SIAM Journal on Applied Dynamical Systems最新文献_第10页

Mitigating Model Error via a Multimodel Method and Application to Tropical Intraseasonal Oscillations 多模式方法减轻模式误差及其在热带季内振荡中的应用

4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2023-11-03 DOI: 10.1137/22m152551x

Jason L. Torchinsky, Samuel Stechmann

{"title":"Mitigating Model Error via a Multimodel Method and Application to Tropical Intraseasonal Oscillations","authors":"Jason L. Torchinsky, Samuel Stechmann","doi":"10.1137/22m152551x","DOIUrl":"https://doi.org/10.1137/22m152551x","url":null,"abstract":"Developing a model to capture all aspects of a complex dynamical system is an immense task, and each model will have deficiencies in some areas, such as global climate models having difficulty in capturing tropical intraseasonal variability such as the Madden–Julian oscillation. Besides complex models, it is possible to create simplified, low-dimensional models to capture specific phenomena while ignoring many aspects of the full system. Here, we propose a strategy to allow complex models to communicate with simplified models throughout a simulation. The communication allows one to leverage the strengths of each model, without needing to change their dynamics, to mitigate model error. Furthermore, to ensure ease of implementation in complex systems, the strategy is based on common data assimilation techniques that are normally used to combine models and real-world data. This strategy is investigated here in a test case that is nonlinear, non-Gaussian, and high-dimensional (approximately degrees of freedom), and the multiple models have different state spaces. In particular, it is an idealized tropical climate model in three spatial dimensions. The multimodel communication strategy is seen to mitigate model error and reproduce statistical features akin to those of the truth model when the communication is sufficiently frequent. In these tests, the low-dimensional model contributes only two degrees of freedom, which suggests that, in some systems, large amounts of model error can possibly be reduced by focusing on a small set of model components.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1

Rate-Induced Tipping in Heterogeneous Reaction-Diffusion Systems: An Invariant Manifold Framework and Geographically Shifting Ecosystems 非均相反应-扩散系统的速率诱导引爆:一个不变流形框架和地理转移生态系统

4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2023-10-30 DOI: 10.1137/22m1536625

Cris R. Hasan, Ruaidhrí Mac Cárthaigh, Sebastian Wieczorek

引用次数: 3

Modeling Polarity-Driven Laminar Patterns in Bilayer Tissues with Mixed Signaling Mechanisms 用混合信号机制模拟极性驱动的双层组织层流模式

4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2023-10-16 DOI: 10.1137/22m1522565

Joshua W. Moore, Trevor C. Dale, Thomas E. Woolley

{"title":"Modeling Polarity-Driven Laminar Patterns in Bilayer Tissues with Mixed Signaling Mechanisms","authors":"Joshua W. Moore, Trevor C. Dale, Thomas E. Woolley","doi":"10.1137/22m1522565","DOIUrl":"https://doi.org/10.1137/22m1522565","url":null,"abstract":"Recent advances in high-resolution experimental methods have highlighted the significance of cell signal pathway crosstalk and localized signaling activity in the development and disease of numerous biological systems. The investigation of multiple signal pathways often introduces different methods of cell-cell communication, i.e., contact-based or diffusive signaling, which generates both a spatial and a temporal dependence on cell behaviors. Motivated by cellular mechanisms that control cell-fate decisions in developing bilayer tissues, we use dynamical systems coupled with multilayer graphs to analyze the role of signaling polarity and pathway crosstalk in fine-grain pattern formation of protein activity. Specifically, we study how multilayer graph edge structures and weights influence the layerwise (laminar) patterning of cells in bilayer structures, which are commonly found in glandular tissues. We present sufficient conditions for the existence, uniqueness, and instability of homogeneous cell states in the large-scale spatially discrete dynamical system. Using methods of pattern templating by graph partitioning to generate quotient systems, in combination with concepts from monotone dynamical systems, we exploit the extensive dimensionality reduction to provide existence conditions for the polarity required to induce fine-grain laminar patterns with multiple spatially dependent intracellular components. We then explore the spectral links between the quotient and large-scale dynamical systems to extend the laminar patterning criteria from existence to convergence for sufficiently large amounts of cellular polarity in the large-scale dynamical system, independent of spatial dimension and number of cells in the tissue.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136115189","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

An Unstructured Mesh Approach to Nonlinear Noise Reduction for Coupled Systems 耦合系统非线性降噪的非结构网格方法

4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2023-10-13 DOI: 10.1137/22m152092x

Aaron Kirtland, Jonah Botvinick-Greenhouse, Marianne DeBrito, Megan Osborne, Casey Johnson, Robert S. Martin, Samuel J. Araki, Daniel Q. Eckhardt

{"title":"An Unstructured Mesh Approach to Nonlinear Noise Reduction for Coupled Systems","authors":"Aaron Kirtland, Jonah Botvinick-Greenhouse, Marianne DeBrito, Megan Osborne, Casey Johnson, Robert S. Martin, Samuel J. Araki, Daniel Q. Eckhardt","doi":"10.1137/22m152092x","DOIUrl":"https://doi.org/10.1137/22m152092x","url":null,"abstract":"To address noise inherent in electronic data acquisition systems and real-world sources, Araki et al. [Phys. D, 417 (2021), 132819] demonstrated a grid-based nonlinear technique to remove noise from a chaotic signal, leveraging a clean high-fidelity signal from the same dynamical system and ensemble averaging in multidimensional phase space. This method achieved denoising of a time series data with 100% added noise but suffered in regions of low data density. To improve this grid-based method, here an unstructured mesh based on triangulations and Voronoi diagrams is used to accomplish the same task. The unstructured mesh more uniformly distributes data samples over mesh cells to improve the accuracy of the reconstructed signal. By empirically balancing bias and variance errors in selecting the number of unstructured cells as a function of the number of available samples, the method achieves asymptotic statistical convergence with known test data and reduces synthetic noise on experimental signals from Hall effect thrusters with greater success than the original grid-based strategy.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135919878","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 2

Regression-Based Projection for Learning Mori–Zwanzig Operators 基于回归投影的Mori-Zwanzig算子学习

4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2023-10-13 DOI: 10.1137/22m1506146

Yen Ting Lin, Yifeng Tian, Danny Perez, Daniel Livescu

{"title":"Regression-Based Projection for Learning Mori–Zwanzig Operators","authors":"Yen Ting Lin, Yifeng Tian, Danny Perez, Daniel Livescu","doi":"10.1137/22m1506146","DOIUrl":"https://doi.org/10.1137/22m1506146","url":null,"abstract":"We propose to adopt statistical regression as the projection operator to enable data-driven learning of the operators in the Mori–Zwanzig formalism. We present a principled method to extract the Markov and memory operators for any regression models. We show that the choice of linear regression results in a recently proposed data-driven learning algorithm based on Mori’s projection operator, which is a higher-order approximate Koopman learning method. We show that more expressive nonlinear regression models naturally fill in the gap between the highly idealized and computationally efficient Mori’s projection operator and the most optimal yet computationally infeasible Zwanzig’s projection operator. We performed numerical experiments and extracted the operators for an array of regression-based projections, including linear, polynomial, spline, and neural network–based regressions, showing a progressive improvement as the complexity of the regression model increased. Our proposition provides a general framework to extract memory-dependent corrections and can be readily applied to an array of data-driven learning methods for stationary dynamical systems in the literature.","PeriodicalId":49534,"journal":{"name":"SIAM Journal on Applied Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135918366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 4

Fast Adjoint Algorithm for Linear Responses of Hyperbolic Chaos 双曲型混沌线性响应的快速伴随算法

4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2023-10-12 DOI: 10.1137/22m1522383

Angxiu Ni

引用次数: 2

Equilibria Analysis of a Networked Bivirus Epidemic Model Using Poincaré–Hopf and Manifold Theory 用poincar<s:1> - hopf和流形理论分析网络双病毒流行病模型的均衡

4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2023-10-12 DOI: 10.1137/22m1529981

Brian D. O. Anderson, Mengbin Ye

引用次数: 0

Generalized Eigenvalues of the Perron–Frobenius Operators of Symbolic Dynamical Systems 符号动力系统Perron-Frobenius算子的广义特征值

4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2023-10-12 DOI: 10.1137/22m1476204

Hayato Chiba, Masahiro Ikeda, Isao Ishikawa

引用次数: 0

Stability of Equilibrium Points in the Spatially Restricted ({boldsymbol{N+1}}) -Body Problem with Manev Potential 空间受限({boldsymbol{N+1}}) -具有Manev势的体问题中平衡点的稳定性

4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2023-10-11 DOI: 10.1137/23m1551912

Mauricio Ascencio, Esther Barrabés, Josep M. Cors, Claudio Vidal

引用次数: 0

Optimal Control of the Controlled Lotka–Volterra Equations with Applications. The Permanent Case 被控Lotka-Volterra方程的最优控制及其应用。永久性案件

4区数学

SIAM Journal on Applied Dynamical Systems Pub Date : 2023-10-11 DOI: 10.1137/22m151978x

Bernard Bonnard, Jérémy Rouot

引用次数: 0