IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2024-09-27 DOI: 10.1016/j.chaos.2024.115538

{"title":"AI-Lorenz: A physics-data-driven framework for Black-Box and Gray-Box identification of chaotic systems with symbolic regression","authors":"","doi":"10.1016/j.chaos.2024.115538","DOIUrl":"10.1016/j.chaos.2024.115538","url":null,"abstract":"<div><div>Discovering mathematical models that characterize the observed behavior of dynamical systems remains a major challenge, especially for systems in a chaotic regime, due to their sensitive dependence on initial conditions and the complex non-linear interactions within the system. The challenge is even greater when the physics underlying such systems is not yet understood, and scientific inquiry must solely rely on empirical data. Despite advancements such as the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, which has shown success in identifying chaotic systems with reasonable accuracy, challenges remain in dealing with noise, sparse data, and the need for models that generalize well across different chaotic systems. Driven by the need to fill this gap, we develop a framework named AI-Lorenz that learns mathematical expressions modeling complex dynamical behaviors by identifying differential equations from noisy and sparse observable data. We train a physics-informed neural network (PINN) with the eXtreme Theory of Functional Connections (X-TFC) algorithm by using data and known physics (when available) to learn the dynamics of a system, its rate of change in time, and missing model terms, which are used as input for a symbolic regression algorithm (PySR) to autonomously distill the explicit mathematical terms. This, in turn, enables us to predict the future evolution of the dynamical behavior. The performance of this framework is validated by recovering the right-hand sides and unknown terms of certain complex, chaotic systems, such as the well-known Lorenz system, a six-dimensional hyperchaotic system, the non-autonomous Sprott chaotic system, and the slow-fast Duffing system, and comparing them with their known analytical expressions and state-of-the-art regression and system identification methods.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142327873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

Linear codes with few weights over finite fields 有限域上权重较少的线性编码

IF 1.2 3区数学

Finite Fields and Their Applications Pub Date : 2024-09-27 DOI: 10.1016/j.ffa.2024.102509

引用次数: 0

Evolution of cooperation with asymmetric rewards 奖励不对称情况下的合作演变

IF 3.5 2区数学

Applied Mathematics and Computation Pub Date : 2024-09-27 DOI: 10.1016/j.amc.2024.129075

引用次数: 0

A robust shape model for blood vessels analysis 用于血管分析的稳健形状模型

IF 3.5 2区数学

Applied Mathematics and Computation Pub Date : 2024-09-26 DOI: 10.1016/j.amc.2024.129078

{"title":"A robust shape model for blood vessels analysis","authors":"","doi":"10.1016/j.amc.2024.129078","DOIUrl":"10.1016/j.amc.2024.129078","url":null,"abstract":"<div><div>The availability of digital twins for the cardiovascular system will enable insightful computational tools both for research and clinical practice. This, however, demands robust and well defined models and methods for the different steps involved in the process. We present a vessel coordinate system (VCS) that enables the unambiguous definition of locations in a vessel section, by adapting the idea of cylindrical coordinates to the vessel geometry. Using the VCS model, point correspondence can be defined among different samples of a cohort, allowing data transfer, quantitative comparison, shape coregistration or population analysis. Furthermore, the VCS model allows for the generation of specific meshes (e.g. cylindrical grids, OGrids) necessary for an accurate reconstruction of the geometries used in fluid simulations. We provide the technical details for coordinates computation and discuss the assumptions taken to guarantee that they are well defined. The VCS model is tested in a series of applications. We present a robust, low dimensional, patient specific vascular model and use it to study phenotype variability analysis of the thoracic aorta within a cohort of patients. Point correspondence is exploited to build an haemodynamics atlas of the aorta for the same cohort. The atlas originates from fluid simulations (Navier-Stokes with Finite Volume Method) conducted using OpenFOAMv10. We finally present a relevant discussion on the VCS model, which covers its impact in important areas such as shape modeling and computer fluids dynamics (CFD).</div></div>","PeriodicalId":55496,"journal":{"name":"Applied Mathematics and Computation","volume":null,"pages":null},"PeriodicalIF":3.5,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Approximation algorithm of maximizing non-submodular functions under non-submodular constraint 非次模化约束条件下的非次模化函数最大化近似算法

IF 1 3区数学

Discrete Applied Mathematics Pub Date : 2024-09-26 DOI: 10.1016/j.dam.2024.09.022

引用次数: 0

Greedy trial subspace selection in meshfree time-stepping scheme with applications in coupled bulk-surface pattern formations 无网格时间步进方案中的贪婪试验子空间选择及其在体表耦合模式形成中的应用

IF 4.4 2区数学

Mathematics and Computers in Simulation Pub Date : 2024-09-26 DOI: 10.1016/j.matcom.2024.09.018

引用次数: 0

On the Borel summability of formal solutions of certain higher-order linear ordinary differential equations 论某些高阶线性常微分方程形式解的伯累尔求和性

IF 2.4 2区数学

Journal of Differential Equations Pub Date : 2024-09-26 DOI: 10.1016/j.jde.2024.09.041

引用次数: 0

On the occurrence of freak waves in negative ion plasmas 关于负离子等离子体中出现的怪浪

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2024-09-26 DOI: 10.1016/j.chaos.2024.115531

{"title":"On the occurrence of freak waves in negative ion plasmas","authors":"","doi":"10.1016/j.chaos.2024.115531","DOIUrl":"10.1016/j.chaos.2024.115531","url":null,"abstract":"<div><div>A theoretical investigation of the existence of electrostatic freak waves (FWs), also known as rogue waves (RWs), in a multicomponent plasma with negative ions is presented, from first principles. A three component plasma is considered, consisting of positive ions, negative ions and electrons. Both ion species (distinguished by their different mass and absolute charge) are modeled as cold inertial fluids, for simplicity, while the electrons are assumed to be thermalized, given the dynamical scale of interest. Based on a multiscale perturbation technique, a nonlinear Schrödinger (NLS) type equation is derived, describing the evolution of an electrostatic wavepacket amplitude (envelope). By means of a modulational stability analysis, we have determined the conditions for bright envelope solitons (breathers) or, alternatively, for dark-type envelope solitons (envelope holes) to exist. The region of existence of freak waves in configurational parameter space is elucidated, in terms of the negative-ion component (concentration and charge). The parametric dependence of the spatiotemporal characteristics of FWs on the negative-ion parameters is also discussed. It is established that freak waves may occur in a wide region in parameter space. Our analytical predictions are corroborated by numerical simulations, showing that FWs may occur spontaneously in the dynamics. Our results extend earlier studies and also enable an efficient interpretation of past and future experiments.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The asymptotic preserving unified gas kinetic scheme for the multi-scale kinetic SIR epidemic model 多尺度动力学 SIR 流行病模型的渐近保留统一气体动力学方案

IF 2.9 2区数学

Computers & Mathematics with Applications Pub Date : 2024-09-26 DOI: 10.1016/j.camwa.2024.09.021

{"title":"The asymptotic preserving unified gas kinetic scheme for the multi-scale kinetic SIR epidemic model","authors":"","doi":"10.1016/j.camwa.2024.09.021","DOIUrl":"10.1016/j.camwa.2024.09.021","url":null,"abstract":"<div><div>In this paper, we present an asymptotic preserving scheme for the two-dimensional space-dependent and multi-scale kinetic SIR epidemic model which is widely used to model the spread of infectious diseases in populations. The scheme combines a discrete ordinate method for the velocity variables and finite volume method for the spatial and time variables. The idea of unified gas kinetic scheme (UGKS) is used to construct the numerical boundary fluxes which needs the formal integral solutions of the model. Due to the coupling of the three transfer equations in the SIR model, it is difficult to obtain these integral solutions dependently. We decouple the system by constructing the fluxes in a separate way. Then following the framework of UGKS we can obtain the macro auxiliary quantities which is needed in the scheme. Thus the SIR model can be solved in the sequential way. In addition, we can show numerically that the scheme is second-order accurate both in space and time. Moreover, it can not only capture the solution of the diffusion limit equations without requiring the cell size and time step being related to the smallness of the scaling parameters, but also resolve the solution in hyperbolic regime in a natural way. Furthermore, the positive property of the UGKS is analyzed in detail, and through adding time step constraint conditions and applying nodal limiters together, the positive UGKS, called <span><math><mi>P</mi><mi>P</mi><mi>U</mi><mi>G</mi><mi>K</mi><msup><mrow><mi>S</mi></mrow><mrow><mn>2</mn><mo>−</mo><mi>o</mi><mi>r</mi><mi>d</mi><mi>e</mi><mi>r</mi></mrow></msup></math></span>, is obtained. Moreover, in order release the time step constraints in the diffusion regime, a temporal first-order accuracy positive preserving UGKS, called <span><math><mi>P</mi><mi>P</mi><mi>U</mi><mi>G</mi><mi>K</mi><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>o</mi><mi>r</mi><mi>d</mi><mi>e</mi><mi>r</mi></mrow></msup></math></span>, is proposed. Finally, several numerical tests are included to validate the performance of the proposed schemes.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":null,"pages":null},"PeriodicalIF":2.9,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323875","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Bifurcation dynamics and FPGA implementation of coupled Fitzhugh-Nagumo neuronal system 耦合 Fitzhugh-Nagumo 神经元系统的分岔动力学和 FPGA 实现

IF 5.3 1区数学

Chaos Solitons & Fractals Pub Date : 2024-09-26 DOI: 10.1016/j.chaos.2024.115520

{"title":"Bifurcation dynamics and FPGA implementation of coupled Fitzhugh-Nagumo neuronal system","authors":"","doi":"10.1016/j.chaos.2024.115520","DOIUrl":"10.1016/j.chaos.2024.115520","url":null,"abstract":"<div><div>This paper is devoted to studying the dynamical behaviors of the coupled FHN neural system by the discrete implicit mapping method, including bifurcation, coexistence, firing behaviors and synchronization. Two improved Fitzhugh-Nagumo (FHN) neurons are coupled through an asymmetric electrical synapse to investigate the effect of coupling strength on the firing behavior of neuronal networks, which is crucial to the progress of brain science. The types and stability of time-varying equilibrium points in the FHN neuron model are studied, and the corresponding discrete mapping model is established. The unstable periodic orbits hidden in chaos in the system are explored, and the mechanism of various bifurcations is explained through global eigenvalues. Simultaneously, the coexistence firing patterns are studied by basin of attraction, and the synchronization behavior of neural system is investigated through the normalized mean synchronization error (NMSE). Moreover, FPGA is employed for circuit implementation of the coupled neuronal system, and the correctness of theoretical results is verified. The results of this paper may help to better understand the firing and synchronization mechanisms of neural networks, which have important significance for the treatment of nervous system diseases and the development of neuroscience.</div></div>","PeriodicalId":9764,"journal":{"name":"Chaos Solitons & Fractals","volume":null,"pages":null},"PeriodicalIF":5.3,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142323528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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

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