms, and the network weights are updated using an iterative learning law that incorporates a projection mechanism. Additionally, a robust learning strategy is used to compensate for both the approximation error of the neural network and the external disturbances that vary with each iteration. To relax the requirement of traditional iterative learning control (ILC) for identical initial condition, an equivalent error function is constructed based on the time-varying boundary layer. The tangent-type barrier Lyapunov function (BLF) is designed to ensure that the joint position and speed of the robot system are bounded within a predetermined range. Through stability analysis based on barrier composite energy function (BCEF), it can be proved that the boundedness of all signals in the closed-loop system and the tracking error of the robot system will converge to an adjustable residual set asymptotically. Finally, through simulation experiments conducted on the MATLAB platform, the results demonstrate that the method overcomes the random initial errors of the system effectively, ensures that the system satisfies the full-state constraints, and realizes high-precision trajectory tracking.

Monte Carlo simulation of spacecraft breakup events in Low Lunar Orbit

Monte Carlo simulations of spacecraft breakup events in Low Lunar Orbit are conducted to study the behavior of artificial debris across all orbit types in this environment. 2000 breakup events at random initial states in lunar orbit are simulated, and the resulting nearly 500,000 particles are propagated for five years using a high-fidelity lunar trajectory model. Debris from a smaller sample of 200 breakup events is also propagated for ten years. Trends in the rate of decay of debris from lunar orbit are analyzed to investigate the longevity of debris in lunar orbit, and the locations of lunar surface impacts are plotted to determine if some regions of the Moon would be at greater risk than others from an orbital breakup event. Across all orbits, about 38% of the debris remained in lunar orbit after five years, and the longevity of debris was found to depend significantly on the pre-breakup perilune and inclination. Debris generally remained in lunar orbit for less time as the pre-breakup perilune decreased, although an average of 19% the debris remained in lunar orbit after five years even for pre-breakup perilune altitudes below 50 km. Debris was also found to be highly unstable in certain inclinations. The rates of decay across all orbit types tended to slow greatly after two years, suggesting that a portion of the debris can often remain in lunar orbit for at least a decade. Finally, clusters of lunar surface debris impacts were identified, which could have applications for lunar satellite disposal after mission completion. The results of this study provide novel insights into the consequences of lunar breakup events, helping support the development of debris mitigation recommendations for lunar orbit as international interest in exploration of the Moon grows.

Finite-dimensional probability distributions in the random Burgers-Riemann problem

We fully quantify the uncertainty for the Burgers’ partial differential equation with random Riemann initial states, by obtaining the generalized probability density functions associated to the finite-dimensional distributions of the response. The entropy solution is a mixed random field, decomposed into discrete and continuous parts, therefore the formalism of the Dirac delta function is employed in a novel way to derive closed-form expressions for the generalized densities, both for non-independent and independent initial conditions. This work extends the recent papers that focused on the first and the second finite-dimensional laws.

A COMPARATIVE STUDY OF DEEP ARCHITECTURES FOR VOXEL SEGMENTATION IN VOLUME IMAGES

Abstract. This study investigates the performance of eight different deep learning architectures for voxel segmentation in volume images. The motivation is to segment carbon in carbon reinforced concrete (CRC) in micro-tomography (μ-CT) data. Although there are many 3D convolutional neural networks (CNNs) available, it is not yet clear which one works best for these specific tasks. In this study, the authors compare the following networks: DenseVoxNet, HighResNet, Med3D, Residual 3D U-Net, 3D SkipDenseSeg, 3D U-Net, V-Net, and LV-Net. To provide a more general recommendation for selecting a neural network, three medical datasets were added in addition to the three CRC datasets to facilitate the selection of an appropriate network based on the dataset characteristics. The experiments emphasize the importance of the initial random state, used for example to initialize the network weights. On average, the 3D U-Net is the best generalizing CNN, followed by the Residual 3D U-Net and the 3D SkipDenseSeg. While the 3D U-Net is a good architecture to start with, the experiments show that it does not perform best on all domains. To achieve optimal results, the authors propose recommendations for selecting a 3D neural network based on the dataset attributes.

The soft actor–critic algorithm for automatic mode-locked fiber lasers

With the development of artificial intelligence, deep reinforcement learning (DRL) has been applied for fiber laser. In this paper, the intelligent passively mode-locked fiber laser (PMLFL) with the Soft Actor–Critic (SAC) algorithm is reported. The SAC algorithm is a DRL algorithm with random policy, which combines the Actor–Critic framework and the maximum entropy. The agent learns the logic of mode-locking by outputting actions and inputting states of the laser. Due to the maximum entropy model, more exploration is encouraged, which means that multiple policies can be learned to maximize the reward, and the robustness is enhanced accordingly. The results show that the logic learned by the agent is similar to that of human. In 80 random initial state of polarization mode-locked tests, 37 explorations are needed on average, and the frequency of achieving mode-locked state exceeds 0.8 within 60 explorations. Further, the laser system can be monitored or controlled remotely, which expands the application scenarios.

Approximate time optimal control by deep neural networks trained with numerically obtained optimal trajectories

AbstractThis paper focuses on online time optimal control of nonlinear systems. This is achieved by approximating the results of time optimal control problems (TOCP) with deep neural networks (DNN) depending on the initial and terminal system state. In general, solving a TOCP for nonlinear systems is a computationally challenging task. Especially in the context of time optimal nonlinear model predictive control (TMPC) with hard real time constraints successful termination of a TOCP within sample times suitable for controlling mechanical systems cannot be guaranteed. Therefore, our approach is to train three DNNs with different aspects of numerical solutions of TOCPs with random initial and terminal state. These networks can then be used to approximate the TMPC by a one step model predictive control scheme with a significantly simpler structure and decreased calculation time. In order to verify this procedure by simulation, it is applied to a prove of concept example as well as the model of an industrial robot.

A Numerical Study for Uncertainty in two Predators-One Prey Model

In this article, a mathematical model had been presented, which delved into the dynamics of a system featuring two predators and one prey, characterized by a growth rate of the predator dependent on a specific ratio. When facing uncertain initial conditions in the model, it had become imperative to adapt the mathematical descriptions by treating these initial conditions as random variables governed by specific distribution functions. The beta distribution had been employed to represent the stochastic initial state of the two predators-one prey model, allowing for an examination of how the random initial state of the prey had impacted the dynamic behavior of the system. Given the lack of an analytical solution for the model, computer simulations had been resorted to in order to delve into the dynamics of the system. Consequently, various properties of the resulting numerical solution had been thoroughly discussed, shedding light on the intricacies of the system's behavior. In addition, the research had offered invaluable insights into understanding the impact of uncertainty on predator-prey interactions and the subsequent stability and behavior of the ecological system in uncertain conditions, further bolstered by the numerical results obtained.

Model and Data Driven Machine Learning Approach for Analyzing the Vulnerability to Cascading Outages With Random Initial States in Power Systems

In this paper, a hybrid machine learning model is applied to evaluate the relationship between random initial states and the power system’s vulnerability to cascading outages. A cascading outage simulator (CS), which uses off-line AC power flows, is proposed for generating training data. The initial states are randomly selected and the CS model is deployed for each initial state, where power system generation and loads are adjusted dynamically and power flows are redistributed to quantify the vulnerability metric. Furthermore, the proposed hybrid machine learning model deploys a combined Support Vector Machine (SVM) classification and Gradient Boosting Regression (GBR) to improve the learning precision. The classification model is trained by SVM, which divides the data into two categories with and without load shedding. Then, GBR is adopted only for the data with load shedding to determine the relationship between input power outage states and the vulnerability metric. The proposed vulnerability analysis approach is applied to several test systems and the results are analyzed. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The power system vulnerability can be quantified by cascading outage simulations. However, there are two challenges: i) there are a huge number of possible initial states and we cannot enumerate all these initial states for the cascading outage simulation. Neither can we precisely quantify the bus vulnerability. ii) The cascading outage simulation may be time-consuming for large-scale power systems, which is challenging for the online application. To address the above challenges, we expect to design a machine learning technique to predict the power system vulnerability, which can train the model in an offline way and then use it for the online application. Firstly, since there is not enough operation data from practical power systems, we develop a cascading outage simulator, using off-line AC power flows, for generating synthetic training data. Secondly, we observe that the training precision by directly applying the regression model may be very poor because the output of the machine learning model may take on an uneven distribution concerning input parameters. Thus, we propose a hybrid machine learning model with a combined classification and regression method, where the classification model is employed to remove the data without the load shedding, and the regression model then determines the relationship between input power outage states and the vulnerability metric. The proposed model and method have been tested on several systems including a practical large-scale Polish power system to show the effectiveness.

Programmable Synchronous 2-Bit Counter in Quantum-Dot Cellular Automata

Quantum-dot Cellular Automata (QCA) is a newly-developed nanoscale electron device that has the potential to replace the conventional transistor in the future. Owing to the unique field-coupling mechanism of QCA, several constraints must be fulfilled during the design of QCA sequential circuits, which makes the construction of sequential circuits a relatively intractable issue in QCA research. In this paper, a programmable synchronous 2-bit counter in QCA is proposed, which is consisted of combinational logic and falling edge-triggered JK flip-flops. The count mode of the programmable counter can be changed on-demand by mode control signals. Moreover, an initial state setting method of the QCA circuit is also proposed during the design of the counter so that the effects of random initial states can be avoided. Simulation with QCADesigner software demonstrates the validity of the proposed counter.

Feedback higher-order iterative learning control for nonlinear systems with non-uniform iteration lengths and random initial state shifts

For nonlinear discrete-time systems with non-uniform iteration lengths and random initial state shifts, this paper developed a feedback higher-order iterative learning control (ILC) approach. To compensate the absent information of last iteration caused by non-uniform iteration lengths, the tracking information in both iteration domain and time domain is included in ILC design with the help of higher-order control and feedback control, respectively, while the general ILC schemes just adopt the information in iteration domain. A sufficient condition based on the higher-order ILC gains is derived. It is guaranteed that as the iteration number goes to infinity, the asymptotic bound of tracking error is proportional to random initial state shifts in mathematical expectation sense. Specifically, as the expectation of initial state shifts is zero, the ILC tracking error can be controlled to zero along the iteration direction. Two examples with different initial conditions are provided to validate the proposed ILC approach.

Deep learning-based model predictive control for real-time supply chain optimization

This paper presents a deep learning-based model predictive control (MPC) method for operational supply chain optimization in real time. The method follows an offline-online procedure. In the offline phase, the state-space model of a supply chain system is developed and the MPC problem for supply chain operation is formulated. Then, the MPC problem is solved for a set of initial states to obtain the corresponding optimal inputs. A deep neural network (DNN) is built and trained by using the optimal state-input pairs as training data to approximate the optimal MPC law. In the online phase, the DNN controller is employed to provide real-time decisions. In this paper, the MPC problem for supply chain operation is formulated as a mixed-integer linear program. A deep learning-based MPC method is proposed to accommodate time delays in the system. Moreover, a heuristic method is proposed for feasibility recovery with the binary decision variables taken into account. The training set for the DNN controller contains two subsets, one formed from MPC solutions corresponding to random initial states, and the other formed from optimal state-input pairs in closed-loop simulations. The deep learning-based MPC is validated via two case studies through closed-loop simulation. The first case study involves a linear MPC, and the second case study involves a more complicated mixed-integer linear MPC. Results show that deep learning-based MPC can achieve a high accuracy in approximating the MPC decisions and a significant reduction in the online computation time. Compared with MPC, the average performance loss of using deep learning-based MPC in the two cases is 0.43% and 1.8%, respectively.

Two-dimensional probability distribution of the solution to the random Burgers–Riemann problem

We investigate Burgers’ partial differential equation with random Riemann initial states and random-field solution. Previous works obtained the generalized probability density function in the one-dimensional case, by using different methods. We explore a technique that has not been employed in this context before, which fully develops the potential of the Dirac delta function. We start with the one-dimensional scenario and afterward extend to two dimensions. The generalized probability density function is derived in those cases, both for non-independent and independent initial conditions, and general statistics are obtained as a consequence.

Arresting dynamics in hardcore spin models

We study the dynamics of hardcore spin models on the square and triangular lattice, constructed by analogy to hard spheres, where the translational degrees of freedom of the spheres are replaced by orientational degrees of freedom of spins on a lattice and the packing fraction as a control parameter is replaced by an exclusion angle. In equilibrium, models on both lattices exhibit a Kosterlitz-Thouless transition at an exclusion angle $\Delta_{\rm KT}$. We devise compression protocols for hardcore spins and find that {\it any} protocol that changes the exclusion angle nonadiabatically, if endowed with only local dynamics, fails to compress random initial states beyond an angle $\Delta_{\rm J}> \Delta_{\rm KT}$. This coincides with a doubly algebraic divergence of the relaxation time of compressed states towards equilibrium. We identify a remarkably simple mechanism underpinning this divergent timescale: topological defects involved in the phase ordering kinetics of the system become incompatible with the hardcore spin constraint, leading to a vanishing defect mobility as $\Delta\rightarrow\Delta_{\rm J}$.

Neural networks determination of material elastic constants and structures in nematic complex fluids

Supervised machine learning and artificial neural network approaches can allow for the determination of selected material parameters or structures from a measurable signal without knowing the exact mathematical relationship between them. Here, we demonstrate that material nematic elastic constants and the initial structural material configuration can be found using sequential neural networks applied to the transmmited time-dependent light intensity through the nematic liquid crystal (NLC) sample under crossed polarizers. Specifically, we simulate multiple times the relaxation of the NLC from a random (qeunched) initial state to the equilibirum for random values of elastic constants and, simultaneously, the transmittance of the sample for monochromatic polarized light. The obtained time-dependent light transmittances and the corresponding elastic constants form a training data set on which the neural network is trained, which allows for the determination of the elastic constants, as well as the initial state of the director. Finally, we demonstrate that the neural network trained on numerically generated examples can also be used to determine elastic constants from experimentally measured data, finding good agreement between experiments and neural network predictions.

Adaptive iteration learning control with iteration‐varying event‐triggered mechanism for discrete‐time nonlinear systems with random initial states

AbstractIn this work, a novel adaptive event‐trigered iterative learning control (ILC) scheme is designed for discrete‐time nonlinear systems with time‐varying parameters and random initial states. The reference trajectory can be iteration‐invariant or iteration‐varying. The control input is updated when the event‐triggering condition is satisfied, which reduces the action time of controller and consequently the unnecessary waste of communication resource. An adaptive event‐triggering condition parameter is designed to improve the efficiency of the event generator. Moreover, the parameter updating law of adaptive iterative learning controller is designed based on the recursive least squares algorithm. With the proposed adaptive ILC with event‐triggered mechanism, the learning convergence along the iteration axis is guaranteed and communication burden is reduced. Finally, rigorous theoretical analysis under Lyapunov theory and illustrative examples are given to demonstrate the efficacy of the proposed method.

Reliability Analysis Based on a Bivariate Degradation Model Considering Random Initial State and Its Correlation With Degradation Rate

Dependent degradation processes of performance characteristics are ubiquitous in engineered systems. The initial state of each degradation process is usually random and relates to the degradation rate. Unfort unately, most existing Wiener-based bivariate degradation models fail to consider these two features, which may limit the accuracy of system reliability assessment. In order to surmount this limitation, in this article, we develop a new bivariate degradation model, which involves a generalized Wiener process-based marginal degradation model that considers the random initial state and the correlation between the initial state and the degradation rate and a corresponding degradation increment-based dependence structure (DS). The proposed bivariate degradation model and its reliability function are derived first. Then, a two-stage statistical inference is introduced using the maximum likelihood estimation method. Furthermore, a simulation study investigates the performance of the statistical inference and the misspecification effects of DSs and marginal degradation models. Finally, an illustrative example demonstrates the effectiveness of the proposed model.

Prescribed time convergence and robust zeroing neural network for solving time-varying linear matrix equation

Zeroing neural network offers a new solution method to solve the time-varying linear matrix equation. As an important component, the activation function directly affects the performance of zeroing neural network in solving time-varying linear matrix equation. Focusing on the unification of prescribed time convergence and strong robustness without changing the basic structure of zeroing neural network, a novel activation function is proposed for the first time in this paper. Compared with commonly used activation functions in previous work, the novel activation function has superior performance for zeroing neural network to solve the time-varying linear matrix equation. The first item is global asymptotic convergence, capable of converging from random initial states to the theoretical solution. The second item is the prescribed time convergence, i.e. the upper bound of convergence time is only related to the parameters of the novel activation function and zeroing neural network, which facilitates the prediction of the convergence process. The third item is strong robustness, which ensures that the solution converges in various noisy environments. Theoretical analysis and comparative simulation experiments verify that zeroing neural network with the novel activation function has these performances for both low- or high-dimensional time-varying linear matrix equation.