Related papers: Some Mathematical Models for ELM Signal
Exponential random graph models (ERGMs) are very flexible for modeling network formation but pose difficult estimation challenges due to their intractable normalizing constant. Existing methods, such as MCMC-MLE, rely on sequential…
Ball lightning is an impressive natural electromagnetic phenomenon occurring in atmosphere under suitable circumstances. Its origin, composition and stability issues are a matter of debate, due to presence of many evidences still…
ML models have errors when used for predictions. The errors are unknown but can be quantified by model uncertainty. When multiple ML models are trained using the same training points, their model uncertainties may be statistically…
Turbulence Models represent the workhorse for simulations used in engineering design and analysis. Despite their low computational cost and robustness, these models suffer from substantial predictive uncertainty, most of which is epistemic.…
Sources of uncertainty are reviewed for calculated atomic and molecular data that are important for plasma modeling: atomic and molecular structure and cross sections for electron-atom, electron-molecule, and heavy particle collisions. We…
In this paper we present a mathematical model of the Empirical Mode Decomposition (EMD). Although EMD is a powerful tool for signal processing, the algorithm itself lacks an appropriate theoretical basis. The interpolation and iteration…
The ambiguity involved in the use of Maxwell's equation particularly in electron plasmas is discussed. It is pointed out that in the slow time scale perturbations the displacement current is ignored but it does not imply that the electron…
Bell-Szekeres (BS) solution for colliding electromagnetic waves in Einstein-Maxwell (EM) theory describes also colliding waves in nonlinear electrodynamics (NED) with an emergent cosmological constant. Our NED model covers the first leading…
The eletromagnetic field in a linear absorptive dielectric medium, is quantized in the framework of the damped polarization model. A Hamiltonian containing a reservoir with continuous degrees of freedom, is proposed. The reservoir minimally…
The EMD algorithm, first proposed in [11], made more robust as well as more versatile in [12], is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of…
Despite many successes of quantum electrodynamics (QED), we do not presently have a good understanding of this field of physics. QED has all of the foundational problems that standard non-relativistic quantum mechanics has, and further ones…
Trained ML models are commonly embedded in optimization problems. In many cases, this leads to large-scale NLPs that are difficult to solve to global optimality. While ML models frequently lead to large problems, they also exhibit…
Despite the number of successful applications of the Extreme Learning Machine (ELM), we show that its underlying foundational principles do not have a rigorous mathematical justification. Specifically, we refute the proofs of two main…
We use ensemble machine learning algorithms to study the evolution of magnetic fields in magnetohydrodynamic (MHD) turbulence that is helically forced. We perform direct numerical simulations of helically forced turbulence using mean field…
Electric dipole moments constitute highly sensitive probes for CP-violating effects beyond the Standard Model. The upper limits obtained in various precision experiments can therefore be used to strongly restrict new physics models.…
Energy-based models (EBMs) are a simple yet powerful framework for generative modeling. They are based on a trainable energy function which defines an associated Gibbs measure, and they can be trained and sampled from via well-established…
The search of ways to generalize the theory of strong MHD turbulence for the case of non-zero cross-helicity (or energy imbalance) has attracted considerable interest recently. In our earlier publications we performed three-dimensional…
In this article we detail the use of machine learning for spatiotemporally dynamic turbulence model classification and hybridization for the large eddy simulations (LES) of turbulence. Our predictive framework is devised around the…
In unsupervised classification, Hidden Markov Models (HMM) are used to account for a neighborhood structure between observations. The emission distributions are often supposed to belong to some parametric family. In this paper, a…
Numerical approaches to the correlated electron problem have achieved considerable success, yet are still constrained by several bottlenecks, including high order polynomial or exponential scaling in system size, long autocorrelation times,…