High-dimensional Complex Systems Research Articles

Feedback stabilization of probabilistic finite state machines based on deep Q-network.

As an important mathematical model, the finite state machine (FSM) has been used in many fields, such as manufacturing system, health care, and so on. This paper analyzes the current development status of FSMs. It is pointed out that the traditional methods are often inconvenient for analysis and design, or encounter high computational complexity problems when studying FSMs. The deep Q-network (DQN) technique, which is a model-free optimization method, is introduced to solve the stabilization problem of probabilistic finite state machines (PFSMs). In order to better understand the technique, some preliminaries, including Markov decision process, ϵ-greedy strategy, DQN, and so on, are recalled. First, a necessary and sufficient stabilizability condition for PFSMs is derived. Next, the feedback stabilization problem of PFSMs is transformed into an optimization problem. Finally, by using the stabilizability condition and deep Q-network, an algorithm for solving the optimization problem (equivalently, computing a state feedback stabilizer) is provided. Compared with the traditional Q learning, DQN avoids the limited capacity problem. So our method can deal with high-dimensional complex systems efficiently. The effectiveness of our method is further demonstrated through an illustrative example.

Estimating Kolmogorov–Sinai entropy from time series of high-dimensional complex systems

A method is presented to estimate KS entropy from time series of a high-dimensional complex system. We focus on partitioned entropy, which measures the complexity of data points localized in a delay-coordinate space. By quantifying the time evolution of the partitioned entropy, we show that its growth rate gives a good estimate of the KS entropy. Our method is computationally efficient, since a time series is discretized into a coarse-grained symbolic sequence by a vector quantization technique. Using numerical data sets generated from prototypical models of chaotic systems, we showed that our approach works quite well for high-dimensional complex systems. Application to experimental data measured from physical models of the vocal membranes confirmed that our method is effective for characterizing the complexity of real-world systems.

Multi-Task Learning for Design Under Uncertainty With Multi-Fidelity Partially Observed Information

Abstract The assessment of system performance and identification of failure mechanisms in complex engineering systems often requires the use of computation-intensive finite element software or physical experiments, which are both costly and time-consuming. Moreover, when accounting for uncertainties in the manufacturing process, material properties, and loading conditions, the process of reliability-based design optimization (RBDO) for complex engineering systems necessitates the repeated execution of expensive tasks throughout the optimization process. To address this problem, this paper proposes a novel methodology for RBDO. First, a multi-fidelity surrogate modeling strategy is presented, leveraging partially observed information (POI) from diverse sources with varying fidelity and dimensionality to reduce computational cost associated with evaluating expensive high-dimensional complex systems. Second, a multi-task surrogate modeling framework is proposed to address the concurrent evaluation of multiple constraints for each design point. The multi-task framework aids in the development of surrogate models and enhances the effectiveness of reliability analysis and design optimization. The proposed multi-fidelity multi-task machine learning model utilizes a Bayesian framework, which significantly improves the performance of the predictive model and provides uncertainty quantification of the prediction. Additionally, the model provides a highly accurate and efficient framework for reliability-based design optimization through knowledge sharing. The proposed method was applied to two design case studies. By incorporating POI from various sources, the proposed approach improves the accuracy and efficiency of system performance prediction, while simultaneously addressing the cost and complexity associated with the design of complex systems.

The causality measure of partial mutual information from mixed embedding (PMIME) revisited.

The measure of partial mutual information from mixed embedding (PMIME) is an information theory-based measure to accurately identify the direct and directional coupling, termed Granger causality or simply causality, between the observed variables or subsystems of a high-dimensional dynamical and complex system, without any a priori assumptions about the nature of the coupling relationship. In its core, it is a forward selection procedure that aims to iteratively identify the lag-dependence structure of a given observed variable (response) to all the other observed variables (candidate drivers). This model-free approach is capable of detecting nonlinear interactions, abundantly present in real-world complex systems, and it was shown to perform well on multivariate time series of moderately high dimension. However, the PMIME presents some inefficiencies in its performance mainly when applied on strongly stochastic (linear or nonlinear) systems as it may falsely detect non-existent relationships. Moreover, and by construction, the measure cannot extract purely synergetic relationships present in a system. In the current work, the issue of false detections is addressed by introducing an improved resampling significance test and a procedure of rechecking the identified drivers (backward revision). Regarding the inability to detect synergetic relationships, the PMIME is further enhanced by checking pairs as candidate drivers for the response variable after having considered all drivers individually. The effects of these modifications are investigated in a systematic simulation study on properly designed systems involving strong stochasticity, regressor terms with synergetic effects, and a system dimension ranging from 3 to 30. The overall results of the simulations indicate that these modifications indeed improve the performance of PMIME and alleviate to a significant degree the issues of the original algorithm. Guidelines for balancing between accuracy and computational efficiency are also given, particularly relevant for real-world applications. Finally, the measure performance is investigated in the study of futures of various government bonds and stock market indices in the period around COVID-19 pandemic.

Review and analysis of model order reduction techniques for high-dimensional complex systems

Review and analysis of model order reduction techniques for high-dimensional complex systems

A novel dimensionality reduction approach by integrating dynamics theory and machine learning

This paper aims to introduce a technique that utilizes both dynamical mechanisms and machine learning to reduce dimensionality in high-dimensional complex systems. Specifically, the method employs Hopf bifurcation theory to establish a model paradigm and use machine learning to train location parameters. The effectiveness of the proposed method is evaluated by testing the Van Der Pol equation and it is found that it possesses good predictive ability. In addition, simulation experiments are conducted using a hunting motion model, which is a well-known practice in high-speed rail, demonstrating positive results. To ensure the robustness of the proposed method, we tested it on noisy data. We introduced simulated Gaussian noise into the original dataset at different signal-to-noise ratios (SNRs) of 10 db, 20 db, 30 db, and 40 db. All data and codes used in this paper have been uploaded to GitHub.

SS-MASVM: An advanced technique for assessing failure probability of high-dimensional complex systems using the multi-class adaptive support vector machine

The integrity of structures in contemporary engineering practices is heavily influenced by inherent uncertainties, which necessitates the development of reliable structural reliability analysis methods for uncertainty quantification and probabilistic analysis. This paper investigates the integration of surrogate models and subset simulation (SS) to accurately compute the failure probabilities of high-dimensional complex systems. Focus is placed on enhancing the computational efficiency and accuracy through using the multi-class adaptive support vector machine (MASVM). The proposed SS-MASVM method incorporates more efficient learning functions, integrates K-means clustering, and employs SS technology for precise estimation of failure probabilities of high-dimensional complex systems. Numerical and engineering structural examples validate the effectiveness of the proposed method and highlight its potential in practical reliability analysis, and the results disclose that the SS-MASVM is efficient and accurate for assessing the complex system reliability.

Statistical performance of local attractor dimension estimators in non-Axiom A dynamical systems.

We investigate various estimators based on extreme value theory (EVT) for determining the local fractal dimension of chaotic dynamical systems. In the limit of an infinitely long time series of an ergodic system, the average of the local fractal dimension is the system's global attractor dimension. The latter is an important quantity that relates to the number of effective degrees of freedom of the underlying dynamical system, and its estimation has been a central topic in the dynamical systems literature since the 1980s. In this work, we propose a framework that combines phase space recurrence analysis with EVT to estimate the local fractal dimension around a particular state of interest. While the EVT framework allows for the analysis of high-dimensional complex systems, such as the Earth's climate, its effectiveness depends on robust statistical parameter estimation for the assumed extreme value distribution. In this study, we conduct a critical review of several EVT-based local fractal dimension estimators, analyzing and comparing their performance across a range of systems. Our results offer valuable insights for researchers employing the EVT-based estimates of the local fractal dimension, aiding in the selection of an appropriate estimator for their specific applications.

Fuzzy Graph Modeling and Clustering Analysis of Nonlinear Dynamical Systems

Analyzing stability and designing control strategies for interconnected nonlinear dynamical systems poses mathematical challenges due to combinatorial growth in complexity. This paper develops a methodology integrating fuzzy graph theory with spectral clustering techniques to enable tractable certification of stability properties. Fuzzy similarity relations between state variables model imprecise couplings within the nonlinear dynamics. Representing these relations through graph adjacency matrices facilitates partitioning strongly connected states using spectral algorithms. Stability of the overall fuzzy state graph is inferred from the spectral radii of decoupled fuzzy subgraphs. The graph-theoretic abstraction provides a coarse-grained lens into nonlinear stability properties while circumventing computational barriers. The fuzzy graph modeling and spectral partitioning pipeline ultimately streamlines control synthesis targeting local clustered subdynamics. Case studies on power network stabilization, swarm navigation, and process operations showcase scalable applications to high-dimensional complex systems. The integrated fuzzy graph and spectral clustering approach provides a systematic toolkit for analysis and control of heavily interconnected nonlinear dynamical systems across engineering domains.

Inferring the interaction rules of complex systems with graph neural networks and approximate Bayesian computation.

Inferring the underlying processes that drive collective behaviour in biological and social systems is a significant statistical and computational challenge. While simulation models have been successful in qualitatively capturing many of the phenomena observed in these systems in a variety of domains, formally fitting these models to data remains intractable. Recently, approximate Bayesian computation (ABC) has been shown to be an effective approach to inference if the likelihood function for a model is unavailable. However, a key difficulty in successfully implementing ABC lies with the design, selection and weighting of appropriate summary statistics, a challenge that is especially acute when modelling high dimensional complex systems. In this work, we combine a Gaussian process accelerated ABC method with the automatic learning of summary statistics via graph neural networks. Our approach bypasses the need to design a model-specific set of summary statistics for inference. Instead, we encode relational inductive biases into a neural network using a graph embedding and then extract summary statistics automatically from simulation data. To evaluate our framework, we use a model of collective animal movement as a test bed and compare our method to a standard summary statistics approach and a linear regression-based algorithm.

Estimating comparable distances to tipping points across mutualistic systems by scaled recovery rates.

Mutualistic systems can experience abrupt and irreversible regime shifts caused by local or global stressors. Despite decades of efforts to understand ecosystem dynamics and determine whether a tipping point could occur, there are no current approaches to estimate distances (in state/parameter space) to tipping points and compare the distances across various mutualistic systems. Here we develop a general dimension-reduction approach that simultaneously compresses the natural control and state parameters of high-dimensional complex systems and introduces a scaling factor for recovery rates. Our theoretical framework places various systems with entirely different dynamical parameters, network structure and state perturbations on the same scale. More importantly, it compares distances to tipping points across different systems on the basis of data on abundance and topology. By applying the method to 54 real-world mutualistic networks, our analytical results unveil the network characteristics and system parameters that control a system's resilience. We contribute to the ongoing efforts in developing a general framework for mapping and predicting distance to tipping points of ecological and potentially other systems.

Safe Reinforcement Learning Algorithm and Its Application in Intelligent Control for CPS

PDF HTML XML Export Cite reminder Safe Reinforcement Learning Algorithm and Its Application in Intelligent Control for CPS DOI: 10.21655/ijsi.1673-7288.00284 Author: Affiliation: Clc Number: Fund Project: Article | Figures | Metrics | Reference | Related | Cited by | Materials | Comments Abstract:The design of a safe controller for a Cyber-Physical System (CPS) is a hot research topic. The existing safety controller design based on formal methods has problems such as excessive reliance on models and poor scalability. Intelligent control based on Deep Reinforcement Learning (DRL) can handle high-dimensional nonlinear complex systems and uncertain systems and is becoming a very promising CPS control technology, but it lacks safety guarantees. This study addresses the safety issues of Reinforcement Learning (RL) control by analyzing a typical case of an industrial oil pump control system and carries out research on a Safe Reinforcement Learning (SRL) algorithm and intelligent control application. First, the SRL issue of the industrial oil pump control system is formalized, and a simulation environment of the oil pump is built. Then, by designing the structure and activation function of the output layer, an oil pump controller in the form of a neural network is constructed to satisfy the linear inequality constraints of the on-off operations of the oil pump. Finally, in order to better balance the safety and optimality control objectives, a new SRL algorithm is designed based on the Augmented Lagrange Multiplier (ALM) method. A comparative experiment on the industrial oil pump shows that the controller synthesized by the proposed algorithm surpasses existing similar algorithms both in safety and optimality. During the evaluation, the neural network controllers synthesized in this study pass rigorous formal verification with a probability of 90%. Meanwhile, compared with the theoretically optimal controller, neural network controllers achieve an optimal objective value loss of 2%. The proposed method is expected to be applied in more scenarios, and the case study scheme may provide a reference for other researchers in the field of safe intelligent control and formal verification. Reference Related Cited by

A FAST SOLVER BASED ON DEEP NEURAL NETWORK FOR DIFFERENCE EQUATION

In recent years, artificial neural networks (ANNs), especially deep neural networks (DNNs), have become a promising new approach in the field of numerical computation due to their high computational efficiency on heterogeneous platforms and their ability to fit high-dimensional complex systems. In the process of numerically solving the partial differential equations, the large-scale linear equations are usually the most time-consuming problems; therefore, utilizing the neural network methods to solve linear equations has become a promising new idea. However, the direct prediction of deep neural networks still has obvious shortcomings in numerical accuracy, which becomes one of the bottlenecks for its application in the field of numerical computation. To break this limitation, a solving algorithm combining Residual network architecture and correction iteration method is proposed in this paper. In this paper, a deep neural network-based method for solving linear equations is proposed to accelerate the solving process of partial differential equations on heterogeneous platforms. Specifically, Residual network resolves the problems of network degradation and gradient vanishing of deep network models, reducing the loss of the network to 1/5000 of the classical network model; the correction iteration method iteratively reduce the error of the prediction solution based on the same network model, and the residual of the prediction solution has been decreased to 10−5 times of that before the iteration. To verify the effectiveness and universality of the proposed method, we combined the method with the finite difference method to solve the heat conduction equation and the Burger’s equation. Numerical results demonstrate that the algorithm has more than 10 times the acceleration effect for equations of size larger than 1000, and the numerical error is lower than the discrete error of the second-order difference scheme.

A Review of Model Order Reduction Methods for Large-Scale Structure Systems

The large-scale structure systems in engineering are complex, high dimensional, and variety of physical mechanism couplings; it will be difficult to analyze the dynamic behaviors of complex systems quickly and optimize system parameters. Model order reduction (MOR) is an efficient way to address those problems and widely applied in the engineering areas. This paper focuses on the model order reduction of high-dimensional complex systems and reviews basic theories, well-posedness, and limitations of common methods of the model order reduction using the following methods: center manifold, Lyapunov–Schmidt (L-S), Galerkin, modal synthesis, and proper orthogonal decomposition (POD) methods. The POD is a powerful and effective model order reduction method, which aims at obtaining the most important components of a high-dimensional complex system by using a few proper orthogonal modes, and it is widely studied and applied by a large number of researchers in the past few decades. In this paper, the POD method is introduced in detail and the main characteristics and the existing problems of this method are also discussed. POD is classified into two categories in terms of the sampling and the parameter robustness, and the research progresses in the recent years are presented to the domestic researchers for the study and application. Finally, the outlooks of model order reduction of high-dimensional complex systems are provided for future work.

A polynomial dimensional decomposition framework based on topology derivatives for stochastic topology sensitivity analysis of high-dimensional complex systems and a type of benchmark problems

In this paper, a new computational framework based on the topology derivative concept is presented for evaluating stochastic topological sensitivities of complex systems. The proposed framework, designed for dealing with high dimensional random inputs, dovetails a polynomial dimensional decomposition (PDD) of multivariate stochastic response functions and deterministic topology derivatives. On one hand, it provides analytical expressions to calculate topology sensitivities of the first three stochastic moments which are often required in robust topology optimization (RTO). On another hand, it offers embedded Monte Carlo Simulation (MCS) and finite difference formulations to estimate topology sensitivities of failure probability for reliability-based topology optimization (RBTO). For both cases, the quantification of uncertainties and their topology sensitivities are determined concurrently from a single stochastic analysis. Moreover, an original example of two random variables is developed for the first time to obtain analytical solutions for topology sensitivity of moments and failure probability. Another 53-dimension example is constructed for analytical solutions of topology sensitivity of moments and semi-analytical solutions of topology sensitivity of failure probabilities in order to verify the accuracy and efficiency of the proposed method for high-dimensional scenarios. Those examples are new and make it possible for researchers to benchmark stochastic topology sensitivities of existing or new algorithms. In addition, it is unveiled that under certain conditions the proposed method achieves better accuracies for stochastic topology sensitivities than for the stochastic quantities themselves.

Monte Carlo basin bifurcation analysis

Many high-dimensional complex systems exhibit an enormously complex landscape of possible asymptotic states. Here, we present a numerical approach geared towards analyzing such systems. It is situated between the classical analysis with macroscopic order parameters and a more thorough, detailed bifurcation analysis. With our machine learning method, based on random sampling and clustering methods, we are able to characterize the different asymptotic states or classes thereof and even their basins of attraction. In order to do this, suitable, easy to compute, statistics of trajectories with randomly generated initial conditions and parameters are clustered by an algorithm such as DBSCAN. Due to its modular and flexible nature, our method has a wide range of possible applications in many disciplines. While typical applications are oscillator networks, it is not limited only to ordinary differential equation systems, every complex system yielding trajectories, such as maps or agent-based models, can be analyzed, as we show by applying it the Dodds–Watts model, a generalized SIRS-model, modeling social and biological contagion. A second order Kuramoto model, used, e.g. to investigate power grid dynamics, and a Stuart–Landau oscillator network, each exhibiting a complex multistable regime, are shown as well. The method is available to use as a package for the Julia language.

Current Strategies and Applications for Precision Drug Design.

Since Human Genome Project (HGP) revealed the heterogeneity of individuals, precision medicine that proposes the customized healthcare has become an intractable and hot research. Meanwhile, as the Precision Medicine Initiative launched, precision drug design which aims at maximizing therapeutic effects while minimizing undesired side effects for an individual patient has entered a new stage. One of the key strategies of precision drug design is target based drug design. Once a key pathogenic target is identified, rational drug design which constitutes the major part of precision drug design can be performed. Examples of rational drug design on novel druggable targets and protein–protein interaction surfaces are summarized in this review. Besides, various kinds of computational modeling and simulation approaches increasingly benefit for the drug discovery progress. Molecular dynamic simulation, drug target prediction and in silico clinical trials are discussed. Moreover, due to the powerful ability in handling high-dimensional data and complex system, deep learning has efficiently promoted the applications of artificial intelligence in drug discovery and design. In this review, deep learning methods that tailor to precision drug design are carefully discussed. When a drug molecule is discovered, the development of specific targeted drug delivery system becomes another key aspect of precision drug design. Therefore, state-of-the-art techniques of drug delivery system including antibody-drug conjugates (ADCs), and ligand-targeted conjugates are also included in this review.

Entropy-based generating Markov partitions for complex systems.

Finding the correct encoding for a generic dynamical system's trajectory is a complicated task: the symbolic sequence needs to preserve the invariant properties from the system's trajectory. In theory, the solution to this problem is found when a Generating Markov Partition (GMP) is obtained, which is only defined once the unstable and stable manifolds are known with infinite precision and for all times. However, these manifolds usually form highly convoluted Euclidean sets, are a priori unknown, and, as it happens in any real-world experiment, measurements are made with finite resolution and over a finite time-span. The task gets even more complicated if the system is a network composed of interacting dynamical units, namely, a high-dimensional complex system. Here, we tackle this task and solve it by defining a method to approximately construct GMPs for any complex system's finite-resolution and finite-time trajectory. We critically test our method on networks of coupled maps, encoding their trajectories into symbolic sequences. We show that these sequences are optimal because they minimise the information loss and also any spurious information added. Consequently, our method allows us to approximately calculate the invariant probability measures of complex systems from the observed data. Thus, we can efficiently define complexity measures that are applicable to a wide range of complex phenomena, such as the characterisation of brain activity from electroencephalogram signals measured at different brain regions or the characterisation of climate variability from temperature anomalies measured at different Earth regions.

Technical Analysis of Climate Time Series Data

The application of chart pattern, or technical, analysis to climate time series was updated and extended on the previous working paper using up-to-date data. The full time span of the global average temperature anomalies (HadCRUT4) was examined for chart patterns. An alternating sequence of rising wedges and consolidation periods was revealed. Their details were evaluated to compare with as well as to supplement financial technical analysis. Chart pattern features in the climate time series matched those reported for the same pattern (rising wedge) in US stock price time series quite well. A tentative prediction arrived at a consolidation period that may last for roughly the next four decades. The results further support the idea of technical analysis as a tool to analyse time series data of high-dimensional complex systems in general. In addition, research on chart pattern reproducing differential equations is encouraged to globally describe the climate system.

An adaptive proper orthogonal decomposition method for model order reduction of multi-disc rotor system

The proper orthogonal decomposition (POD) method is a main and efficient tool for order reduction of high-dimensional complex systems in many research fields. However, the robustness problem of this method is always unsolved, although there are some modified POD methods which were proposed to solve this problem. In this paper, a new adaptive POD method called the interpolation Grassmann manifold (IGM) method is proposed to address the weakness of local property of the interpolation tangent-space of Grassmann manifold (ITGM) method in a wider parametric region. This method is demonstrated here by a nonlinear rotor system of 33-degrees of freedom (DOFs) with a pair of liquid-film bearings and a pedestal looseness fault. The motion region of the rotor system is divided into two parts: simple motion region and complex motion region. The adaptive POD method is compared with the ITGM method for the large and small spans of parameter in the two parametric regions to present the advantage of this method and disadvantage of the ITGM method. The comparisons of the responses are applied to verify the accuracy and robustness of the adaptive POD method, as well as the computational efficiency is also analyzed. As a result, the new adaptive POD method has a strong robustness and high computational efficiency and accuracy in a wide scope of parameter.