Dynamic hyperpolarizability calculations of large systems: The linear-scaling divide-and-conquer approach

2012 ◽  
Vol 136 (8) ◽  
pp. 084108 ◽  
Author(s):  
Masato Kobayashi ◽  
Tsuguki Touma ◽  
Hiromi Nakai
Keyword(s):  
Divide And Conquer ◽  
Linear Scaling ◽  
Large Systems

A DIVIDE-AND-CONQUER STRATEGY FOR QUALITATIVE SIMULATION AND FUZZY IDENTIFICATION OF COMPLEX DYNAMICAL SYSTEMS

2011 ◽  
Vol 19 (03) ◽  
pp. 423-452 ◽  
Author(s):  
RAFFAELLA GUGLIELMANN ◽  
LILIANA IRONI
Keyword(s):  
Scale Up ◽  
Fuzzy Rule ◽  
Qualitative Reasoning ◽  
Divide And Conquer ◽  
Rule Base ◽  
Qualitative Simulation ◽  
Biological Domain ◽  
Large Systems ◽  
Behavioural Description

Fuzzy systems properly integrated with Qualitative Reasoning approaches yield a hybrid identification method, called FS-QM, that outperforms traditional data-driven approaches in terms of robustness, interpretability and efficiency in both rich and poor data contexts. This results from the embedment of the entire system dynamics predicted by the simulation of its qualitative model, represented by fuzzy-rules, into the fuzzy system. However, the intrinsic limitation of qualitative simulation to scale up to complex and large systems significantly reduces its efficient applicability to real-world problems. The novelty of this paper deals with a divide-and-conquer approach that aims at making qualitative simulation tractable and the derived behavioural description comprehensible and exhaustive, and consequently usable to perform system identification. The partition of the complete model into smaller ones prevents the generation of a complete temporal ordering of all unrelated events, that is one of the major causes of intractable branching in qualitative simulation. The set of generated behaviours is drastically but beneficially reduced as it still captures the entire range of possible dynamical distinctions. Thus, the properties of the correspondent fuzzy-rule base, that guarantee robustness and interpretability of the identified model, are preserved. The strategy we propose is discussed through a case study from the biological domain.

A Novel Scheme for Accurate Md Simulations of Large Systems

1997 ◽  
Vol 491 ◽  
Author(s):  
Alessandro De Vita ◽  
Roberto Car
Keyword(s):  
Electronic Structure ◽  
Material Science ◽  
Tight Binding ◽  
Md Simulations ◽  
Model Potential ◽  
Black Box ◽  
Linear Scaling ◽  
Large Systems ◽  
Large Material ◽  
Ab Initio Models

ABSTRACTWe present a simple and informationally efficient approach to electronic-structure-based simulations of large material science systems. The algorithm is based on a flexible embedding scheme, in which the parameters of a model potential are fitted at run time to some precise information relevant to localised portions of the system. Such information is computed separately on small subsystems by electronic-structure “black box” subprograms, e.g. based on tight-binding and/or ab initio models. The scheme allows to enforce electronic structure precision only when and where needed, and to minimise the computed information within a desired accuracy, which can be systematically controlled. Moreover, it is inherently linear scaling, and highly suitable for modern parallel platforms, including those based on non-uniform processing. The method is demonstrated by performing computations of tight-binding accuracy on solid state systems in the ten thousand atoms size scale.

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