Physica D: Nonlinear Phenomena最新文献

{"title":"Learning dynamical systems from data: A simple cross-validation perspective, part II: Nonparametric kernel flows","authors":"Matthieu Darcy ,&nbsp;Boumediene Hamzi ,&nbsp;Jouni Susiluoto ,&nbsp;Amy Braverman ,&nbsp;Houman Owhadi","doi":"10.1016/j.physd.2025.134641","DOIUrl":"10.1016/j.physd.2025.134641","url":null,"abstract":"<div><div>In previous work, we showed that learning dynamical system Hamzi and Owhadi (2021) with kernel methods can achieve state of the art, both in terms of accuracy and complexity, for predicting climate/weather time series Hamzi et al., (2021) as well as for a family of 133 chaotic systems Lu et al., (2023), Yang et al., (2024), when the kernel is also learned from data. While the kernels considered in previous work were parametric, in this follow-up paper, we test a non-parametric approach and tune warping kernels (with kernel flows, a variant of cross-validation) for learning prototypical dynamical systems. We train the kernel using the regression relative error between two interpolants (measured in the RKHS norm of the kernel) as the quantity to minimize, as well as using the Maximum Mean Discrepancy between two different samples, and that characterizes the statistical properties of the dynamical system, as a the quantity to minimize.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134641"},"PeriodicalIF":2.7,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777650","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}

{"title":"Periodic waves in the pgKdV equation with two arbitrarily high-order nonlinearities","authors":"Yanfei Dai ,&nbsp;Changjian Liu ,&nbsp;Yangjian Sun","doi":"10.1016/j.physd.2025.134656","DOIUrl":"10.1016/j.physd.2025.134656","url":null,"abstract":"<div><div>In this paper, the existence and number of periodic wave solutions in a perturbed generalized KdV equation of high-order with weak backward diffusion and dissipation effects are studied. These can be converted into studying the periodic waves on a manifold via geometric singular perturbation theory. By using bifurcation theory and analyzing the number of real zeros of some linear combination of Abelian integrals whose integrand and integral curve both have two arbitrarily high-order terms, we prove the persistence of periodic waves with certain wave speeds under small perturbation. The persistence of periodic waves for any energy parameter in an open interval and sufficiently small parameter is also established. Furthermore, the monotonicity of the limit wave speed is given, and the upper and lower bounds of limit wave speed are obtained. It is the first time to prove the existence of periodic waves in this kind of equation with two arbitrarily high-order nonlinearities.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134656"},"PeriodicalIF":2.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777100","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}

{"title":"Augmenting KZ finite flux solutions and nonlocal resonant transfer","authors":"Alan C. Newell ,&nbsp;Sergey V. Nazarenko","doi":"10.1016/j.physd.2025.134642","DOIUrl":"10.1016/j.physd.2025.134642","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This short paper is dedicated to Volodja Zakharov, a unique and original scientist, leader, mentor, poet and great friend for more than forty years. We will speak more of the man and his work in the body of the paper. One of his many and singular contributions to science was the development of a special and extremely relevant class of solutions for wave turbulence theory, the study of the statistical evolution of a sea of weakly nonlinear, dispersive waves (Zakharov et al., 1992). The closed kinetic equation describing the evolution of the spectral energy or, equivalently, number density, had been known for many years, and had been explicitly derived in the context of surface gravity waves by Hasselmann in 1962 (Hasselmann, 1962). Many works addressing the questions of natural closure (Benney and Saffman, 1966; Benney and Newell, 1969; Newell, 1968), other examples such as Rossby waves (Longuet-Higgins and Gill, 1967), surface tension dominated waves (Zakharov and Filonenko, 1967), plasma waves (Vedenov, 1967) soon followed. Before Zakharov, there was not much discussion of the statistical steady states, other than the equipartition spectra, to which the solutions of the kinetic equation might relax. The equipartition of conserved density solutions were obvious, readily seen by inspection. But, despite the fact that many of the western authors were familiar with the ideas of Kolmogorov in fully developed hydrodynamic turbulence, Zakharov (Zakharov, 1965; Zakharov and Filonenko 1967) was the only one who realized that there should also be statistical steady states in the wave turbulence context corresponding to the finite fluxes of the conserved densities such as energy and wave action from scales at which they were introduced to scales at which they were dissipated or absorbed. The kinetic equation has hidden symmetries that Zakharov understood should be there and he found them. They led him to solutions that are now called Kolmogorov-Zakharov (or KZ) spectra. For those insights, and in particular for the discovery of inverse fluxes, Zakharov, along with Kraichnan, was awarded the 2003 Dirac Medal. However, as recognized by the present authors (Newell et al. 2001), these solutions have limited validity in two respects. First, they are rarely universally valid throughout the whole spectrum. Second, in some cases certain integrals, associated with physically important functionals, may not converge. The term nonlocal is often used to describe such situations but quantitative definitions of local and nonlocal remain open challenges. Colloquially, local connotes that the dominant transfer is between neighboring (in scale) wavenumbers; nonlocal connotes that there is significant and direct transfer between widely separated scales. KZ solutions connote local, a cascade, a la Richardson (big whirls make little whirls that feed on their velocity …), of some conserved density. In this short paper, we discuss remedies for these two challenges. Fir","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134642"},"PeriodicalIF":2.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143777101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamic behavior of taxis-driven intraguild predation model of three species with BD functional response","authors":"Wenhai Shan ,&nbsp;Guoqiang Ren","doi":"10.1016/j.physd.2025.134654","DOIUrl":"10.1016/j.physd.2025.134654","url":null,"abstract":"<div><div>In this paper, we study a chemotaxis-based model for three-species intraguild predation model. We present global boundedness of classical solutions in any dimension without any restrictions on initial data and <span><math><mi>χ</mi></math></span>. Moreover, it is asserted that the considered system will approach prey-only steady state and semi-coexistence steady state in the large time limit. Finally, using the spectral analysis, we investigate the effect of Beddington-deAngelis type production term on the stability and instability of a linearized problem around the coexistence steady state, and we then extend our analysis to the nonlinear system, which makes up for the stability of coexistence steady state. Additionally, we apply our theoretical results to several concrete Holling type II functions, discuss the theoretical conditions through numerical simulations, and verify the predictions of our analysis.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134654"},"PeriodicalIF":2.7,"publicationDate":"2025-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143785056","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}

{"title":"Operator-valued kernels, machine learning, and dynamical systems","authors":"Palle E.T. Jorgensen ,&nbsp;James Tian","doi":"10.1016/j.physd.2025.134657","DOIUrl":"10.1016/j.physd.2025.134657","url":null,"abstract":"<div><div>In the context of kernel optimization, we prove a result that yields new factorizations and realizations. Our initial context is that of general positive operator-valued kernels. We further present implications for Hilbert space-valued Gaussian processes, as they arise in applications to dynamics and to machine learning. Further applications are given in non-commutative probability theory, including a new non-commutative Radon–Nikodym theorem.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134657"},"PeriodicalIF":2.7,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768178","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}

{"title":"Modularized data-driven approximation of the Koopman operator and generator","authors":"Yang Guo ,&nbsp;Manuel Schaller ,&nbsp;Karl Worthmann ,&nbsp;Stefan Streif","doi":"10.1016/j.physd.2025.134651","DOIUrl":"10.1016/j.physd.2025.134651","url":null,"abstract":"<div><div>Extended Dynamic Mode Decomposition (EDMD) is a widely-used data-driven approach to learn an approximation of the Koopman operator. Consequently, it provides a powerful tool for data-driven analysis, prediction, and control of nonlinear dynamical (control) systems. In this work, we propose a novel modularized EDMD scheme tailored to interconnected systems. To this end, we utilize the structure of the Koopman generator that allows to learn the dynamics of subsystems individually and thus alleviates the curse of dimensionality by considering observable functions on smaller state spaces. Moreover, our approach canonically enables transfer learning if a system encompasses multiple copies of a model as well as efficient adaption to topology changes without retraining. We provide probabilistic finite-data bounds on the estimation error using tools from graph theory. The efficacy of the method is illustrated by means of various numerical examples.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134651"},"PeriodicalIF":2.7,"publicationDate":"2025-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Understanding latent timescales in neural ordinary differential equation models of advection-dominated dynamical systems","authors":"Ashish S. Nair ,&nbsp;Shivam Barwey ,&nbsp;Pinaki Pal ,&nbsp;Jonathan F. MacArt ,&nbsp;Troy Arcomano ,&nbsp;Romit Maulik","doi":"10.1016/j.physd.2025.134650","DOIUrl":"10.1016/j.physd.2025.134650","url":null,"abstract":"<div><div>The neural ordinary differential equation (ODE) framework has shown considerable promise in recent years in developing highly accelerated surrogate models for complex physical systems characterized by partial differential equations (PDEs). For PDE-based systems, state-of-the-art neural ODE strategies leverage a two-step procedure to achieve this acceleration: a nonlinear dimensionality reduction step provided by an autoencoder, and a time integration step provided by a neural-network based model for the resultant latent space dynamics (the neural ODE). This work explores the applicability of such autoencoder-based neural ODE strategies for PDEs in which advection terms play a critical role. More specifically, alongside predictive demonstrations, physical insight into the sources of model acceleration (i.e., how the neural ODE achieves its acceleration) is the scope of the current study. Such investigations are performed by quantifying the effects of both autoencoder and neural ODE components on latent system time-scales using eigenvalue analysis of dynamical system Jacobians. To this end, the sensitivity of various critical training parameters – de-coupled versus end-to-end training, latent space dimensionality, and the role of training trajectory length, for example – to both model accuracy and the discovered latent system timescales is quantified. This work specifically uncovers the key role played by the training trajectory length (the number of rollout steps in the loss function during training) on the latent system timescales: larger trajectory lengths correlate with an increase in limiting neural ODE time-scales, and optimal neural ODEs are found to recover the largest time-scales of the full-order (ground-truth) system. Demonstrations are performed across fundamentally different unsteady fluid dynamics configurations influenced by advection: (1) the Kuramoto–Sivashinsky equations (2) Hydrogen-Air channel detonations (the compressible reacting Navier–Stokes equations with detailed chemistry), and (3) 2D Atmospheric flow.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134650"},"PeriodicalIF":2.7,"publicationDate":"2025-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143791386","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}

{"title":"Time asymptotic behavior of non-equilibrium flows in one space dimension","authors":"Yanni Zeng","doi":"10.1016/j.physd.2025.134647","DOIUrl":"10.1016/j.physd.2025.134647","url":null,"abstract":"<div><div>We study long time behavior of polyatomic gas flows in both translational and vibrational non-equilibrium. The author previously established global existence of solution and obtained optimal <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> time-decay rates for the solution towards an equilibrium state for the Cauchy problem. The current paper is a continuation in studying the solution behavior. An asymptotic solution is constructed explicitly using a heat kernel along the particle path and two Burgers kernels along the equilibrium acoustic directions. Convergence of the exact solution to the asymptotic solution is studied in a pointwise sense in both space and time to give a complete picture of wave propagation. The study lays a foundation for a future work on solution behavior around a shock wave, a mechanism that induces Richtmyer–Meshkov instability in mixing problems .</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134647"},"PeriodicalIF":2.7,"publicationDate":"2025-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143768101","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}

{"title":"Interaction of hydrodynamic turbulence with stratified flows and internal waves: The role of turbulent diffusion and density fluctuations","authors":"L.A. Ostrovsky","doi":"10.1016/j.physd.2025.134661","DOIUrl":"10.1016/j.physd.2025.134661","url":null,"abstract":"<div><div>An outline of studies of the interaction of small-scale turbulence with stratified turbulent flows and internal waves (IW) is presented. They include elements of general theory of such flows, internal waves’ damping on small-scale turbulence, and support and amplification of turbulence by shear flows and internal waves. It is shown that perturbation of turbulent exchange parameters (such as the diffusion coefficient) results in significant wave damping in a long-wave range. On the other hand, density fluctuations or, equivalently, variation of potential energy of turbulence due to stratification allow the shear flows and waves to support turbulence at any Richardson numbers, with no finite threshold. Publications of different years outlined here include analytical and numerical modeling, as well as applications to the available data of measurements in the upper layer of the ocean in different geographic sites.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134661"},"PeriodicalIF":2.7,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143791385","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}

{"title":"Spatiotemporal evolution model for compression of mixing width in reshocked Richtmyer-Meshkov turbulence","authors":"Fang-ping Sun (孙方平) ,&nbsp;Chang-wen Liu (刘昌文) ,&nbsp;Yu Song (宋玉) ,&nbsp;Yu-hui Wang (王宇辉) ,&nbsp;You-sheng Zhang (张又升)","doi":"10.1016/j.physd.2025.134659","DOIUrl":"10.1016/j.physd.2025.134659","url":null,"abstract":"<div><div>Turbulent mixing induced by reshocked Richtmyer-Meshkov (RM) instability is a critical process in both natural phenomena and high-energy-density applications. Among the physical quantities describing RM turbulent mixing, the mixing width is of fundamental importance. Although its temporal evolution has been extensively studied in the past several decades, there is currently no quantitative model for the compression of the mixing width caused by second shock waves. This study presents a model to predict its spatiotemporal evolution in compression process. By combining the Whitham method with Rankine–Hugoniot relations, we quantify the spatiotemporal evolution of the associated physical quantities when shock waves traverse variable-density mixing zones. Furthermore, using these quantities, we derive a model for the spatiotemporal evolution of mixing width, as well as compression rate. Good agreement between the model predictions and numerical simulations across cases with varying density ratios, incident shock waves, and density profiles confirms the model's accuracy. These findings are crucial for developing a unified model for the entire multi-stage evolution of RM turbulent mixing width, with significant implications for high-energy-density physics and engineering applications.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"476 ","pages":"Article 134659"},"PeriodicalIF":2.7,"publicationDate":"2025-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143799804","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}