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学者姓名：张挺
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Abstract ：
To address complex flood wave propagation problems characterized by discontinuity and anisotropic superposition, Split Coefficient-based Physical Informed Neural Network (SC-PINN) is proposed. The Split Coefficient (SC) strategy is employed to decompose the spatial features of flood waves along different propagation directions. Spatial derivatives, matching each spatial feature component, are obtained through the Taylor series, ensuring that each component contains only the information of waves propagating in a single positive or negative direction. This approach captures flow characteristics in each direction, thereby reducing the spectral bias encountered by PINN when learning complex flow regimes during flood wave propagation. To verify the effectiveness and accuracy, the proposed SC-PINN is applied to three classical dam-break scenarios. Additionally, an investigation is conducted into why the SC strategy assists PINN in improving the accuracy of flood forecasting. The results indicate that as the changing rate in water depth increases, the flow characteristics of asymmetric propagation and superposition become more pronounced, which leads to PINN failing to capture the complex flow regime effectively. In contrast, the proposed SC-PINN splits the total changing rate in water depth along different propagation directions, enabling the network model to independently learn the changing rate component in water depth in each direction. Consequently, the new method accurately captures not only the strong discontinuity regions in shallow water flow but also the phenomena of double shock system, vortex, and wake formed by the interaction between flood waves and obstacles. Furthermore, the proposed approach successfully describes asymmetric flow around the dam breach and local high-water levels induced by irregular breaches. It provides a potent solution for addressing complex flood wave propagation problems characterized by discontinuity and anisotropic superposition.
Keyword ：
Asymmetric propagation Asymmetric propagation Physical Informed Neural Network Physical Informed Neural Network Shallow water flows Shallow water flows Split Coefficient Split Coefficient Strong discontinuous flows Strong discontinuous flows
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| GB/T 7714 | Zhan, Changxun , Zhang, Ting , Zhang, Siqian et al. Solving complex flood wave propagation using split Coefficient-based Physical Informed Neural Network [J]. | JOURNAL OF HYDROLOGY , 2025 , 654 . |
| MLA | Zhan, Changxun et al. "Solving complex flood wave propagation using split Coefficient-based Physical Informed Neural Network" . | JOURNAL OF HYDROLOGY 654 (2025) . |
| APA | Zhan, Changxun , Zhang, Ting , Zhang, Siqian , Yang, Dingying . Solving complex flood wave propagation using split Coefficient-based Physical Informed Neural Network . | JOURNAL OF HYDROLOGY , 2025 , 654 . |
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In scenarios involving coupled excitations from multiple forces, structures exhibit complex vibrational patterns with superimposed high and low-frequency. This is particularly evident in thin-walled structures such as submarine pipelines, where the coupling of internal and external flows leads to more intricate superimposed vibrations compared to scenarios with only internal flow excitation. However, neural networks encounter challenges in capturing these superimposed vibrations due to inherent spectral bias. To address this, the multiple Fourier features physics-informed neural network (MFF-PINN) is proposed. Through multiple Fourier mappings for refined multi-scale and multi-frequency decomposition, facilitating PINN in accurately capturing multifrequency superposed vibrations. Additionally, the correspondence between hyperparameters and eigenvector frequencies is established, while the effects of different hyperparameters and number of mappings on the network is analyzed. The MFF-PINN with multiple mapping decomposition outperforms single mapping in synchronizing the learning of high and low-frequency, improving convergence speed and enhancing the ability to handle multi-frequency superposition. It provides an effective solution for modeling and simulating multifrequency superposed problems in science and engineering.
Keyword ：
Multiple fourier feature Multiple fourier feature Multiple frequency superposition Multiple frequency superposition Physics-informed neural network Physics-informed neural network Submarine pipeline Submarine pipeline Vortex-induced vibration Vortex-induced vibration
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| GB/T 7714 | Zhang, Ting , Yan, Rui , Zhang, Siqian et al. Multi-frequency superposed vortex-induced vibration modeling based on multiple Fourier features physics-informed neural network [J]. | THIN-WALLED STRUCTURES , 2025 , 212 . |
| MLA | Zhang, Ting et al. "Multi-frequency superposed vortex-induced vibration modeling based on multiple Fourier features physics-informed neural network" . | THIN-WALLED STRUCTURES 212 (2025) . |
| APA | Zhang, Ting , Yan, Rui , Zhang, Siqian , Yang, Dingying , Zhan, Changxun . Multi-frequency superposed vortex-induced vibration modeling based on multiple Fourier features physics-informed neural network . | THIN-WALLED STRUCTURES , 2025 , 212 . |
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The slit-cut method for the rockburst prevention and control is believed effective with its easiness in operation, adjustment and compatibility. However, there is limited advance knowledge of the physics of the slit-cut method, which is vital for the engineering designs. In this study, the biaxial compression tests with a synchronous AE (acoustic emission)-DIC (digital image correlation) monitoring are creatively carried out on the slit-contained circular opening specimens with different slit configurations to demonstrate the academic thoughts and mechanisms of the slit-cut method. The experiments document the two typical failure types namely the internal crack propagation and the dynamic rockburst, which occupy different AE hit rate characteristics and different entropy properties. With the occurrence of rockburst, the AE hit rate presents a bouncing ascend-descend trend, and a higher disorder and chaos is faithfully exhibited. Depending on the slit parameters, the slit-cut method can efficiently mitigate rockburst in terms of the occurrence frequency and magnitude. The underlying mechanism lies in the enhancement of the shear mechanism and the development of the internal cracks through which the stored energy can be greatly dissipated. However, due to the unrestricted shear failure in the slit-contained opening specimens, the opening-scale inward instability can be triggered by the internal crack coalescence, thus posing a threat to the safety of the opening. Implementing the slit-cut method with a consideration of the insitu stress conditions is evidently essential for the safe excavation.
Keyword ：
Biaxial compression tests Biaxial compression tests Crack propagation Crack propagation Hard rock excavation Hard rock excavation Rockburst Rockburst Slit-cut method Slit-cut method
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| GB/T 7714 | Zhang, Jian-Zhi , Zhou, Yi-Jie , Liu, Cheng-Yu et al. Experimental investigations on the failure characteristics of the slit-contained circular opening under biaxial compression: Insights into the rockburst prevention [J]. | THEORETICAL AND APPLIED FRACTURE MECHANICS , 2024 , 134 . |
| MLA | Zhang, Jian-Zhi et al. "Experimental investigations on the failure characteristics of the slit-contained circular opening under biaxial compression: Insights into the rockburst prevention" . | THEORETICAL AND APPLIED FRACTURE MECHANICS 134 (2024) . |
| APA | Zhang, Jian-Zhi , Zhou, Yi-Jie , Liu, Cheng-Yu , Yu, Jin , Li, Xing-Shang , Zhang, Ting . Experimental investigations on the failure characteristics of the slit-contained circular opening under biaxial compression: Insights into the rockburst prevention . | THEORETICAL AND APPLIED FRACTURE MECHANICS , 2024 , 134 . |
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Granular fracture holds significant implications in material mechanics. However, the previous studies in ordinary state-based peridynamic (OSB-PD) framework often neglect the internal crystalline structure of particles or only consider limited crystal orientation. To address this gap, a novel OSB-PD model for granular fracture within polycrystalline materials is proposed, in which the periodic functions are incorporated in the PD strain energy density, taking into account the inherent random orientation in cubic crystals. By comparing energy density from PD and the classical continuum mechanics, four PD material parameters are defined. Moreover, the corresponding surface correction method in the global coordinate system is also proposed. Several numerical examples including fracture analysis of polycrystalline materials are conducted to validate the effectiveness of the proposed method. The proposed ordinary state-based peridynamic model offers a fresh perspective for investigating granular fracture behaviors within polycrystalline materials.
Keyword ：
Cubic crystals Cubic crystals Grain orientation Grain orientation Granular fracture Granular fracture Peridynamics Peridynamics Polycrystalline materials Polycrystalline materials
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| GB/T 7714 | Zhang, Ting , Gu, Tiantian , Jiang, Jin et al. An ordinary state-based peridynamic model for granular fracture in polycrystalline materials with arbitrary orientations in cubic crystals [J]. | ENGINEERING FRACTURE MECHANICS , 2024 , 301 . |
| MLA | Zhang, Ting et al. "An ordinary state-based peridynamic model for granular fracture in polycrystalline materials with arbitrary orientations in cubic crystals" . | ENGINEERING FRACTURE MECHANICS 301 (2024) . |
| APA | Zhang, Ting , Gu, Tiantian , Jiang, Jin , Zhang, Jianzhi , Zhou, Xiaoping . An ordinary state-based peridynamic model for granular fracture in polycrystalline materials with arbitrary orientations in cubic crystals . | ENGINEERING FRACTURE MECHANICS , 2024 , 301 . |
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为准确获取山区小流域的降水空间分布及其资源量, 采用Kriging插值法对低分辨率卫星数据进行空间降尺度处理, 通过长短期记忆网络(Long Short-Term Memory, LSTM)将局部卫星与观测数据进行降水融合, 引入前期降水信息加强卫星与观测降水之间的时间相关性, 并利用该模型进行流域降水空间分布估计。结果表明: 从空间分布来看, 融合模型对暴雨中心位置的捕捉更加精确; 从降水量来看, 所提模型在短时强降水下的探测率和临界成功指数分别为0.60和0.50, 能够改善原始低分辨率卫星降水数据, 使其更接近实际情况; 从雨量站数量来看, 融合降水的精度随着站点数量的增加而提高, 当站点数量达到某个临界值时, 融合降水的精度趋于稳定。Kriging-LSTM模型为准确获取山区小流域的降水资源提供了新思路。
Keyword ：
Kriging插值法 Kriging插值法 山区小流域 山区小流域 长短期记忆网络(LSTM) 长短期记忆网络(LSTM) 降水空间估计 降水空间估计 降水融合 降水融合
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| GB/T 7714 | 詹昌洵 , 张挺 , 蒋嘉伟 . 基于多源数据的山区小流域降水融合模型 [J]. | 水科学进展 , 2024 , 35 (1) : 74-84 . |
| MLA | 詹昌洵 et al. "基于多源数据的山区小流域降水融合模型" . | 水科学进展 35 . 1 (2024) : 74-84 . |
| APA | 詹昌洵 , 张挺 , 蒋嘉伟 . 基于多源数据的山区小流域降水融合模型 . | 水科学进展 , 2024 , 35 (1) , 74-84 . |
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Objective In large-scale motion simulation problems, the search efficiency for nearest neighbor points critically influences the overall operational efficiency. This study applies correlation analysis to establish an adaptive relationship between the maximum depth of the kd-tree (dmax) and the total number of particles (N). A novel automatic termination criterion for the kd-tree, known as ATC-kd-tree, addresses the impact of the leaf node size threshold (n0) on nearest neighbor search efficiency. This method effectively addresses the challenges of recalibrating dmax as N varies, enhancing the efficiency and applicability of the kd-tree in various scenarios. Methods The ATC-kd-tree framework is designed to dynamically adjust the kd-tree structure based on the current particle count, ensuring optimal performance for efficient searches in real-time applications. This method involves a comprehensive analysis of particle distributions, enabling the algorithm to adaptively modify dmax based on the specific characteristics of the particle set at any given time. The ATC-kd-tree effectively responds to the spatial arrangement of particles, enhancing search accuracy and speed by integrating data-driven adjustments. In addition, a two-step parameter optimization algorithm that combines grid search with coordinate descent methods (GSCD) is introduced. This hybrid approach expedites the calibration of variable parameters crucial for optimizing ATC-kd-tree performance, facilitating a more precise search process. The GSCD method accelerates the pace of parameter adjustment and increases accuracy by ensuring that the most appropriate parameters are selected based on empirical evidence. A comprehensive series of experimental trials is conducted involving various particle distribution models, such as uniform, random, and clustered configurations. These trials are designed to assess the efficiency of the ATC-kd-tree and the GSCD optimization process. Key performance metrics, including search time, cache miss rates, and overall computational efficiency, are diligently monitored and analyzed. Rigorous comparisons against baseline methods, comprising traditional kd-trees and alternative sorting algorithms, are executed to ensure a thorough evaluation of the proposed techniques. Results and Discussions The study’s findings demonstrated that the ATC-kd-tree framework significantly improves the efficiency of nearest neighbor searches, especially in large-scale motion simulations characterized by dynamically fluctuating particle distributions. Experiments involving particle distribution shapes, such as rectangular, cuboidal, notched cuboidal, spherical, and annular, are frequently employed in fluid dynamics studies to corroborate their efficiency. The ATC-kd-tree achieved an impressive average reduction in search time of up to 30.3% compared to traditional unsorted kd-tree implementations across all tested configurations. When analyzing datasets comprising 40 000 and 575 000 particles, the search times exhibit significant enhancement: the ATC-kd-tree reduces the search time from 1.75 seconds with traditional methods to 1.22 seconds for the former dataset and from 7.12 seconds to 4.97 seconds for the latter. This performance improvement is particularly marked in environments with high spatial divergence among particles, where traditional methods often falter with inconsistent search paths. In addition, an average reduction of 24.2% in cache miss rates is observed when employing the ATC-kd-tree. In scenarios with larger particle counts, the cache miss rate decreases from 35% in the traditional unsorted kd-tree to 26% with the ATC-kd-tree, which directly contributes to enhanced computational efficiency, facilitating quicker data retrieval during neighbor searches. The ATC-kd-tree demonstrated exceptional adaptability to rapidly evolving particle configurations in computational fluid dynamics (CFD) simulations. In a specific experiment involving 50 000 particles exposed to external forces causing irregular movements, the ATC-kd-tree shows a 20% reduction in cache misses and a 15% decrease in overall computational time compared to traditional methods. This capacity to effectively manage irregular particle movements underscores the ATC-kd-tree’s robustness for real-time applications that demand rapid adaptability to dynamic changes. The GSCD optimization method further augments the performance of the ATC-kd-tree, as the analysis indicates that GSCD accelerates parameter calibration by 205% relative to traditional grid search methods. In experiments, the GSCD method reduces calibration time significantly, from over 120 seconds in traditional methods to approximately 40 seconds. This enhancement enables rapid adjustments to the parameters of the kd-tree and ensures that the tree remains optimally configured to the specific characteristics of the particle distributions encountered during simulations. The adaptability of the ATC-kd-tree is evident across various particle distribution scenarios. This algorithm consistently surpasses traditional unsorted kd-trees and alternative sorting methods in clustered configurations, such as the Z-index sort. In these configurations, the search time is significantly reduced, demonstrating the ATC-kd-tree’ s ability to dynamically reorganize its structure based on real-time analysis of particle distributions. This capability maximizes cache utilization and minimizes cache misses. The findings indicated that the ATC-kd-tree is particularly effective in scenarios involving non-uniform particle distributions, as its capacity to adjust dmax based on the number of particles eliminates the cumbersome recalibration processes typically required by traditional methods. Hence, this leads to a smoother and more efficient search process, even as particle distributions experience significant changes. These results highlight the critical importance of incorporating adaptive techniques into kd-tree implementations to improve search efficiency in large-scale simulations. The improvements in search time and cache utilization achieved by the ATC-kd-tree provide compelling evidence of its potential to transform how nearest neighbor searches are conducted in dynamic environments. Conclusions The introduction of the ATC-kd-tree provides a valuable approach to optimizing kd-tree-based nearest neighbor searches, particularly in dynamic and large-scale motion simulations. This research aims to enhance search efficiency and deliver a scalable solution for managing varying particle distributions by integrating an automatic termination criterion with a rapid parameter optimization method. The results showed that the ATC-kd-tree can improve operational performance, reducing computational overhead and cache misses, which is crucial for real-time applications where efficiency is paramount. In addition, the principles explored in this study can extend beyond the kd-tree framework, demonstrating new avenues for research into adaptive data access techniques that can prove beneficial across various computational domains, including machine learning, computer graphics, and robotics. Future efforts will concentrate on integrating the ATC-kd-tree with advanced cache management strategies to optimize performance and investigate methods to reduce computational complexity in high-dimensional contexts, which remains a critical area of investigation. This study aims to address these challenges and broaden the applicability of kd-tree methods in real-time environments, making them more adaptable to complex and dynamic conditions. It contributes to enhancing the functionality of kd-trees and provides insights into the broader field of data structure optimization, laying a foundation for future developments in efficient data processing techniques. © 2024 Sichuan University. All rights reserved.
Keyword ：
Adaptive algorithms Adaptive algorithms Adaptive boosting Adaptive boosting Convergence of numerical methods Convergence of numerical methods Decision trees Decision trees Flow visualization Flow visualization Image segmentation Image segmentation Nearest neighbor search Nearest neighbor search
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| GB/T 7714 | Zhang, Ting , Wang, Zongkai , Lin, Zhenhuan et al. Improved Kd-tree Particle Nearest Neighbor Search Based on Automatic Termination Criterion [J]. | Advanced Engineering Sciences , 2024 , 56 (6) : 217-229 . |
| MLA | Zhang, Ting et al. "Improved Kd-tree Particle Nearest Neighbor Search Based on Automatic Termination Criterion" . | Advanced Engineering Sciences 56 . 6 (2024) : 217-229 . |
| APA | Zhang, Ting , Wang, Zongkai , Lin, Zhenhuan , Zheng, Xianghan . Improved Kd-tree Particle Nearest Neighbor Search Based on Automatic Termination Criterion . | Advanced Engineering Sciences , 2024 , 56 (6) , 217-229 . |
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To accurately acquire the spatial distribution and resources of precipitation in small mountainous watersheds, this study employed the Kriging interpolation method for spatial downscaling of low- resolution satellite data. It integrated local satellite and observational data using the long short- term memory (LSTM) network, enhancing the temporal correlation between satellite and observed precipitation by incorporating antecedent precipitation information. This model was further utilized to estimate the spatial distribution of watershed precipitation. The results indicate that, spatially, the fusion model captures the location of rainstorm centers with greater precision. In terms of precipitation amount, the proposed model shows a probability of detection and a critical success index of 0. 60 and 0. 50, respectively, under short- duration intense rainfall, improving the original low-resolution satellite rainfall data to better approximate actual conditions. As for the number of precipitation stations, the accuracy of the merged precipitation data increases with the number of stations, reaching stability when a critical value of station density is achieved. The Kriging- LSTM model offers a novel approach for precisely acquiring precipitation resources in small mountainous watersheds. © 2024 International Research and Training Center on Erosion and Sedimentation and China Water and Power Press. All rights reserved.
Keyword ：
Brain Brain Interpolation Interpolation Long short-term memory Long short-term memory Rain Rain Satellites Satellites Spatial distribution Spatial distribution Storms Storms Watersheds Watersheds
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| GB/T 7714 | Zhan, Changxun , Zhang, Ting , Jiang, Jiawei . Multi-source data-based precipitation fusion model for small mountainous watersheds∗ [J]. | Advances in Water Science , 2024 , 35 (1) : 74-84 . |
| MLA | Zhan, Changxun et al. "Multi-source data-based precipitation fusion model for small mountainous watersheds∗" . | Advances in Water Science 35 . 1 (2024) : 74-84 . |
| APA | Zhan, Changxun , Zhang, Ting , Jiang, Jiawei . Multi-source data-based precipitation fusion model for small mountainous watersheds∗ . | Advances in Water Science , 2024 , 35 (1) , 74-84 . |
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Neural network models have been widely used in runoff forecasting, but are often criticized for their lack of physical interpretability. In this study, we present a simple but useful approach to developing hydrological models by designing neural networks based on the principles of runoff generation and concentration, which we refer to as a Hydrological Process-based Neural Network (HPNN) model. The Convolutional neural network (CNN) and softmax function are used because of their similar formula to the conventional runoff generation and unit hydrograph approach used in hydrology. We apply the HPNN model and four other benchmark models to forecast runoff in two catchments (Yutan and Chenda) in China. Results show that the HPNN model has higher computational efficiency, its parameters are interpretable and closely linked to the processes of runoff generation and concentration, and the HPNN model outperforms conventional GRU-based models.
Keyword ：
HPNN model HPNN model Neural network Neural network Physical interpretability Physical interpretability Runoff forecasting Runoff forecasting
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| GB/T 7714 | Gao, Shuai , Zhang, Shuo , Huang, Yuefei et al. A hydrological process-based neural network model for hourly runoff forecasting [J]. | ENVIRONMENTAL MODELLING & SOFTWARE , 2024 , 176 . |
| MLA | Gao, Shuai et al. "A hydrological process-based neural network model for hourly runoff forecasting" . | ENVIRONMENTAL MODELLING & SOFTWARE 176 (2024) . |
| APA | Gao, Shuai , Zhang, Shuo , Huang, Yuefei , Han, Jingcheng , Zhang, Ting , Wang, Guangqian . A hydrological process-based neural network model for hourly runoff forecasting . | ENVIRONMENTAL MODELLING & SOFTWARE , 2024 , 176 . |
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Study region: The Minjiang River, located on the western side of the Taiwan Strait of East Asia, serves as a typical mountain river estuary system. Study focus: This research investigates the impact of reduced sediment discharge on the geomorphological changes in the Minjiang River estuary delta and its adjacent coasts. By integrating 45 years of shoreline data and nautical chart bathymetry, the study quantitatively delineates tempo-spatial change patterns and reveals the rapid response mechanisms to sediment discharge decrease. New hydrological insights for the region: The study demonstrates that the sandy shoreline near the Minjiang River estuary exhibits distinct tempo-spatial evolution patterns primarily due to decreased sediment discharge. The estuarine transition zone shows greater coastal resilience, with shoals providing essential sediment sources for development, while the shoreline south of the transition zone experiences progressively delayed erosion. The Minjiang River delta reacts swiftly to decreased sediment discharge, with a response time of significantly under ten years. Despite the temporary influence of extreme weather events such as typhoons on erosion states, continuous sediment discharge decrease remains the dominant factor. These insights highlight the heightened sensitivity and rapid adaptability of mountain rivers to environmental shifts, providing significant implications for understanding the repercussions of human activities on estuarine geomorphological alterations.
Keyword ：
Delta Delta Human activities Human activities Mountain river Mountain river Sediment discharge Sediment discharge Shoreline Shoreline
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| GB/T 7714 | Wang, Chengtao , Cai, Feng , Qi, Hongshuai et al. Response patterns of mountain river deltas and adjacent coasts to the changes in sediment discharge: A case study of Minjiang River, China [J]. | JOURNAL OF HYDROLOGY-REGIONAL STUDIES , 2024 , 56 . |
| MLA | Wang, Chengtao et al. "Response patterns of mountain river deltas and adjacent coasts to the changes in sediment discharge: A case study of Minjiang River, China" . | JOURNAL OF HYDROLOGY-REGIONAL STUDIES 56 (2024) . |
| APA | Wang, Chengtao , Cai, Feng , Qi, Hongshuai , Zhao, Shaohua , Liu, Gen , He, Yanyu et al. Response patterns of mountain river deltas and adjacent coasts to the changes in sediment discharge: A case study of Minjiang River, China . | JOURNAL OF HYDROLOGY-REGIONAL STUDIES , 2024 , 56 . |
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In addressing the intricate dynamic responses of pipeline conveying fluid characterized by spatiotemporal multiscales and multi-modal contributions, Fourier feature-embedded physics-information neural network (FF-PINN) is proposed. By introducing Fourier feature mapping to decompose the temporal and spatial scale information, FF-PINN precisely captures the relatively low-frequencies on the macroscopic time scale as well as the relatively high-frequencies on the microscopic scale of the pipeline's vibration. This approach significantly overcomes the spectral bias encountered by PINN when learning high-frequency information. To verify the effectiveness and accuracy of this method, the proposed FF-PINN is applied to solve the pipeline conveying fluid model with fixed support at both ends. The relative L2 error between the obtained results and the reference solution is 1.8 x 10-2, concurrently with a significant reduction in computational time. Additionally, an analysis of hyperparameter sigma selection is conducted to evaluate its impact on the performance of FF-PINN, while establishing the correspondence between hyperparameter and eigenvector frequency. The results demonstrate that choosing appropriate hyperparameters empowers FF-PINN to better learn the vibration of specific frequencies, enabling the accurate modeling of pipeline vibrations' dynamic response. It provides a potent solution for solving spatiotemporal multi-scale complexity problems involving the superposition of high-and low-frequencies.
Keyword ：
Fourier feature Fourier feature Physics-information neural network Physics-information neural network Pipeline conveying fluid Pipeline conveying fluid Spatiotemporal multi-scales Spatiotemporal multi-scales Vibration characteristics Vibration characteristics
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| GB/T 7714 | Zhang, Ting , Yan, Rui , Zhang, Siqian et al. Application of Fourier feature physics-information neural network in model of pipeline conveying fluid [J]. | THIN-WALLED STRUCTURES , 2024 , 198 . |
| MLA | Zhang, Ting et al. "Application of Fourier feature physics-information neural network in model of pipeline conveying fluid" . | THIN-WALLED STRUCTURES 198 (2024) . |
| APA | Zhang, Ting , Yan, Rui , Zhang, Siqian , Yang, Dingying , Chen, Anhao . Application of Fourier feature physics-information neural network in model of pipeline conveying fluid . | THIN-WALLED STRUCTURES , 2024 , 198 . |
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