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We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…

Machine Learning · Computer Science 2021-11-24 Zhen Chen , Victor Churchill , Kailiang Wu , Dongbin Xiu

The cosmological fluid equations are used to study the nonlinear mode coupling of density fluctuations. We find that for realistic cosmological spectra there is a significant contribution to the nonlinear evolution on scales of interest to…

Astrophysics · Physics 2007-05-23 Bhuvnesh Jain , Edmund Bertschinger

Current and future large scale structure surveys aim to constrain the neutrino mass and the equation of state of dark energy. We aim to construct accurate and interpretable symbolic approximations to the linear and nonlinear matter power…

Cosmology and Nongalactic Astrophysics · Physics 2025-05-28 Ce Sui , Deaglan J. Bartlett , Shivam Pandey , Harry Desmond , Pedro G. Ferreira , Benjamin D. Wandelt

We examine the influence of percent-level dark energy corrections to the nonlinear matter power spectrum on constraints of the dark energy equation of state from future weak lensing probes. We explicitly show that a poor approximation (off…

Cosmology and Nongalactic Astrophysics · Physics 2010-04-28 Shahab Joudaki , Asantha Cooray , Daniel E. Holz

Recent observations of DESI hint that dark matter (DM) may not be cold but have a non-zero equation of state (EoS) parameter, and that dark energy (DE) may not be a cosmological constant. In this work, we explore the possibility of a…

Cosmology and Nongalactic Astrophysics · Physics 2025-09-03 Tian-Nuo Li , Peng-Ju Wu , Guo-Hong Du , Yan-Hong Yao , Jing-Fei Zhang , Xin Zhang

In the context of high penetration of renewables, the need to build dynamic models of power system components based on accessible measurement data has become urgent. To address this challenge, firstly, a neural ordinary differential…

Systems and Control · Electrical Eng. & Systems 2022-08-02 Tannan Xiao , Ying Chen , Shaowei Huang , Tirui He , Huizhe Guan

The equation of state (EoS) of dark energy plays an important role in the evolution of the universe and arouses great interests in recent years. With the progress on observational technique, precise constraint on the EoS of dark energy…

General Relativity and Quantum Cosmology · Physics 2019-08-19 Hai-Nan Lin , Xin Li , Li Tang

{abridged} We study the imprints on the formation and evolution of cosmic structures of dynamical dark energy models, characterized by an oscillating equation of state. The redshift evolution of the equation of state parameter w(z) for dark…

Cosmology and Nongalactic Astrophysics · Physics 2015-03-19 F. Pace , C. Fedeli , L. Moscardini , M. Bartelmann

Dark energy affects the CMB through its perturbations and affects both CMB and Sn-Ia through its background evolution. Using recent CMB and Sn-Ia data sets, together with the most general parameterization of the dark energy equation of…

One of the central challenges in modern cosmology is understanding the nature of dark energy and its evolution throughout the history of the Universe. Dark energy is commonly modeled as a perfect fluid with a time-varying equation-of-state…

Cosmology and Nongalactic Astrophysics · Physics 2025-02-26 Samsuzzaman Afroz , Suvodip Mukherjee

We perform a detailed study of the cosmological dynamics of a recently proposed infrared modification of the Einstein equations, based on the introduction of a non-local term constructed with $m^2g_{\mu\nu}\Box^{-1} R$, where $m$ is a mass…

High Energy Physics - Theory · Physics 2015-06-17 Stefano Foffa , Michele Maggiore , Ermis Mitsou

One of the unresolved questions currently in cosmology is that of the non-linear accelerated expansion of the universe. This has been attributed to the so called Dark Energy (DE). The accelerated expansion of the universe is deduced from…

General Physics · Physics 2017-08-31 Kenath Arun , S B Gudennavar , A Prasad , C Sivaram

In order to constrain ultra light dark matter models with current and near future weak lensing surveys we need the predictions for the non-linear dark matter power-spectrum. This is commonly extracted from numerical simulations or from…

Cosmology and Nongalactic Astrophysics · Physics 2025-10-15 Dennis Fremstad , Hans A. Winther

The nature of dark matter remains one of the most fundamental and unresolved questions in modern cosmology. In most cosmological models, dark matter is typically modeled as pressureless dust with an equation of state (EoS) parameter $w_{\rm…

Cosmology and Nongalactic Astrophysics · Physics 2025-12-22 Tian-Nuo Li , Yi-Min Zhang , Yan-Hong Yao , Peng-Ju Wu , Jing-Fei Zhang , Xin Zhang

We investigate a spherical overdensity model for the non-clustering dark energy (DE) with the constant equation of state, w in a flat universe. In this case, the exact solution for the evolution of the scale factor is obtained for general…

Cosmology and Nongalactic Astrophysics · Physics 2010-10-27 Seokcheon Lee , Kin-Wang Ng

Dark energy as a quintessence component causes a typical modification of the background cosmic expansion, which in addition to its clustering properties, can leave a potentially distinctive signature on large scale structures. Many previous…

Cosmology and Nongalactic Astrophysics · Physics 2010-02-04 J. -M. Alimi , A. Fuzfa , V. Boucher , Y. Rasera , J. Courtin , P. -S. Corasaniti

We explore the properties of dark energy models for which the equation-of-state, w, defined as the ratio of pressure to energy density, crosses the cosmological-constant boundary w = -1. We adopt an empirical approach, treating the dark…

Astrophysics · Physics 2010-04-06 Robert R. Caldwell , Michael Doran

Modern sky surveys are returning precision measurements of cosmological statistics such as weak lensing shear correlations, the distribution of galaxies, and cluster abundance. To fully exploit these observations, theorists must provide…

Cosmology and Nongalactic Astrophysics · Physics 2015-06-15 Katrin Heitmann , Earl Lawrence , Juliana Kwan , Salman Habib , David Higdon

The present thesis aims to tackle two critical aspects of present and future cosmological analysis of Large-Scale Structure (LSS): accurate modelling of the nonlinear matter power spectrum beyond $\Lambda$CDM, and efficient computational…

Cosmology and Nongalactic Astrophysics · Physics 2025-08-15 Karim Carrion

Several independent cosmological data, collected within the last twenty years, revealed the accelerated expansion rate of the Universe, usually assumed to be driven by the so called dark energy, which, according to recent estimates,…

Cosmology and Nongalactic Astrophysics · Physics 2020-10-16 Marek Demianski , Elisabeta Lusso , Maurizio Paolillo , Ester Piedipalumbo , Guido Risaliti