Dynamic Neural Network Research Articles

NotFYCEX: A Simulation Based Price Prediction and Notification System Using Continuous Machine Learning Method

This research study presents NotFyCEX - a price notification systems model based on Internet of Things (IoT) and Blockchain technology for reporting important trends in a Cryptocurrency Exchange (CRYPTEX) market. The system is simulated in near real time using a co-simulator approach including web-based PHP server-side application for emulating price fluctuations, a dynamic neural network model application integrated within the MATLAB/SIMULINK software environment and ArduinoUNO hardware for continual physical signalling/alerting. Dynamic simulation results showed exact matches between synthesized price state representations and the predicted pattern states. Thus, we consider NotFyCEX a novel effort that can effectively serve as a notification and price prediction system to the end-user or cryptocurrency trader in a given CRYPTEX market.

An Adaptive and Dynamical Neural Network for Machine Remaining Useful Life Prediction

Recently, many neural networks have been proposed for machine remaining useful life (RUL) prediction. However, most network architectures of existing approaches are fixed. Since the sequential information depends on the input data and distributes differently, these fixed networks which cannot be dynamically adjusted according to the input data, may not be able to capture these sequential information well, resulting sub-optimal performances. To mitigate this issue, we propose an adaptive and dynamical neural network (AdaNet), which can dynamically adjust its architecture according to the input data. Neural network is generally determined by kernel size, depth and channel size. In this paper, we aim to enable our proposed AdaNet to adjust its kernel size and channel size dynamically. Firstly, we explore to adapt the deformable convolution to time series data, which allows the convolutional kernel to change according to the feature map. With this deformable convolution, the convolutional kernels in AdaNet become adjustable, which is beneficial to fully exploit the sequential information in time series data, leading to accurate RUL prediction. Additionally, a channel selection module is devised, which can selectively activate the feature channel according to the input, further improving the performance of our AdaNet. Extensive experiments have been carried out on the C-MAPSS dataset, demonstrating that our proposed AdaNet achieves state-of-the-art performances.

Automatic tuning of PID controllers using deep recurrent neural networks with pruning based on tracking error

Although PID controllers are common in industry, they are often poorly tuned; especially, in uncertain environments. Modern industries, with increasing complexity, motivate us to employ new intelligent methods in order to extend PID controllers beyond their usual capabilities. In this paper, an advanced machine learning scheme is utilized to improve PID controllers; for the first time, a deep dynamic neural network is employed to tune online the parameters of the traditional PID controller in order to overcome the effects of uncertainties in the closed-loop control system. To reduce the computational burden of deep recurrent neural network, a novel structural learning technique is applied to optimize the configuration. Unlike existing pruning methods, the network is pruned based on the values of neurons and the total value of the corresponding layer. Simulation of a benchmark CSTR system demonstrate that the proposed scheme performs more efficiently compared to a shallow network tuner, in the presence of uncertainties.

DYNAP-SE2: a scalable multi-core dynamic neuromorphic asynchronous spiking neural network processor

With the remarkable progress that technology has made, the need for processing data near the sensors at the edge has increased dramatically. The electronic systems used in these applications must process data continuously, in real-time, and extract relevant information using the smallest possible energy budgets. A promising approach for implementing always-on processing of sensory signals that supports on-demand, sparse, and edge-computing is to take inspiration from biological nervous system. Following this approach, we present a brain-inspired platform for prototyping real-time event-based spiking neural networks. The system proposed supports the direct emulation of dynamic and realistic neural processing phenomena such as short-term plasticity, NMDA gating, AMPA diffusion, homeostasis, spike frequency adaptation, conductance-based dendritic compartments and spike transmission delays. The analog circuits that implement such primitives are paired with a low latency asynchronous digital circuits for routing and mapping events. This asynchronous infrastructure enables the definition of different network architectures, and provides direct event-based interfaces to convert and encode data from event-based and continuous-signal sensors. Here we describe the overall system architecture, we characterize the mixed signal analog-digital circuits that emulate neural dynamics, demonstrate their features with experimental measurements, and present a low- and high-level software ecosystem that can be used for configuring the system. The flexibility to emulate different biologically plausible neural networks, and the chip’s ability to monitor both population and single neuron signals in real-time, allow to develop and validate complex models of neural processing for both basic research and edge-computing applications.

Wastewater-based epidemiology for COVID-19 using dynamic artificial neural networks

Global efforts in vaccination have led to a decrease in COVID-19 mortality but a high circulation of SARS-CoV-2 is still observed in several countries, resulting in some cases of severe lockdowns. In this sense, wastewater-based epidemiology remains a powerful tool for supporting regional health administrations in assessing risk levels and acting accordingly. In this work, a dynamic artificial neural network (DANN) has been developed for predicting the number of COVID-19 hospitalized patients in hospitals in Valladolid (Spain). This model takes as inputs a wastewater epidemiology indicator for COVID-19 (concentration of RNA from SARS-CoV-2 N1 gene reported from Valladolid Wastewater Treatment Plant), vaccination coverage, and past data of hospitalizations. The model considered both the instantaneous values of these variables and their historical evolution. Two study periods were selected (from May 2021 until September 2022 and from September 2022 to July 2023). During the first period, accurate predictions of hospitalizations (with an overall range between 6 and 171) were favored by the correlation of this indicator with N1 concentrations in wastewater (r = 0.43, p < 0.05), showing accurate forecasting for 1 day ahead and 5 days ahead. The second period's retraining strategy maintained the overall accuracy of the model despite lower hospitalizations. Furthermore, risk levels were assigned to each 1 day ahead prediction during the first and second periods, showing agreement with the level measured and reported by regional health authorities in 95 % and 93 % of cases, respectively. These results evidenced the potential of this novel DANN model for predicting COVID-19 hospitalizations based on SARS-CoV-2 wastewater concentrations at a regional scale. The model architecture herein developed can support regional health authorities in COVID-19 risk management based on wastewater-based epidemiology.

A workload identification method of industrial robot combining dynamic model and convolutional neural network

The motion joint system of industrial robot has obvious nonlinear characteristics, high dimensional running data and limited number of experimental samples. If mature neural network algorithm is used for identifying the workload of robots, it is easy to have over-learning problems, which seriously restricts the generalization ability of load identification method. In this paper, a load identification method combining the dynamic model of industrial robots with the neural network data model is proposed. A UR5 robot is used for carrying out multiple dynamic load testings to verify the effectiveness of the proposed identification method. Firstly, the workload identification by CNN algorithm is given, and the influence of parameters of prediction model and different neutral network are analyzed. Then the classical dynamic model of industrial robots with multi-degrees of freedom is established. The identified workload by dynamic model is also analyzed. At last, the deterministic information such as velocity and displacement is extracted from the calculation results of the dynamic model as the initial anchoring value. Then convolutional neural network is applied for compensating the residual highly nonlinear information. An improved mixing combination method is also proposed. This method can effectively deal with the interaction of different types of information in the data, and preliminarily cooperate the dynamic model and convolutional neural network. This provides a basic framework and method for solving the problem of parameter identification in multi-degree-of-freedom systems with small samples.

Robot skill learning system of multi-space fusion based on dynamic movement primitives and adaptive neural network control

This article develops a robot skill learning system with multi-space fusion, simultaneously considering motion/stiffness generation and trajectory tracking. To begin with, surface electromyography (sEMG) signals from the human arm is captured based on the MYO armband to estimate endpoint stiffness. Gaussian Process Regression (GPR) is combined with dynamic movement primitive (DMP) to extract more skills features from multi-demonstrations. Then, the traditional DMP formulation is improved based on the Riemannian metric to encode the robot’s quaternions with non-Euclidean properties. Furthermore, an adaptive neural network (NN)-based finite-time admittance controller is designed to track the trajectory generated by the motion model and to reflect the learned stiffness characteristics. In this controller, a radial basis function neural network (RBFNN) is employed to compensate for the uncertainty of the robot dynamics. Finally, experimental validation is conducted using the ROKAE collaborative robot, confirming the effectiveness of the proposed approach. In summary, the presented framework is suitable for human-robot skill transfer method that require simultaneous consideration of position and stiffness in Euclidean space, as well as orientation on Riemannian manifolds.

Dynamic load prediction of charging piles for energy storage electric vehicles based on Space-time constraints in the internet of things environment

Abstract This paper puts forward the dynamic load prediction of charging piles of energy storage electric vehicles based on time and space constraints in the Internet of Things environment, which can improve the load prediction effect of charging piles of electric vehicles and solve the problems of difficult power grid control and low power quality caused by the randomness of charging loads in time and space. After constructing a traffic road network model based on the Internet of Things, a travel chain model with different complexity and an electric vehicle charging model, the travel chain is randomly extracted. With the shortest travel time as a constraint, combined with the traffic road network model based on the Internet of Things, the travel route and travel time are determined. According to the State of Charge (SOC) and the travel destination, the location and charging time of the energy storage electric vehicle charging pile are determined. After obtaining the time-space distribution information of the energy storage electric vehicle charging pile at different times and in different regions, it is used as the input of the deep multi-step time-space dynamic neural network, and the network output is the dynamic electric vehicle charging pile. The experimental results show that this method can realize the dynamic load prediction of electric vehicle charging piles. When the number of stacking units is 11, the indexes of Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) are the lowest and the index of R 2 is the largest. The load of charging piles in residential areas and work areas exists in the morning and evening peak hours, while the load fluctuation of charging piles in other areas presents a decentralized change law; The higher the complexity of regional traffic network, the greater the load of electric vehicle charging piles in the morning rush hour.

Cognitive training and brain stimulation in patients with cognitive impairment: a randomized controlled trial

BackgroundRepeated sessions of training and non-invasive brain stimulation have the potential to enhance cognition in patients with cognitive impairment. We hypothesized that combining cognitive training with anodal transcranial direct current stimulation (tDCS) will lead to performance improvement in the trained task and yield transfer to non-trained tasks.MethodsIn our randomized, sham-controlled, double-blind study, 46 patients with cognitive impairment (60–80 years) were randomly assigned to one of two interventional groups. We administered a 9-session cognitive training (consisting of a letter updating and a Markov decision-making task) over 3 weeks with concurrent 1-mA anodal tDCS over the left dorsolateral prefrontal cortex (20 min in tDCS, 30 s in sham group). Primary outcome was trained task performance (letter updating task) immediately after training. Secondary outcomes included performance in tasks testing working memory (N-back task), decision-making (Wiener Matrices test) and verbal memory (verbal learning and memory test), and resting-state functional connectivity (FC). Tasks were administered at baseline, at post-assessment, and at 1- and 7-month follow-ups (FU). MRI was conducted at baseline and 7-month FU. Thirty-nine participants (85%) successfully completed the intervention. Data analyses are reported on the intention-to-treat (ITT) and the per-protocol (PP) sample.ResultsFor the primary outcome, no difference was observed in the ITT (β = 0.1, 95%-CI [− 1.2, 1.3, p = 0.93] or PP sample (β = − 0.2, 95%-CI [− 1.6, 1.2], p = 0.77). However, secondary analyses in the N-back working memory task showed that, only in the PP sample, the tDCS outperformed the sham group (PP: % correct, β = 5.0, 95%-CI [− 0.1, 10.2], p = 0.06, d-prime β = 0.2, 95%-CI [0.0, 0.4], p = 0.02; ITT: % correct, β = 3.0, 95%-CI [− 3.9, 9.9], p = 0.39, d-prime β = 0.1, 95%-CI [− 0.1, 0.3], p = 0.5). Frontoparietal network FC was increased from baseline to 7-month FU in the tDCS compared to the sham group (pFDR < 0.05). Exploratory analyses showed a correlation between individual memory improvements and higher electric field magnitudes induced by tDCS (ρtDCS = 0.59, p = 0.02). Adverse events did not differ between groups, questionnaires indicated successful blinding (incidence rate ratio, 1.1, 95%-CI [0.5, 2.2]).ConclusionsIn sum, cognitive training with concurrent brain stimulation, compared to cognitive training with sham stimulation, did not lead to superior performance enhancements in patients with cognitive impairment. However, we observed transferred working memory benefits in patients who underwent the full 3-week intervention. MRI data pointed toward a potential intervention-induced modulation of neural network dynamics. A link between individual performance gains and electric fields suggested dosage-dependent effects of brain stimulation. Together, our findings do not support the immediate benefit of the combined intervention on the trained function, but provide exploratory evidence for transfer effects on working memory in patients with cognitive impairment. Future research needs to explore whether individualized protocols for both training and stimulation parameters might further enhance treatment gains.Trial registrationThe study is registered on ClinicalTrials.gov (NCT04265378). Registered on 7 February 2020. Retrospectively registered.

A new multiregional carbon emissions forecasting model based on a multivariable information fusion mechanism and hybrid spatiotemporal graph convolution network

Developing scientific and effective carbon emissions reduction policies relies heavily on precise carbon emission trend prediction. The existing complex spatiotemporal correlation and diverse range of influencing factors associated with multi-regional carbon emissions pose significant challenges to accurately modeling these trends. Under this constraint, this study is inspired by graph learning to establish a hybrid dynamic and static graph-based regional carbon emission network framework, which introduces a novel research standpoint for investigating short-term carbon emissions prediction (CEP). Specifically, a parallel framework of attribute-augmented dynamic multi-modal graph convolutional neural networks (ADMGCN) and temporal convolutional networks with adaptive fusion multi-scale receptive fields (AFMRFTCN) is proposed. The proposed model is evaluated against nineteen state-of-the-art models using daily carbon emission data from 30 regions in China, demonstrating its effectiveness in accurately predicting the trends of multi-regional carbon emissions. Conclusions are drawn as follows: First, especially in regions with marked periodicity, compared with the best baseline model, the mean absolute percentage error (MAPE) of our model is reduced by 20.19%. Second, incorporating graph convolutional neural networks (GCNs) with dynamic and static graphs is advantageous in extracting the spatial features of China's carbon emission network, which are influenced by geographical, economic, and industrial factors. Third, the parallel ADMGCN-AFMRFTCNs framework effectively captures the influence of external information on carbon emissions while mitigating the issue of low prediction accuracy resulting from univariate information. Fourth, the analysis reveals significant differences in the short-term (30-day) growth rate of carbon emissions among different regions. For example, Henan exhibits the highest growth rate (37.38%), while Guizhou has the lowest growth rate (−7.46%). It is valuable for policymakers and stakeholders seeking to identify regions with distinct emission patterns and prioritize mitigation efforts accordingly.

Trajectory tracking control of autonomous vehicles based on Lagrangian neural network dynamics model

The autonomous vehicles make decisions and plans based on the environmental perception and generate the target command of the control layer. The vehicle dynamics model is an important factor that affects the vehicle control. The dynamic mechanism model has strong interpretability and good stability. However, in extreme conditions, the model accuracy is reduced due to the tire entering the nonlinear region. The data-driven dynamic model achieves high modeling accuracy. However, due to the lack of physical constraints and rationality in the data-driven models, the interpretability and stability of the control is reduced, which in turn increases the unpredictable risk in the driving process. This paper innovatively proposes a deep Lagrangian neural network dynamics model (DeLaN) for autonomous vehicles based on the Lagrangian mechanics and uses a neural network to encode the differential equations. This not only retains the interpretability of the physical model but also makes full use of the learning ability and fitting ability of the neural network to effectively capture the complex dynamic characteristics of the vehicle. To improve the robustness of the control system, this work uses DeLaN as feed-forward control and preview error feedback control to form a closed loop of trajectory tracking control for autonomous vehicles. The experimental results show that the trajectory tracking error of the proposed DeLaN is significantly reduced, the yaw stability and comfort are significantly improved, good longitudinal and lateral cooperative control performance is achieved, and the physical rationality of the neural network is also improved. Therefore, the proposed DeLaN has important engineering application value.

Stability Analysis of Anti-Periodic Solutions for Cohen–Grossberg Neural Networks with Inertial Term and Time Delays

This work is dedicated to exploring the globally exponential stability of anti-periodic solutions in inertial CGNNs that incorporate time delays. This is based on a strategic variable substitution to transform the complex system into a first-order differential equation. By leveraging the Lyapunov functional and demonstrating uniformly converging properties, we establish sufficient conditions that guarantee the existence and global exponential stability of anti-periodic solutions for the system. Finally, examples are presented to illustrate the effectiveness of the obtained theoretical results. This work contributes significantly to enhancing our understanding of the stability dynamics in neural networks with time delays and provides valuable insights for applications across various fields.

Short-term wind speed prediction based on improved Hilbert–Huang transform method coupled with NAR dynamic neural network model

Wind energy, as a renewable energy source, offers the advantage of clean and pollution-free power generation. Its abundant resources have positioned wind power as the fastest-growing and most widely adopted method of electricity generation. Wind speed stands as a key characteristic when studying wind energy resources. This study primarily focuses on predictive models for wind speed in wind energy generation. The intense intermittency, randomness, and uncontrollability of wind speeds in wind power generation present challenges, leading to high development costs and posing stability challenges to power systems. Consequently, scientifically forecasting wind speed variations becomes imperative to ensure the safety of wind power equipment, maintain grid integration of wind power, and ensure the secure and stable operation of power systems. This holds significant guiding value and significance for power production scheduling institutions. Due to the complexity of wind speed, scientifically predicting its fluctuations is crucial for ensuring the safety of wind power equipment, maintaining wind power integration systems, and ensuring the secure and stable operation of power systems. This research aims to enhance the accuracy and stability of wind speed prediction, thereby reducing the costs associated with wind power generation and promoting the sustainable development of renewable energy. This paper utilizes an improved Hilbert–Huang transform (HHT) using complementary ensemble empirical mode decomposition (CEEMD) to overcome issues in the traditional empirical mode decomposition (EMD) method, such as component mode mixing and white noise interference. Such an approach not only enhances the efficiency of wind speed data processing but also better accommodates strong stochastic and nonlinear characteristics. Furthermore, by employing mathematical analytical methods to compute weights for each component, a dynamic neural network model is constructed to optimize wind speed time series modeling, aiming for a more accurate prediction of wind speed fluctuations. Finally, the optimized HHT-NAR model is applied in wind speed forecasting within the Xinjiang region, demonstrating significant improvements in reducing root mean square errors and enhancing coefficient of determination. This model not only showcases theoretical innovation but also exhibits superior performance in practical applications, providing an effective predictive tool within the field of wind energy generation.

Robust state of charge estimation of LiFePO4 batteries based on Sage_Husa adaptive Kalman filter and dynamic neural network

Robust and accurate state of charge estimation for LiFePO4 batteries has tremendous significance, since they are constituted the basis of reliable operation for battery management system. However, the nature flat voltage curve poses challenges in both the accuracy and robustness of state of charge estimation. Here, we present a state of charge estimation framework for LiFePO4 batteries with integrating physics calculation, adaptive Kalman filter, and machine learning, where nonlinearity of flat voltage curve can be captured with strong robustness by optimized machine learning. To address the parameter sensitivity problem for dynamic neural network, the sine cosine algorithm is adopted to obtain the optimal parameters. Then, the offline training model is established based on nonlinear autoregressive models with exogenous inputs and sine cosine algorithm, and the adaptive Kalman filter is selected for online estimation. The observed data from 26,650 and 18,650 LiFePO4 batteries at 25 and 40 °C has been used to verify the accuracy and robustness of the proposed method under four working conditions. Compared to the existing methods, the proposed method can achieve strong robustness and higher accuracy in state of charge estimation with a maximum relative error below 2 %.

Control of a Active Filter Using Dynamic Neural Networks

At this paper the “dynamic multilayer perceptron” (MLP) neural network has been applied to the control of an active power filter (APF). The objective is developing a new suitable control technique by APF’s for compensation of harmonic distortion present in nonlinear loads current by electric power circuits. The strategy has been extracting the instantaneous value of the fundamental harmonic from the load current by means of this artificial neural network (ANN) topology. A previous training with waveforms distorted by harmonics up to the 29th order showed to be enough for a high accuracy, working with typical nonlinear loads. By using this fundamental harmonic, the shunt APF reference distortion signal is obtained. This has been applied, at simulation, to a practical case of a power circuit containing an AC regulator and a series RL load. The results show the ability of this type of ANN to supply the APF with the reference signal necessary for its control.

A Dynamic Weights-Based Wavelet Attention Neural Network for Defect Detection.

Automatic defect detection plays an important role in industrial production. Deep learning-based defect detection methods have achieved promising results. However, there are still two challenges in the current defect detection methods: 1) high-precision detection of weak defects is limited and 2) it is difficult for current defect detection methods to achieve satisfactory results dealing with strong background noise. This article proposes a dynamic weights-based wavelet attention neural network (DWWA-Net) to address these issues, which can enhance the feature representation of defects and simultaneously denoise the image, thereby improving the detection accuracy of weak defects and defects under strong background noise. First, wavelet neural networks and dynamic wavelet convolution networks (DWCNets) are presented, which can effectively filter background noise and improve model convergence. Second, a multiview attention module is designed, which can direct the network attention toward potential targets, thereby guaranteeing the accuracy for detecting weak defects. Finally, a feature feedback module is proposed, which can enhance the feature information of defects to further improve the weak defect detection accuracy. The DWWA-Net can be used for defect detection in multiple industrial fields. Experiment results illustrate that the proposed method outperforms the state-of-the-art methods (mean precision: GC10-DET: 6.0%; NEU: 4.3%). The code is made in https://github.com/781458112/DWWA.

A Novel Method to Identify Mild Cognitive Impairment Using Dynamic Spatio-Temporal Graph Neural Network.

Resting-state functional magnetic resonance imaging (rs-fMRI) has been widely used in the identification of mild cognitive impairment (MCI) research, MCI patients are relatively at a higher risk of progression to Alzheimer's disease (AD). However, almost machine learning and deep learning methods are rarely analyzed from the perspective of spatial structure and temporal dimension. In order to make full use of rs-fMRI data, this study constructed a dynamic spatiotemporal graph neural network model, which mainly includes three modules: temporal block, spatial block, and graph pooling block. Our proposed model can extract the BOLD signal of the subject's fMRI data and the spatial structure of functional connections between different brain regions, and improve the decision-making results of the model. In the study of AD, MCI and NC, the classification accuracy reached 83.78% outperforming previously reported, which manifested that our model could effectively learn spatiotemporal, and dynamic spatio-temporal method plays an important role in identifying different groups of subjects. In summary, this paper proposed an end-to-end dynamic spatio-temporal graph neural network model, which uses the information of the temporal dimension and spatial structure in rs-fMRI data, and achieves the improvement of the three classification performance among AD, MCI and NC.

Event-Triggered Adaptive Antidisturbance Switching Control for Switched Systems With Dynamic Neural Network Disturbance Modeling.

In this article, a dynamic event-triggered adaptive antidisturbance (ETAAD) switching control strategy is proposed for switched systems subject to multisource disturbances. The disturbances are divided into two categories: the available unmodeled disturbance and the unavailable dynamic neural network modeled disturbance. First, a dynamic ET criterion is set based on the system state. Then, a novel dynamic ETA disturbance estimator is introduced to observe the modeled disturbance. Furthermore, according to the ET rule and adaptive disturbance observer, a switched controller is designed. Next, under the controller and switching criterion with the average dwell time limitation, sufficient conditions are given to force the switched systems to realize multisource disturbance suppression (DS), trajectory tracking, and communication resource (CR) saving simultaneously. Meanwhile, the Zeno phenomenon may be caused by the ET rule being excluded. In addition, the presented ETAAD approach is also applicable to the nonswitched systems case. Finally, a simulation case is given to validate the effectiveness of the dynamic ETAAD switching control method.

Neural Networks for Portfolio Analysis With Cardinality Constraints.

Portfolio analysis is a crucial subject within modern finance. However, the classical Markowitz model, which was awarded the Nobel Prize in Economics in 1991, faces new challenges in contemporary financial environments. Specifically, it fails to consider transaction costs and cardinality constraints, which have become increasingly critical factors, particularly in the era of high-frequency trading. To address these limitations, this research is motivated by the successful application of machine learning tools in various engineering disciplines. In this work, three novel dynamic neural networks are proposed to tackle nonconvex portfolio optimization under the presence of transaction costs and cardinality constraints. The neural dynamics are intentionally designed to exploit the structural characteristics of the problem, and the proposed models are rigorously proven to achieve global convergence. To validate their effectiveness, experimental analysis is conducted using real stock market data of companies listed in the Dow Jones Index (DJI), covering the period from November 8, 2021 to November 8, 2022, encompassing an entire year. The results demonstrate the efficacy of the proposed methods. Notably, the proposed model achieves a substantial reduction in costs (which combines investment risk and reward) by as much as 56.71% compared with portfolios that are averagely selected.

Information cascade prediction of complex networks based on physics-informed graph convolutional network

Cascade prediction aims to estimate the popularity of information diffusion in complex networks, which is beneficial to many applications from identifying viral marketing to fake news propagation in social media, estimating the scientific impact (citations) of a new publication, and so on. How to effectively predict cascade growth size has become a significant problem. Most previous methods based on deep learning have achieved remarkable results, while concentrating on mining structural and temporal features from diffusion networks and propagation paths. Whereas, the ignorance of spread dynamic information restricts the improvement of prediction performance. In this paper, we propose a novel framework called Physics-informed graph convolutional network (PiGCN) for cascade prediction, which combines explicit features (structural and temporal features) and propagation dynamic status in learning diffusion ability of cascades. Specifically, PiGCN is an end-to-end predictor, firstly splitting a given cascade into sub-cascade graph sequence and learning local structures of each sub-cascade via graph convolutional network , then adopting multi-layer perceptron to predict the cascade growth size. Moreover, our dynamic neural network, combining PDE-like equations and a deep learning method, is designed to extract potential dynamics of cascade diffusion, which captures dynamic evolution rate both on structural and temporal changes. To evaluate the performance of our proposed PiGCN model, we have conducted extensive experiment on two well-known large-scale datasets from Sina Weibo and ArXIv subject listing HEP-PH to verify the effectiveness of our model. The results of our proposed model outperform the mainstream model, and show that dynamic features have great significance for cascade size prediction.