Neural network-based ANC algorithms: a review

3.1. Topological structure

In the area of network structure improvement, Recurrent Neural Networks (RNNs) have emerged as the dominant architecture in neural network-based Active Noise Control (ANC) algorithms. Incorporating recurrent neurons into the network enhances the model’s memory capability, which offers distinct advantages for processing time-series data such as signals. Table 2 summarizes recent innovations in topological structures of such algorithms, including different network models and their respective advantages.

Zhang and Gan applied the Simplified Fuzzy Neural Network (SFNN) to ANC systems, reducing the number of parameters and achieving a computational complexity only one-eighth that of a traditional Fuzzy Neural Network (FNN). In experiments involving 100 Hz nonlinear harmonic noise, the SFNN outperformed the Multilayer Perceptron (MLP) in terms of noise reduction. This algorithm improves convergence speed while retaining nonlinear processing capability, making it well-suited for implementation on DSP platforms [8]. Fig. 1 shows the topology of the SFNN.

Building on this, they proposed an adaptive recurrent fuzzy neural network (RFNN) framework to address the issue of the static fuzzy neural network (SFNN) lacking dynamic memory capabilities and thus struggle to handle. The RFNN reduces the number of parameters by 40 % compared to the SFNN and increases the inference speed by 30 %. Simulation experiments demonstrate that in a noise scenario with a 100 Hz fundamental frequency plus 200 Hz harmonics, the RFNN achieves a 20 dB attenuation of the fundamental frequency and an 18 dB attenuation of the harmonics, yielding an 8 dB improvement over the SFNN [9]. Fig. 2 illustrates the topological structure of the RFNN, which introduces a recurrent structure based on the SFNN.

Fig. 1Structure of the SFNN

Guo et al. proposed the Reinforced Even-Mirrored Fourier Nonlinear Filter (REMFNL) and its channel-reduced variant, which employs a diagonal channel structure to accelerate the computation of cross terms. This approach addresses the limitations of traditional recursive filters, such as low control accuracy for mixed noise due to the absence of linear recursive components and the lack of guaranteed stability in recursive structures. In scenarios involving chaotic, saturated, or real measured acoustic paths, the method achieved a 2-12 dB reduction in NMSE compared to baseline methods. Additionally, the stability control led to a 50 % improvement in convergence speed under disturbances [10]. Huynh and Chang proposed an Adaptive Fuzzy Feedback Neural Network Controller (AFFNNC), which integrates fuzzy inference and feedback neural networks through a five-layer architecture, enabling the system to respond to nonlinear disturbances in real time. The output layer directly adjusts filter parameters using an adaptive algorithm without the need for pre-training, significantly reducing computational complexity. Under comparable conditions, its multiplication operations account for only 1 % of those required by a Functional Link Artificial Neural Network (FLANN) [11]. Zhang and Wang introduced the Deep ANC framework, which reformulates active noise control as a supervised learning problem. This framework employs a Convolutional Recurrent Network (CRN) to directly learn the complex spectral mapping from the reference signal to the anti-noise signal. Through large-scale, multi-condition training, it achieves end-to-end optimization. In untrained noise and acoustic environments with nonlinear distortion, the proposed method outperforms FxLMS by more than 6 dB in noise attenuation (NMSE) [12]. Zhang et al. employed a notch filter based on Nearest Neighbor Regression (NNR) as an adaptive controller, featuring a unique structure composed of an adaptive notch filter and a residual control loop. This architecture significantly enhances noise control performance for narrowband tonal noise. By integrating NNR filter banks and an adaptive gain controller, it demonstrates fast convergence and strong tracking capabilities in both ideal and real noise control experiments [13]. Huang et al. proposed an end-to-end nonlinear active noise control algorithm based on Deep Neural Network (DNN). The innovation of this method lies in leveraging the universal nonlinear approximation capability of DNN to simultaneously model the coupling effects of the acoustic channel transfer function and speaker saturation nonlinearity. By directly optimizing the generation of anti-noise signals, the approach avoids the error accumulation problems associated with the step-by-step modeling of nonlinear components in traditional method [14].

Fig. 2Structure of the RFNN

3.2. Functional link artificial neural networks

Improvements in Functional Link Artificial Neural Networks (FLANNs) have primarily focused on selecting various functional expansions of noise signals based on different application scenarios and designing tailored network architectures. These modifications aim to reduce computational complexity while enhancing the ability to process nonlinear noise. Fig. 3 illustrates the structure of a Functional Link Artificial Neural Network.

Table 3 summarizes various improvements related to functional-link artificial neural networks, primarily reflected in the incorporation of different nonlinear functions into the network. Das et al. proposed a multi-reference active noise control framework based on the Functional Link Artificial Neural Network (FLANN) to address the challenge of multi-source active control in nonlinear acoustic noise processes. By employing trigonometric function expansion, FLANN enhances nonlinear fitting capabilities while avoiding the computational burden associated with hidden layers in multilayer neural networks (MLANN) [15]. Patra and Kot introduced an improved FLANN structure called the Chebyshev Functional Link Artificial Neural Network (CFLANN). This method offers the advantage of maintaining dynamic system identification accuracy while overcoming the heavy computational load of traditional MLPs and addressing the lack of noise robustness validation in existing FLANN structures [16].

Fig. 3Internal structure of the functional link neural network

George and Panda proposed an innovative cascaded adaptive nonlinear filter structure, termed CLFLANN (Cascaded FLANN and Legendre). The core idea of this method is to cascade a FLANN filter with a Legendre Polynomial Network (LeNN), thereby combining the strengths of both architectures: the FLANN provides rich nonlinear mapping capabilities at the front end through trigonometric function, while the LeNN performs further nonlinear approximation at the back end using computationally efficient Legendre polynomials. This hybrid structure effectively addresses the performance and efficiency bottlenecks faced by existing single-structure NANC methods (such as the high computations of FLANN and the potentially limited representational power of LeNN) when dealing with complex nonlinear noise [17]. Zhao et al. proposed an adaptive FLANN filter based on convex combination, aiming to overcome the performance limitations caused by fixed step sizes in single FLANN filters. The approach runs two independent adaptive FLANN filters in parallel: one with a large step size for fast convergence, and the other with a small step size for low steady-state error. By using a dynamically adjusted convex combination parameter $\lambda \left(n\right)$ to blend the outputs of the two filters, the proposed algorithm simultaneously optimizes convergence speed and steady-state accuracy [18]. Luo et al. addressed the issue of coefficient dependency in the nonlinear parts of FLANN filters by inserting a correction filter before the trigonometric expansion, thereby enhancing the handling of cross terms [19]. Le et al. proposed a Generalized Exponential Function-Link Artificial Neural Network with Channel-Reduced Diagonal structure (GE-FLANN-CRD) filter. By introducing appropriate cross terms and adaptive exponential factors within the trigonometric expansion, this filter improves nonlinear processing capability in nonlinear active noise control (NANC) [20]. Kukde et al. proposed an Incremental Learning-based Adaptive Exponential Function-Link Network (AE-FLN) approach, a distributed active noise control method that addresses the challenges of existing centralized schemes (such as Volterra series and FLANN) which suffer from performance degradation caused by nonlinear acoustic paths (NPP/NSP) and excessive computational/communication overhead in large-scale deployments [21]. Yin et al. introduced a family of adaptive algorithms based on a Hermite Polynomial-based FLANN (HFLANN) and the Fractional Lower Order Moment (FLOM) criterion. This approach effectively addresses challenges faced by existing neural ANC (NANC) methods in Internet of Vehicles (IoV) scenarios, such as sensitivity to impulsive noise, high computational complexity, and limited structural flexibility [22]. Mylonas et al. proposed an innovative framework that couples a mixed-error second-order Functional Link Neural Network (FLNN) with first-order sound pressure prediction. Designed with a lightweight architecture, the framework overcomes challenges such as nonlinear acoustic path suppression and silent zone localization. It reduces computational cost by 36 % while improving harmonic attenuation at 48 Hz from 1 dB to 17 dB using the FxLMS algorithm [23].

Le and Mai. proposed an Efficiently Extended Functional Link Artificial Neural Network (EE-FLANN) controller to address a critical bottleneck in the application of Generalized Functional Link Artificial Neural Networks (GFLANNs): the rapid increase in computational complexity – scaling quadratically with the input memory length – when handling memory nonlinearities in nonlinear active noise control. By employing a symmetric cross-term truncation technique and a data-dependent partial update algorithm, EE-FLANN significantly reduces computational complexity by over 20 %, while maintaining noise suppression performance comparable to GFLANN in terms of NMSE metrics [24]. Zhu and Zhao et al. proposed a filter based on Laguerre Function Link Neural Networks (Laguerre-FLNNs) along with a corresponding Information-Theoretic Learning (ITL) adaptive algorithm. This method addresses two major challenges faced by traditional Functional Link Neural Networks (FLNNs) in handling long-impulse-response nonlinear active noise control (NANC) systems: the high computational burden caused by the use of Finite Impulse Response (FIR) filter structures, and the sharp performance degradation in non-Gaussian impulsive noise environments. By employing Laguerre series orthogonal basis functions to approximate the system’s dynamic characteristics, the method significantly reduces the required filter length. In addition, it incorporates entropy-based criteria and an online vector quantization (VQ) technique to maintain robustness comparable to complex ITL algorithms, while reducing computational complexity to a level close to that of lightweight Minimum Correntropy Criterion (MCC) algorithms. Ultimately, the proposed method achieves a well-balanced performance in complex scenarios involving long acoustic paths, strong nonlinearities, and impulsive noise – delivering outstanding noise reduction (ANR improved by 5-10 dB) and enhanced computational efficiency (MEE computation speed increased by a factor of four) [25]. To address the performance limitations of existing methods in impulsive noise environments and nonlinear path scenarios, Yin et al. proposed a q-gradient-based Functional Link Artificial Neural Network (FLANN) filtering method. By reconstructing gradient computation using Jackson derivatives, the approach significantly amplifies the gradient magnitude, thereby accelerating convergence and suppressing impulsive interference. Moreover, a time-varying q-strategy is introduced to dynamically adjust the gradient step size: large q-values are used during the initial phase to speed up convergence, while smaller $q$-values are applied in the steady state to reduce residual error [26].

3.3. Hidden layer improvements

In terms of hidden layer improvements, current trends focus on enhancing the precision of noise signal control, improving the accuracy of weight vector prediction, and accelerating convergence speed. Additionally, some studies have proposed innovative combinations of convolutional neural networks with fuzzy neural networks, indicating that neural network architectures will not be limited to recurrent networks but will integrate with other types of network structures Table 4 shows the summary of hidden layer improvements

Leng et al. proposed an optimization method for secondary path identification based on BP neural networks. This method addresses the limitations of traditional Finite Impulse Response (FIR) models, which struggle to accurately represent nonlinear factors in the secondary path, leading to insufficient modeling accuracy and reduced control performance [27]. Huynh and Chang introduced a Nonlinear Adaptive Feedback Neural Controller (NAFNC). The innovation of this approach lies in its use of a three-layer feedback neural network structure combined with an online learning mechanism, which overcomes the issues of offline training and slow convergence commonly seen in early neural network controllers [28]. Wu et al. proposed a multi-channel ANC algorithm based on a decoupled PID neural network, solving the dilemma in multi-channel ANC systems where nonlinear coupling and real-time performance cannot be simultaneously achieved [29]. Cha et al. designed a deep learning feedback ANC algorithm named DNoiseNet, which integrates causal convolutional layers, dilated convolution modules, RNNs, and fully connected layers. Through the collaboration of these modules, the algorithm effectively extracts noise features and generates anti-noise signals. Experiments demonstrate that this method achieves an average noise reduction of 23.30 dB on a dataset of 12 types of noise (including non-stationary construction noise and high-frequency aircraft noise), representing a 70 % performance improvement over baseline deep models such as LSTM, CNN, and RNN [30]. Li et al. proposed an error-free sensor active noise cancellation method based on Convolutional Fuzzy Neural Networks (C-FNN). This method employs convolutional neural networks (CNNs) to extract noise signal features and fit virtual error signals, addressing issues found in other methods such as weak feature extraction and poor convergence stability. The fuzzy neural network (FNN) adaptively adjusts filter weight coefficients [31]. Luo et al. introduced the GFANC-Bayes and GFANC-Kalman methods to address critical shortcomings of Selective Fixed Filter ANC (SFANC). Luo proposed the GFANC-Bayes and GFANC-Kalman methods to address critical shortcomings of Selective Fixed Filter ANC (SFANC). Traditional SFANC relies on a limited number of pre-trained control filters, which leads to a sharp decline in noise reduction performance when the input noise differs significantly from the training noise (such as dynamic traffic noise or aircraft noise in real scenarios. These methods employ a 1D CNN to predict the combination weights of sub-control filters. By incorporating Bayesian filtering and Kalman filtering, they improve the accuracy and robustness of weight vector prediction while maintaining low computational complexity [32], [33].

Singh et al. proposed an attention-based convolutional neural network (CNN) for ANC, aiming to address performance bottlenecks faced by traditional adaptive filters (such as the FxLMS algorithm) and existing deep learning ANC models in nonlinear distortion scenarios (especially speaker saturation effects). While conventional methods can handle linear noise, they lack robustness against nonlinear distortion; and although standard CNN models can learn complex mapping relationships, they struggle to dynamically focus on critical acoustic features. The proposed approach embeds an attention layer to enhance the CNN’s feature selection capability, enabling the model to adaptively focus on key spatiotemporal noise patterns, and combines piecewise linear functions to explicitly compensate for hardware nonlinearity [34]. Zhang et al. developed a time-domain Attention Recurrent Network (ARN) architecture that combines delay compensation training with a revised Overlap-Add (OLA) method to achieve a zero-latency deep ANC system overcoming causal constraints. This study addresses two core challenges with systematic solutions: 1) To tackle the high latency caused by frequency-domain methods requiring long frame lengths (> 20 ms) for frequency resolution, they designed a time-domain ARN processing framework that maintains excellent noise reduction performance even with ultra-short frame lengths (4 ms), achieving a 2.06 dB improvement in NMSE over frequency-domain CRN models; 2) To overcome the performance limitations of adaptive filtering (e.g., FxLMS) in nonlinear distortion environments, they employed an end-to-end ARN to directly model speaker nonlinear characteristics, significantly enhancing robustness. Experimental results demonstrate that the ARN’s noise prediction capability (compensating a 15 ms delay with only a 0.95 dB performance loss) combined with the optimized frame processing of the revised OLA method ultimately achieves a negative algorithmic delay of –2 ms, with performance degradation controlled within 0.47 dB [35].

4.1. Loss function

The loss functions listed below can enhance noise reduction performance under different noise environments while also reducing computational complexity. It is essential to select them flexibly based on the application context of the algorithm. Table 5 presents various loss functions used in such algorithms and their respective advantages.

Most neural network-based ANC algorithms adopt Eq. (1) as the loss function:

In a hybrid narrowband active noise control (HNANC) system under multi-noise environments, Padhi et al. introduced a modified loss function Eq. (2):

where, $y_{pc}^{}\left(j\right)$ represents the purely feedforward-correlated noise component separated from the total error. This loss function, which precisely targets the relevant error, significantly improves the convergence accuracy of the feedforward path [36]. Yin et al. defined the loss function Eq. (3) based on the Fractional Lower Order Moment (FLOM) criterion:

The functions above can effectively enhance the algorithm’s robustness and convergence performance when dealing with non-Gaussian noise and nonlinear systems [22]. Shi et al. introduced Eq. (4) as the loss function:

with a forgetting factor $\lambda \in \left(\mathrm{0,1}\right]$ for Model-Agnostic Meta-Learning (MAML) by incorporating a forgetting factor into the traditional mean squared error function. This approach forces the optimizer to focus on the transient convergence phase during system initialization, significantly shortening the transition time for adaptive algorithms to reach stable noise reduction[37]. Zhu et al. proposed the Fractional-order Ascending Maximum Mixed-Correntropy Criterion (FAMMCC) algorithm, which applies correntropy to Functional Link Artificial Neural Networks (FLANNs) for nonlinear active noise control. The loss function is represented as Eq. (5):

The loss function maximizes correntropy to optimize filter parameters. This approach outperforms traditional algorithms in handling non-Gaussian noise and enhances adaptability to complex noise environments [38], [25]. Jiang et al. introduced a frequency-domain loss function defined by the Euclidean distance between the ideal and generated anti-noise signals, which is represented as Eq. (6):

Compared to time-domain MSE, this formulation better matches the acoustic characteristics and avoids the need for phase alignment, while significantly reducing computational complexity [39].

The loss functions listed above serve different purposes – some are designed to enhance noise reduction performance under varying noise environments, while others aim to reduce computational complexity. It is important to select them flexibly based on the specific application context of the algorithm.

4.2. Weight update algorithms

Improvements in weight update algorithms primarily aim to reduce computational complexity, enhance the accuracy of weight control, accelerate convergence speed, overcome suboptimal solutions, and improve the generalization capability of the neural network model. Table 6 summarizes the advancements in weight update algorithms.

Zhou et al. proposed a weight update algorithm based on SPSA, which requires only two measurements of the loss function to obtain an approximate gradient. This allows for simultaneous updating of all weights in the RFNN, greatly simplifying the derivation process of the adaptive weight algorithm and completely avoiding the need for differentiating the secondary path, thereby accelerating the training speed of the neural network [40]. Bambang proposed a nonlinear active noise control method using recursive fuzzy neural networks based on Kalman filtering. By combining the Extended Kalman Filter (EKF) with the Adjoint Method, this approach addresses the bottleneck of gradient computation lag and convergence efficiency in real-time adaptive control of dynamic nonlinear systems [41].

Sasaki et al. proposed an adaptive learning rate neural network algorithm incorporating an immune feedback law, aiming to improve noise control performance and reduce training time. This algorithm introduces the feedback mechanism of the immune system into the learning rate adjustment of the neural network: when the weight change trend is stable, the learning rate is increased (to accelerate convergence); when the change oscillates, the learning rate is decreased (to avoid divergence) [42]. Krukowicz employed Genetic Algorithm (GA) to train neural networks, effectively overcoming the issue where traditional gradient-based backpropagation (BP) algorithms may converge to suboptimal solutions in multimodal cost functions [43]. Walia and Ghosh proposed an Active Noise Control (ANC) system that optimizes the weights of a hybrid Functional Link Artificial Neural Network (FLANN) and Finite Impulse Response (FIR) filter using the Firefly Algorithm (FA). Their approach addresses two major challenges in nonlinear ANC systems: the tendency of gradient-based optimization to gradient-based optimization to get trapped in local convergence and the premature convergence of heuristic algorithms [44]. Shi et al. introduced an improved Model-Agnostic Meta-Learning (MAML) algorithm, which incorporates a forgetting-weighted loss function and first-order approximate gradient updates. The proposed MAML algorithm generates initial control filter weights with generalization ability, fundamentally resolving the contradiction between computational efficiency and scenario adaptability in traditional methods [37]. Liang et al. proposed the Optimized Decision Feedback-FLANN (ODF-FLANN) structure based on the traditional Functional Link Artificial Neural Network (FLANN), addressing the issues of delayed convergence or even divergence in conventional fixed learning rate algorithms when faced with sudden noise changes [45]. Leng et al. employed the Bayesian Regularization algorithm (trainbr) based on the Levenberg-Marquardt algorithm to train the weights of each layer in a BP neural network, enhancing the network’s generalization ability [27]. Luo et al. proposed an adaptive labeling mechanism that minimizes the error signal using the LMS algorithm to obtain an optimal weight vector, which is then converted into a binary weight vector serving as labels for the training noise. This enables automatic labeling of the training dataset and reduces manual workload [46]. The training algorithms listed above each have distinct advantages in handling complex noise signals and should be applied according to specific application scenarios.

4.3. Other training methods

Wuraola and Patel proposed a criterion-based small-batch noise injection method to accelerate the convergence of neural network training. This method adaptively adjusts the level of noise injected into the network weights during training based on criteria such as absolute error and error variation rate, thereby avoiding the pitfalls of local minima [47]. Zhang and Wang introduced a deep ANC framework that, for the first time, reformulates active noise control as a supervised learning task. By incorporating a physically embedded loss function and a dual-modality training strategy, the framework addresses the performance degradation problem of traditional methods under strong nonlinear distortion [48]. Luo et al. proposed a novel unsupervised learning method for training 1D convolutional neural networks (1D CNNs) in GFANC systems. By integrating the coprocessor and real-time controller into an end-to-end differentiable ANC system, and using cumulative squared error signals as the loss to update network parameters, this approach eliminates the need for labeled data, reduces training costs, and mitigates labeling bias, while achieving strong noise reduction performance in real noise experiments [49]. Luo et al. further proposed a CNN-based zero-latency selective fixed-filter active noise control method (CNN-SFANC), which combines neural networks with adaptive filtering. This algorithm utilizes a neural network model with only 0.25M parameters, working in tandem with the filter, making it suitable for real-time hardware deployment. It achieves zero-latency noise cancellation and can effectively cope with dynamically changing noise [50].

5.1. Summary

This paper systematically reviews the research progress of neural network-based ANC algorithms, with a focus on two core aspects: network architectures and training methods.

At the network structure level, innovations are mainly reflected in topological structure innovations, various Functional Link Artificial Neural Networks (FLANNs), and the deep optimization of hidden layers. Innovations in topological structures, such as the introduction of recurrent mechanisms, endow models with the temporal dependency and memory capabilities required to handle time-varying noise. However, these enhancements come at the cost of increased training complexity and reduced real-time performance due to the structural complexity. FLANN offers the advantage of structural simplicity and typically lower computational complexity compared to multilayer perceptrons (MLPs). By introducing functional expansions, it gains nonlinear capabilities and are relatively easy to deploy on hardware. Nevertheless, its expressive power is constrained by the choice and order of the basis functions used. The deep optimization of hidden layers is primarily achieved through the introduction of deep neural networks, which enable end-to-end learning of complex mappings thanks to their powerful feature extraction and nonlinear modeling capabilities. This approach is well-suited for complex scenarios but typically requires the support of a large amount of training data.

At the training method level, innovations primarily focus on the optimization design of loss functions and the diversification of weight update algorithms. Research on the loss function has moved beyond the limitations of traditional Mean Squared Error (MSE), proposing various improved solutions tailored to specific noise characteristics and system requirements. For example, loss functions defined directly in the frequency domain better align with acoustic properties, help mitigate phase alignment issues, and reduce computational burden. The core objective of the weight update algorithm is to address the bottleneck in gradient computation, enhance convergence speed and accuracy, and avoid local optima. Representative progress includes the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm, which eliminate reliance on secondary path models and their derivatives, significantly simplifying the online training process for complex networks. Meanwhile, other efficient training strategies are also being continuously explored. Although significant progress has been made, current research still faces a prominent contradiction between theory and application: although training paradigms can deliver superior performance, their high computational cost makes it difficult to meet the real-time constraints of embedded devices. Meanwhile, lightweight methods (such as approximate gradient strategies) are often limited by insufficient convergence accuracy and weakened generalization capability. More critically, existing training mechanisms still heavily rely on offline pre-training or idealized assumptions. They lack adaptability to uncontrollable dynamic factors in open environments, such as sudden noise bursts, time-varying acoustic paths, and actuator nonlinear drift. As a result, these algorithms often suffer performance degradation when applied in actual deployment. It is imperative that future research resolves these conflicts by exploring computationally efficient and highly adaptive training mechanisms, thereby advancing neural network-based ANC technology from theoretical advantages toward broader practical applications.

5.2. Future research directions

Based on the summary of current research and the challenges faced, and in light of recent advances in the field of artificial intelligence, future studies on neural network-based ANC can focus on the following key directions:

1) Efficient and Lightweight Network Architectures: Develop more computationally efficient and compact specialized network architectures (such as applying techniques model pruning, quantization, and knowledge distillation to ANC networks) to meet the stringent resource constraints of embedded devices and real-time systems; explore the potential of the novel and efficient architectures (such as Transformer and State Space Model (SSM)) in modeling long-range noise dependencies, striking a better balance between noise suppression performance and computational complexity; and design adaptive network architectures capable of dynamically adjusting model complexity and resource consumption in response to real-time noise characteristics.

2) More Robust and Adaptive Training Strategies: Develop more efficient online learning and meta-learning algorithms that enable neural networks to rapidly adapt to unknown noise source characteristics, time-varying acoustic paths (such as those caused by opening/closing doors and windows or human movement), and nonlinear hardware features (e.g., speaker aging); explore the application potential of unsupervised and self-supervised learning paradigms in ANC to reduce dependence on large amounts of labeled data (e.g., high-precision error signals).

3) Hardware-Friendly Algorithms and Deployment: Optimize neural network models and training algorithms based on the characteristics of specific hardware platforms (such as DSPs and FPGAs); develop dedicated neural network parameter compression and speedup techniques to promote the deployment of high-performance neural network-based ANC in practical applications such as industrial equipment and consumer electronics.

In summary, neural network-based ANC algorithms demonstrate tremendous potential in addressing the challenges of nonlinear noise control. With continued advances in neural network theory, optimization algorithms, and computing hardware, along with the integration of domain-specific knowledge and emerging AI technologies, this field is poised to achieve breakthroughs in algorithm performance, computational efficiency, system robustness, and engineering applicability. These developments will provide more effective active noise reduction solutions for a wider range of real applications.