A note on kernel methods for multiscale systems with critical transitions
Sign Up to like & getrecommendations! Published in 2018 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.5394
Abstract: We study the maximum mean discrepancy (MMD) in the context of critical transitions modelled by fast-slow stochastic dynamical systems. We establish a new link between the dynamical theory of critical transitions with the statistical aspects… read more here.
Keywords: systems critical; kernel methods; methods multiscale; note kernel ... See more keywords
Anisotropic multiscale systems on bounded domains
Sign Up to like & getrecommendations! Published in 2020 at "Advances in Computational Mathematics"
DOI: 10.1007/s10444-020-09784-0
Abstract: We establish a construction of hybrid multiscale systems on a bounded domain Ω ⊂ ℝ 2 ${\Omega } \subset \mathbb {R}^{2}$ consisting of shearlets and boundary-adapted wavelets, which satisfy several properties advantageous for applications to… read more here.
Keywords: systems bounded; anisotropic multiscale; multiscale systems; bounded domains ... See more keywords
Multilevel Monte Carlo for noise estimation in stochastic multiscale systems
Sign Up to like & getrecommendations! Published in 2018 at "Chemical Engineering Research and Design"
DOI: 10.1016/j.cherd.2018.10.006
Abstract: Abstract The purpose of this study is to adapt Multilevel Monte Carlo (MLMC) sampling technique for random noise estimation in stochastic multiscale systems and evaluate the performance of this method. The system under consideration was… read more here.
Keywords: noise estimation; monte carlo; stochastic multiscale; estimation stochastic ... See more keywords
Identification of FIR Models for LTI Multiscale Systems using Sparse Optimization Techniques
Sign Up to like & getrecommendations! Published in 2018 at "IFAC-PapersOnLine"
DOI: 10.1016/j.ifacol.2018.05.091
Abstract: Abstract Finite impulse response (FIR) models are very popular in process industries because of their simple model structure, flexibility to explain arbitrary complex stable linear dynamics and finally their ease of implementation in on-line applications.… read more here.
Keywords: identification fir; fir models; sparse optimization; model ... See more keywords
Effective models and predictability of chaotic multiscale systems via machine learning
Sign Up to like & getrecommendations! Published in 2020 at "Physical review. E"
DOI: 10.1103/physreve.102.052203
Abstract: Understanding and modeling the dynamics of multiscale systems is a problem of considerable interest both for theory and applications. For unavoidable practical reasons, in multiscale systems, there is the need to eliminate from the description… read more here.
Keywords: effective models; predictability; multiscale systems; degrees freedom ... See more keywords
Interface learning of multiphysics and multiscale systems
Sign Up to like & getrecommendations! Published in 2020 at "Physical review. E"
DOI: 10.1103/physreve.102.053304
Abstract: Complex natural or engineered systems comprise multiple characteristic scales, multiple spatiotemporal domains, and even multiple physical closure laws. To address such challenges, we introduce an interface learning paradigm and put forth a data-driven closure approach… read more here.
Keywords: interface learning; methodology; multiscale systems; learning multiphysics ... See more keywords