Nonlinear Function Approximation Research Articles

A multivariable adaptive control method for aeroengine with H∞ performance considering engine output limitation protection based on fully adjustable Neural Network

A multivariable adaptive control method for aeroengine with H∞ performance considering engine output limitation protection based on fully adjustable Neural Network

Efficient nonlinear function approximation in analog resistive crossbars for recurrent neural networks

Analog In-memory Computing (IMC) has demonstrated energy-efficient and low latency implementation of convolution and fully-connected layers in deep neural networks (DNN) by using physics for computing in parallel resistive memory arrays. However, recurrent neural networks (RNN) that are widely used for speech-recognition and natural language processing have tasted limited success with this approach. This can be attributed to the significant time and energy penalties incurred in implementing nonlinear activation functions that are abundant in such models. In this work, we experimentally demonstrate the implementation of a non-linear activation function integrated with a ramp analog-to-digital conversion (ADC) at the periphery of the memory to improve in-memory implementation of RNNs. Our approach uses an extra column of memristors to produce an appropriately pre-distorted ramp voltage such that the comparator output directly approximates the desired nonlinear function. We experimentally demonstrate programming different nonlinear functions using a memristive array and simulate its incorporation in RNNs to solve keyword spotting and language modelling tasks. Compared to other approaches, we demonstrate manifold increase in area-efficiency, energy-efficiency and throughput due to the in-memory, programmable ramp generator that removes digital processing overhead.

Conditions for a quadratic quantum speedup in nonlinear transforms with applications to energy contract pricing

Abstract Computing nonlinear functions over multilinear forms is a general problem with applications in risk analysis. For instance in the domain of energy economics, accurate and timely risk management demands for efficient simulation of millions of scenarios, largely benefiting from computational speedups. We develop a novel hybrid quantum–classical algorithm based on polynomial approximation of nonlinear functions, computed through Quantum Hadamard Products, and we rigorously assess the conditions for its end-to-end speedup for different implementation variants against classical algorithms. In our setting, a quadratic quantum speedup, up to polylogarithmic factors, can be proven only when forms are bilinear and approximating polynomials have second degree, if efficient loading unitaries are available for the input data sets. We also enhance the bidirectional encoding, that allows tuning the balance between circuit depth and width, proposing an improved version that can be exploited for the calculation of inner products. Lastly, we exploit the dynamic circuit capabilities, recently introduced on IBM Quantum devices, to reduce the average depth of the Quantum Hadamard Product circuit. A proof of principle is implemented and validated on IBM Quantum systems.

A Comprehensive Review of Artificial Intelligence and Machine Learning in Control Theory

Traditional control methods, such as proportional-integral-derivative (PID) controllers and linear-quadratic regulators (LQRs), have proven effective for linear and well-modeled systems. However, these methods often perform poorly in nonlinear, complex and dynamic environments. The paper aims to investigate the modern control systems by integrating artificial intelligence (AI) techniques, such as machine learning (ML), reinforcement learning (RL), deep learning, and fuzzy logic, to enhance their adaptive, robust, and predictive capabilities. And it reviews the literature and analyzes AI integration in control systems. The proposed strategies include supervised learning for trajectory optimization and fault detection, reinforcement learning for optimal control in dynamic environments, neural networks for complex nonlinear function approximation, and fuzzy logic for handling uncertainty and imprecise inputs. AI techniques significantly enhance the ability to tackle nonlinear problems and dynamic changes, demonstrating superior performance in applications like self-driving cars adapting to various road conditions and optimal energy distribution in smart grids. Despite the challenges of computational complexity, scalability, and the safety and reliability in the implementation of interpretable AI models, this paper suggests that hybrid approaches combining traditional control and AI techniques, along with the evolution of interpretable AI and convergence with quantum control, hold great promise for advancing AI-driven control systems.

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A Compact Constraint Incremental Method for Random Weight Networks and Its Application.

Incremental random weight networks (IRWNs) face the issues of weak generalization and complicated network structure. There is an important reason: the learning parameters of IRWNs are determined in a random fashion without guidance, which may increase many redundant hidden nodes, and thereby leading to inferior performance. To resolve this issue, a novel IRWN with compact constraint that guides the assignment of random learning parameters (CCIRWN) is developed in this brief. Using the iteration method of Greville, a compact constraint that simultaneously assures the quality of generated hidden nodes and the convergence of the CCIRWN is built to perform learning parameter configuration. Meanwhile, the output weights of the CCIRWN are assessed analytically. Two types of learning methods for constructing the CCIRWN are proposed. Finally, the performance evaluation of the proposed CCIRWN is undertaken on the 1-D nonlinear function approximation, several real-world datasets, and data-driven estimation based on the industrial data. Numerical and industrial examples indicate that the proposed CCIRWN with compact structure can achieve favorable generalization ability.

Online adaptive critic designs with tensor product B-splines and incremental model techniques

Online adaptive critic designs with tensor product B-splines and incremental model techniques

Enhanced support vector machine-based moving regression strategy for response prediction and reliability estimation of complex structure

Enhanced support vector machine-based moving regression strategy for response prediction and reliability estimation of complex structure

Retraction notice: Nonlinear function estimation fuzzy system (NFEFS) as a novel statistical approach to estimate nanofluids’ thermal conductivity according to empirical data

Retraction notice: Nonlinear function estimation fuzzy system (NFEFS) as a novel statistical approach to estimate nanofluids’ thermal conductivity according to empirical data

Operational reliability assessment of complex mechanical systems with multiple failure modes: An adaptive decomposition-synchronous-coordination approach

Operational reliability assessment of complex mechanical systems with multiple failure modes: An adaptive decomposition-synchronous-coordination approach

Identification of nonlinear system model and inverse model based on conditional invertible neural network

In applications such as adaptive inverse control, internal model control, and active noise control, the identification accuracy of the system model and the inverse model directly affects the performance. However, it is not easy to identify inverse models for nonlinear systems. Moreover, existing methods require two identification calculations to obtain the system model and the inverse model. Therefore, an identification method of nonlinear system model and inverse model based on conditional invertible neural network (cINN) is proposed. The invertible structure of cINN enables simultaneous approximation of complex nonlinear functions and simultaneous acquisition of the corresponding inverse functions. Consequently, both the nonlinear system model and the inverse model can be identified concurrently through cINN. Moreover, the identification performance of the cINN-based method is validated and applied to disturbance cancellation in a classical nonlinear simulation system. Finally, the inverse model of the actuator is identified by cINN, and the inverse model is applied to the nonlinear compensation of the actuator.

Multi-variable constrained control for uncertain high-order strict-feedback fully actuated nonlinear systems

Multi-variable constrained control for uncertain high-order strict-feedback fully actuated nonlinear systems

Mini-Workshop: Nonlinear Approximation of High-dimensional Functions in Scientific Computing

Approximation techniques for high dimensional PDEs are crucial for contemporary scientific computing tasks and gained momentum in recent years due to the renewed interest in neural networks. It seems that especially nonlinear parametrizations will play an essential role in efficient and tractable approximations of high dimensional problems. We held a mini-workshop on the relation and possible synergy of neural networks and tensor product approximation. To reliably evaluate the prospect of different numerical experiments, the traditional talks were accompanied by live coding sessions.

Conditional advancement of machine learning algorithm via fuzzy neural network

Conditional advancement of machine learning algorithm via fuzzy neural network

Monotonic Fuzzy Systems With Goniometric Membership Functions

Fuzzy logic-based systems are nowadays commonly used in nonlinear function approximation when incoming data are available. Their main advantage is that the resulting rules can be interpreted understandably. Nevertheless, when the data are noisy an overfitting may occur which leads to poor accuracy and generalization ability. Prior information about the nonlinear function may improve fuzzy system performance. In this paper the case when the function is monotonic with respect to some or all variables is considered. Sufficient conditions for the monotonicity of first-order Takagi–Sugeno fuzzy systems with raised cosine membership functions are derived. Performance of the proposed fuzzy system is tested on two benchmark datasets

Leveraging ANFIS with Adam and PSO optimizers for Parkinson's disease

Parkinson's disease (PD) is an age-related neurodegenerative disorder characterized by motor deficits, including tremor, rigidity, bradykinesia, and postural instability. According to the World Health Organization, about 1% of the global population has been diagnosed with PD, and this figure is expected to double by 2040. Early and accurate diagnosis of PD is critical to slowing down the progression of the disease and reducing long-term disability. Due to the complexity of the disease, it is difficult to accurately diagnose it using traditional clinical tests. Therefore, it has become necessary to develop intelligent diagnostic models that can accurately detect PD. This article introduces a novel hybrid approach for accurate prediction of PD using an ANFIS with two optimizers, namely Adam and PSO. ANFIS is a type of fuzzy logic system used for nonlinear function approximation and classification, while Adam optimizer has the ability to adaptively adjust the learning rate of each individual parameter in an ANFIS at each training step, which helps the model find a better solution more quickly. PSO is a metaheuristic approach inspired by the behavior of social animals such as birds. Combining these two methods has potential to provide improved accuracy and robustness in PD diagnosis compared to existing methods. The proposed method utilized the advantages of both optimization techniques and applied them on the developed ANFIS model to maximize its prediction accuracy. This system was developed by using an open access clinical and demographic data. The chosen parameters for the ANFIS were selected through a comparative experimental analysis to optimize the model considering the number of fuzzy membership functions, number of epochs of ANFIS, and number of particles of PSO. The performance of the two ANFIS models: ANFIS (Adam) and ANFIS (PSO) focusing at ANFIS parameters and various evaluation metrics are further analyzed in detail and presented, The experimental results showed that the proposed ANFIS (PSO) shows better results in terms of loss and precision, whereas, the ANFIS (Adam) showed the better results in terms of accuracy, f1-score and recall. Thus, this adaptive neural-fuzzy algorithm provides a promising strategy for the diagnosis of PD, and show that the proposed models show their suitability for many other practical applications.

Nonlinear approximation of high-dimensional anisotropic analytic functions

Nonlinear approximation of high-dimensional anisotropic analytic functions

A data-driven implicit deep adaptive neuro-fuzzy inference system capable of manifold learning for function approximation

A data-driven implicit deep adaptive neuro-fuzzy inference system capable of manifold learning for function approximation

Methods for controlling heavy metals in environmental soils based on artificial neural networks

The problem of heavy metal pollution in soil has become a global environmental problem, and it is very important to predict and manage the heavy metals in the environmental soil in a timely manner. The changes in heavy metal content in soil have characteristics such as nonlinearity and large delay, making it difficult to predict heavy metals in soil using traditional methods. Traditional prediction methods are complex and cumbersome, which can lead to longer treatment time and easy secondary pollution. This article analyzed the Back Propagation neural network (BPNN) in artificial neural networks (ANN) and applied it to the prediction of heavy metals in environmental soils. BPNN has good nonlinear function approximation ability, so it can be well applied to complex problems such as soil heavy metal prediction. The methods of treating soil heavy metals include physical repair method, chemical repair method, microbial repair method, plant repair method, plant microbial combined repair method and so on. The use of BPNN can predict heavy metals in environmental soils through adaptive dynamic learning. However, the training time of the BPNN is relatively long and the convergence speed is relatively slow. Therefore, additional momentum terms were added to adjust the weights and thresholds of the network to improve the BPNN. In the experiment, the prediction performance of the improved BPNN was compared before and after the improvement. This article took 50 monitoring data of heavy metals in the same soil in a certain region in 2021 as sample data and predicted the content of heavy metals in the soil using improved and improved BPNN. Due to time constraints, this article only conducted experimental analysis on heavy metals such as lead and cadmium. In the first experiment, when the soil sample data was 50, the prediction accuracy of the BPNN for cadmium before and after improvement was 75.95% and 89.56%, respectively. In the second experiment, when the soil sample data was 50, the prediction accuracy of the BPNN for cadmium before and after improvement was 77.99% and 89.85%, respectively. The improved BPNN has good prediction accuracy and can effectively predict the status of heavy metals in soil. The analysis in this article can provide scientific basis for the comprehensive prevention and control of heavy metals in regional soil, and also provide reference for the development of pollution-free agriculture and ensuring food safety.

Piecewise linear approximation for MILP leveraging piecewise convexity to improve performance

Piecewise linear approximation for MILP leveraging piecewise convexity to improve performance