Journal of Systems Science & Complexity最新文献

A New Method for Solving Nonlinear Partial Differential Equations Based on Liquid Time-Constant Networks 基于液体时常网络的非线性偏微分方程求解新方法

3区数学

Journal of Systems Science & Complexity Pub Date : 2024-01-26 DOI: 10.1007/s11424-024-3349-z

Jiuyun Sun, Huanhe Dong, Yong Fang

引用次数: 0

Number of Solitons Emerged in the Initial Profile of Shallow Water Using Convolutional Neural Networks 利用卷积神经网络计算浅水初始剖面中出现的孤子数量

3区数学

Journal of Systems Science & Complexity Pub Date : 2024-01-26 DOI: 10.1007/s11424-024-3337-3

Zhen Wang, Shikun Cui

引用次数: 0

Parallel Physics-Informed Neural Networks Method with Regularization Strategies for the Forward-Inverse Problems of the Variable Coefficient Modified KdV Equation 针对变系数修正 KdV 方程正反问题的并行物理信息神经网络方法与正则化策略

3区数学

Journal of Systems Science & Complexity Pub Date : 2024-01-26 DOI: 10.1007/s11424-024-3467-7

Huijuan Zhou

{"title":"Parallel Physics-Informed Neural Networks Method with Regularization Strategies for the Forward-Inverse Problems of the Variable Coefficient Modified KdV Equation","authors":"Huijuan Zhou","doi":"10.1007/s11424-024-3467-7","DOIUrl":"https://doi.org/10.1007/s11424-024-3467-7","url":null,"abstract":"<h3>Abstract</h3> <p>This paper mainly introduces the parallel physics-informed neural networks (PPINNs) method with regularization strategies to solve the data-driven forward-inverse problems of the variable coefficient modified Korteweg-de Vries (VC-MKdV) equation. For the forward problem of the VC-MKdV equation, the authors use the traditional PINN method to obtain satisfactory data-driven soliton solutions and provide a detailed analysis of the impact of network width and depth on solving accuracy and speed. Furthermore, the author finds that the traditional PINN method outperforms the one with locally adaptive activation functions in solving the data-driven forward problems of the VC-MKdV equation. As for the data-driven inverse problem of the VC-MKdV equation, the author introduces a parallel neural networks to separately train the solution function and coefficient function, successfully addressing the function discovery problem of the VC-MKdV equation. To further enhance the network’s generalization ability and noise robustness, the author incorporates two regularization strategies into the PPINNs. An amount of numerical experimental data in this paper demonstrates that the PPINNs method can effectively address the function discovery problem of the VC-MKdV equation, and the inclusion of appropriate regularization strategies in the PPINNs can improves its performance.</p>","PeriodicalId":50026,"journal":{"name":"Journal of Systems Science & Complexity","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139585373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Pre-Training Physics-Informed Neural Network with Mixed Sampling and Its Application in High-Dimensional Systems 混合采样预训练物理信息神经网络及其在高维系统中的应用

3区数学

Journal of Systems Science & Complexity Pub Date : 2024-01-26 DOI: 10.1007/s11424-024-3321-y

Haiyi Liu, Yabin Zhang, Lei Wang

{"title":"Pre-Training Physics-Informed Neural Network with Mixed Sampling and Its Application in High-Dimensional Systems","authors":"Haiyi Liu, Yabin Zhang, Lei Wang","doi":"10.1007/s11424-024-3321-y","DOIUrl":"https://doi.org/10.1007/s11424-024-3321-y","url":null,"abstract":"<p>Recently, the physics-informed neural network shows remarkable ability in the context of solving the low-dimensional nonlinear partial differential equations. However, for some cases of high-dimensional systems, such technique may be time-consuming and inaccurate. In this paper, the authors put forward a pre-training physics-informed neural network with mixed sampling (pPINN) to address these issues. Just based on the initial and boundary conditions, the authors design the pre-training stage to filter out the set of the misfitting points, which is regarded as part of the training points in the next stage. The authors further take the parameters of the neural network in Stage 1 as the initialization in Stage 2. The advantage of the proposed approach is that it takes less time to transfer the valuable information from the first stage to the second one to improve the calculation accuracy, especially for the high-dimensional systems. To verify the performance of the pPINN algorithm, the authors first focus on the growing-and-decaying mode of line rogue wave in the Davey-Stewartson I equation. Another case is the accelerated motion of lump in the inhomogeneous Kadomtsev-Petviashvili equation, which admits a more complex evolution than the uniform equation. The exact solution provides a perfect sample for data experiments, and can also be used as a reference frame to identify the performance of the algorithm. The experiments confirm that the pPINN algorithm can improve the prediction accuracy and training efficiency well, and reduce the training time to a large extent for simulating nonlinear waves of high-dimensional equations.</p>","PeriodicalId":50026,"journal":{"name":"Journal of Systems Science & Complexity","volume":"3 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139585229","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Physics-Informed Neural Networks with Two Weighted Loss Function Methods for Interactions of Two-Dimensional Oceanic Internal Solitary Waves 采用两种加权损失函数方法的物理信息神经网络与二维海洋内孤波的相互作用

3区数学

Journal of Systems Science & Complexity Pub Date : 2024-01-26 DOI: 10.1007/s11424-024-3500-x

Junchao Sun, Yong Chen, Xiaoyan Tang

{"title":"Physics-Informed Neural Networks with Two Weighted Loss Function Methods for Interactions of Two-Dimensional Oceanic Internal Solitary Waves","authors":"Junchao Sun, Yong Chen, Xiaoyan Tang","doi":"10.1007/s11424-024-3500-x","DOIUrl":"https://doi.org/10.1007/s11424-024-3500-x","url":null,"abstract":"<p>The multiple patterns of internal solitary wave interactions (ISWI) are a complex oceanic phenomenon. Satellite remote sensing techniques indirectly detect these ISWI, but do not provide information on their detailed structure and dynamics. Recently, the authors considered a three-layer fluid with shear flow and developed a (2+1) Kadomtsev-Petviashvili (KP) model that is capable of describing five types of oceanic ISWI, including O-type, P-type, TO-type, TP-type, and Y-shaped. Deep learning models, particularly physics-informed neural networks (PINN), are widely used in the field of fluids and internal solitary waves. However, the authors find that the amplitude of internal solitary waves is much smaller than the wavelength and the ISWI occur at relatively large spatial scales, and these characteristics lead to an imbalance in the loss function of the PINN model. To solve this problem, the authors introduce two weighted loss function methods, the fixed weighing and the adaptive weighting methods, to improve the PINN model. This successfully simulated the detailed structure and dynamics of ISWI, with simulation results corresponding to the satellite images. In particular, the adaptive weighting method can automatically update the weights of different terms in the loss function and outperforms the fixed weighting method in terms of generalization ability.</p>","PeriodicalId":50026,"journal":{"name":"Journal of Systems Science & Complexity","volume":"148 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139585338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A New Random Sampling Method and Its Application in Improving Progressive BKZ Algorithm 一种新的随机抽样方法及其在改进渐进式BKZ算法中的应用

3区数学

Journal of Systems Science & Complexity Pub Date : 2023-10-25 DOI: 10.1007/s11424-023-3107-7

Minghao Sun, Shixiong Wang, Hao Chen, Longjiang Qu

引用次数: 0

A New Class of Strong Orthogonal Arrays of Strength Three 一类新的强度为3的强正交阵列

3区数学

Journal of Systems Science & Complexity Pub Date : 2023-10-25 DOI: 10.1007/s11424-023-3093-9

Chunyan Wang, Min-Qian Liu, Jinyu Yang

引用次数: 0

Fixed-Time Anti-Disturbance Average-Tracking for Multi-Agent Systems Without Velocity Measurements 无速度测量的多智能体系统的固定时间抗干扰平均跟踪

3区数学

Journal of Systems Science & Complexity Pub Date : 2023-10-21 DOI: 10.1007/s11424-023-2461-9

Yuling Li, Chenglin Liu, Ya Zhang, Yangyang Chen

引用次数: 0

Two-Stage Online Debiased Lasso Estimation and Inference for High-Dimensional Quantile Regression with Streaming Data 流数据下高维分位数回归的两阶段在线去偏Lasso估计与推理

3区数学

Journal of Systems Science & Complexity Pub Date : 2023-10-21 DOI: 10.1007/s11424-023-3014-y

Yanjin Peng, Lei Wang

引用次数: 0

The Impact of General Correlation Under Multi-Period Mean-Variance Asset-Liability Portfolio Management 多期均值方差资产负债组合管理下一般相关性的影响

3区数学

Journal of Systems Science & Complexity Pub Date : 2023-10-21 DOI: 10.1007/s11424-023-3019-6

Xianping Wu, Weiping Wu, Yu Lin

引用次数: 0