Showing papers in "Physica D: Nonlinear Phenomena in 2020"

TL;DR: A Machine Learning practitioner seeking guidance for implementing the new augmented LSTM model in software for experimentation and research will find the insights and derivations in this treatise valuable as well.

TL;DR: Lift & Learn is presented, a physics-informed method for learning low-dimensional models for large-scale dynamical systems that are able to capture the system physics in the lifted coordinates at least as accurately as traditional intrusive model reduction approaches.

TL;DR: In this paper, a data-driven method for the approximation of the Koopman generator called gEDMD is proposed, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition).

TL;DR: In this paper, the performance of LSTMs and NODEs in learning latent-space representations of dynamical equations for an advection-dominated problem given by the viscous Burgers equation was studied.

TL;DR: An accurate closed-form solution is obtained to the SIR Epidemic Model through the use of Asymptotic Approximants (Barlow et al., 2017).

TL;DR: In this article, a systematical inverse scattering transform for both focusing and defocusing nonlocal (reverse-space-time) modified Korteweg-de Vries (mKdV) equations with non-zero boundary conditions (NZBCs) at infinity is presented.

TL;DR: A modified SEIRS model with additional exit conditions in the form of death rates and resusceptibility is presented, where the model aims to reflect better on the current scenario and case data reported, such that the spread of the disease and the efficiency of the control action taken can be better understood.

TL;DR: In this article, a SIR (Susceptibles-Infected-Recovered) model with official international data for the COVID-19 pandemics provides a good example of the difficulties inherent in the solution of inverse problems.

TL;DR: In this article, a general line soliton solution with nonzero boundary condition is derived by constraining different tau functions of the Kadomtsev-Petviashvili hierarchy combined with the Hirota bilinear method.

TL;DR: The framework presented here illuminates the property of the KAF method that, under measure-preserving and ergodic dynamics, it consistently approximates the conditional expectation of observables that are acted upon by the Koopman operator of the dynamical system and are conditioned on the observed data at forecast initialization.

TL;DR: It is found that the right tail of this distribution exhibits a power law, with Pareto exponent close to one, which is nearly exactly equal to the exponent estimated directly from the distribution of confirmed cases across counties at the end of March.

TL;DR: In this paper, an uplifted reduced order model (UROM) is proposed, which integrates a physics-based projection model with a memory-embedded LSTM closure layer and a super-resolution model.

TL;DR: In this paper, exact solutions for rogue waves arising on the background of periodic standing waves in the focusing nonlinear Schrodinger equation were obtained by characterizing the Lax spectrum related to the periodic standing wave and by using the one-fold Darboux transformation.

TL;DR: The RODDA framework is applied to a CFD simulation for air pollution, using the CFD software Fluidity, in South London and it is shown that the data forecasted by the coupled model CFD+RODDA are closer to the observations with a gain in terms of execution time with respect to the classic prediction–correction cycle given by coupling CFD with a standard DA.

TL;DR: In this paper, the authors investigated a slightly generalized version of the same model and proposed a scheme for fitting the parameters of the model to real data using the time series only of the deceased individuals.

TL;DR: In this paper, Liu et al. showed that the DSM model does not admit non-constant steady states if either the chemical diffusion rate or the intrinsic growth rate of bacteria is large.

TL;DR: In this article, the authors discuss the most important features to assess the severity of an epidemic are its size and its timescale, and investigate in detail how the size and timescale of the epidemic can be changed by acting on the parameters characterizing the model.

TL;DR: The use of a data-driven method to model the dynamics of the chaotic Lorenz system leads to good prediction scores and does not require statistics of errors to be known, thus providing significant benefits compared to a simple Kalman filter update.

TL;DR: The utility of the analytical form is demonstrated through its application to the COVID-19 pandemic through the form of a modified symmetric Padé approximant that incorporates this damping of the epidemic model.

TL;DR: Wei et al. as discussed by the authors showed that the bubble re-accelerates when R e p is sufficiently large, consistent with Ramaparabhu et.al. (2006) and Wei and Livescu (2012).

TL;DR: In this paper, the inverse scattering transforms with matrix Riemann-Hilbert problems for both focusing and defocusing modified Korteweg-de Vries (mKdV) equations with non-zero boundary conditions (NZBCs) at infinity systematically were explored.

TL;DR: Variants of cross-validation (Kernel Flows and its variants based on Maximum Mean Discrepancy and Lyapunov exponents) are presented as simple approaches for learning the kernel used in these emulators.

TL;DR: In this paper, the authors considered the 3D primitive equations of oceanic and atmospheric dynamics with only horizontal eddy viscosities in the horizontal momentum equations and only vertical diffusivity in the temperature equation.

TL;DR: A class of semi-metric distance measures, which are referred to as MJ distances, are introduced, which provide an advantage over existing options such as the Hausdorff and Wasserstein metrics.

TL;DR: In this article, the authors use standard deep neural networks to classify univariate time series generated by discrete and continuous dynamical systems based on their chaotic or non-chaotic behaviour.

TL;DR: In this article, the Gerdjikov-Ivanov type derivative nonlinear Schrodinger equation was retrieved by using the algebro-geometric method and the Riemann-Hilbert method.

TL;DR: In this paper, the evolution of coherent spatio-temporal patterns in incompressible, time-dependent fluid flows driven by ergodic dynamical systems is detected and predicted.

TL;DR: In this article, the second-order rogue wave solutions of the Sasa-Satsuma evolution equation were presented in explicit form for three free parameter values of the family of rogue wave solution.

TL;DR: In this paper, the effects of different initial density distributions on the evolution of buoyancy-driven homogeneous variable-density turbulence (HVDT) at low (0.05) and high Atwood numbers are studied by using high-resolution direct numerical simulations.

TL;DR: This work develops a non-intrusive method to efficiently and accurately approximate the expensive nonlinear terms that arise in reduced nonlinear dynamical system using deep neural networks.