Stability analysis of a double similarity transformed coupled cluster theory

Agarawal, Valay; Chakraborty, Anish; Maitra, Rahul

doi:10.1063/5.0018383

Cited by 11 publications

(10 citation statements)

References 28 publications

(25 reference statements)

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“…The bias in the DM towards the lower right corner indicates that the dynamics associated with the iterative scheme is convergent towards a unique set of fixed points. Such DM, however, under large input perturbation shows repetitive or chaotic phase space trajectory, as previously established by Agarawal et al 5 . FIG.…”

Section: Establishing Master-slave Dynamicssupporting

confidence: 74%

“…In other words, such an analysis is not system-specific. In a previous paper 5 , a similar analysis was put forward for studying the iteration dynamics under an input perturbation for regions where linear stability is lost. Thus the current work may be considered as a generalization for multivariate iteration dynamics for regions which are characterized by a unique set of fixed-point solutions.…”

Section: Establishing Master-slave Dynamicsmentioning

confidence: 99%

“…Clearly, in a CC scheme with single and double excitations (CCSD), the dimension of t's becomes (n o n v + n 2 o n 2 v ), where n o and n v are the number of hole and particle orbitals respectively, and determining these many amplitudes requires an iterative n 2 o n 4 v scaling. In a recent paper 5 by the present authors, a posteriori analysis of the time series associated with the iterative scheme of a different version of the CC theory was presented. The authors introduced an input perturbation to the amplitude determining equations to probe the nonlinearity associated with the discrete-time dynamics of the iterative scheme.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Accelerating Coupled Cluster Calculations with Nonlinear Dynamics and Shallow Machine Learning

Agarawal,

Roy,

Chakraborty

et al. 2020

Preprint

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The dynamics associated with the time series of the iteration scheme of coupled cluster theory has been analysed. The phase space analysis indicates the presence of a few significant cluster amplitudes, mostly involving valence excitations, which dictate the dynamics, while all other amplitudes are enslaved. Starting with a few initial iterations to establish the inter-relationship among the cluster amplitudes, a supervised Machine Learning scheme with polynomial Kernel Ridge Regression model has been employed to express each of the enslaved variables uniquely in terms of the master amplitudes. The subsequent coupled cluster iterations are restricted to a reduced dimension only to determine those significant excitations, and the enslaved variables are determined through the already established functional mapping. We will show that our scheme leads to tremendous reduction in computational time without sacrificing the accuracy.

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Section: Establishing Master-slave Dynamicssupporting

confidence: 74%

Section: Establishing Master-slave Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Accelerating Coupled Cluster Calculations with Nonlinear Dynamics and Shallow Machine Learning

Agarawal,

Roy,

Chakraborty

et al. 2020

Preprint

Self Cite

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“…• The Squared Root Euclidean Distance Matrix (EDM), or what has simply been defined as distance matrix D in our earlier works. 19,22 The elements of the distance matrix D is defined as…”

Section: Customized Kernel Regression Modelmentioning

confidence: 99%

Assessing the Performance of Nonlinear Regression based Machine Learning Models to Solve Coupled Cluster Theory

Agarawal,

Roy,

Shrawankar

et al. 2021

Preprint

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The iterative solution of the coupled cluster equations exhibits a synergistic relationship among the various cluster amplitudes. The iteration scheme may be viewed as a multivariate discrete time propagation of nonlinearly coupled equations, which is dictated by only a few principal cluster amplitudes. These principal amplitudes usually correspond to only a few valence excitations, whereas all other cluster amplitudes are enslaved, and behave as auxiliary variables. Staring with a few trial iterations, we employ a supervised machine learning strategy to establish an interdependence between

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“…It was also established that there exists interesting inter-relationship among the cluster operators. In a follow-up work 11 , the authors had demonstrated that the macroscopic pattern of the entire iteration dynamics is governed by a few principal cluster operators, which were taken to be the unstable modes, and they were assigned to be the order parameters. On the other hand, there exist numerous amplitudes which are smaller in magnitude, and they are enslaved under the principal amplitudes.…”

Section: Introductionmentioning

confidence: 99%

An Approximate Coupled Cluster Theory via Nonlinear Dynamics and Synergetics: the Adiabatic Decoupling Conditions

Agarawal,

Patra,

Maitra

2021

Preprint

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The coupled cluster iteration scheme is analysed as a multivariate discrete-time map using nonlinear dynamics and synergetics. The nonlinearly coupled set of equations to determine the cluster amplitudes are driven by a fraction of the entire set of the cluster amplitudes. These driver amplitudes enslave all other amplitudes through a synergistic inter-relationship, where the latter class of amplitudes behave as the auxiliary variables. The driver and the auxiliary variables exhibit vastly different time scales of relaxation during the iteration process to reach the fixed points. The fast varying auxiliary amplitudes are small in magnitude, while the driver amplitudes are large, and they have a much longer time scale of relaxation. Exploiting their difference in relaxation time-scale, we employ an adiabatic decoupling approximation, where each of the fast relaxing auxiliary modes are expressed as unique functional of the principal amplitudes. This results in a tremendous reduction in the independent degrees of freedom. On the other hand, only the driver amplitudes are determined accurately via exact coupled cluster equations. We will demonstrate that the iteration scheme has an order of magnitude reduction in computational scaling than the conventional scheme. With a few pilot numerical examples, we would demonstrate that this scheme can achieve very high accuracy with significant savings in computational time.

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Stability analysis of a double similarity transformed coupled cluster theory

Cited by 11 publications

References 28 publications

Accelerating Coupled Cluster Calculations with Nonlinear Dynamics and Shallow Machine Learning

Accelerating Coupled Cluster Calculations with Nonlinear Dynamics and Shallow Machine Learning

Assessing the Performance of Nonlinear Regression based Machine Learning Models to Solve Coupled Cluster Theory

An Approximate Coupled Cluster Theory via Nonlinear Dynamics and Synergetics: the Adiabatic Decoupling Conditions

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