Table
This commit is contained in:
parent
24f2b44dae
commit
0643fb7008
@ -190,7 +190,7 @@ In the algorithm proposed by Rendell\cite{rendell_1991}, for each given triplet
|
||||
|
||||
\subsection{Stochastic formulation}
|
||||
|
||||
We propose an algorithm influenced by the semi-stochastic approach introduced in Ref.~\citenum{garniron_2017}, originally developed for computing the Epstein-Nesbet second-order perturbation correction to the energy.
|
||||
We propose an algorithm influenced by the semi-stochastic approach introduced in Ref.~\citenum{garniron_2017}, originally developed for computing the Epstein-Nesbet second-order perturbation correction to the energy.
|
||||
|
||||
The perturbative triples correction is expressed as a sum of corrections, each indexed solely by virtual orbitals:
|
||||
\begin{equation}
|
||||
@ -212,7 +212,7 @@ P^{abc} = \frac{1}{\mathcal{N}} \frac{1}{\max \left(\epsilon_{\min}, \epsilon_a
|
||||
where $\mathcal{N}$ normalizes the sum such that $\sum_{abc} P^{abc} = 1$, and $\epsilon_{\min}$ is an arbitrary minimal denominator to ensure that $P^{abc}$ does not diverge. In our calculations, we have set $\epsilon_{\min}$ to 0.2~a.u.
|
||||
The perturbative contribution is then evaluated as an average over $M$ samples
|
||||
\begin{equation}
|
||||
E_{(T)} = \left\langle \frac{E^{abc}}{P^{abc}} \right \rangle_{P^{abc}} =
|
||||
E_{(T)} = \left\langle \frac{E^{abc}}{P^{abc}} \right \rangle_{P^{abc}} =
|
||||
\lim_{M \to \infty} \sum_{abc} \frac{n^{abc}}{M} \frac{E^{abc}}{P^{abc}}.
|
||||
\end{equation}
|
||||
where $n^{abc}$ is the number of times the triplet $(a,b,c)$ was drawn with probability $P^{abc}$.
|
||||
@ -383,7 +383,7 @@ Our methodology proves especially advantageous for scenarios requiring the
|
||||
aggregation of numerous CCSD(T) energies, such as neural network training or
|
||||
the exploration of potential energy surfaces.
|
||||
In a recent article, Ceperley \textit{et al} highlight the pivotal role of Quantum Monte
|
||||
Carlo (QMC) in generating data for constructing potential energy surfaces.\cite{ceperley_2024}
|
||||
Carlo (QMC) in generating data for constructing potential energy surfaces.\cite{ceperley_2024}
|
||||
The study suggests that stochastic noise inherent in QMC can facilitate machine
|
||||
learning model training, demonstrating that models can benefit from numerous,
|
||||
less precise data points. These findings are supported by an analysis of
|
||||
@ -434,11 +434,11 @@ On the ARM architecture, we utilized the \textsc{ArmPL} library for BLAS operati
|
||||
\begin{ruledtabular}
|
||||
\begin{tabular}{lccccccc}
|
||||
CPU & $N_{\text{cores}}$ & Shared L3 cache & $V$ & $F$ & Memory Bandwidth & Peak DP & Measured performance \\
|
||||
& (MB) & & & (GHz) & (GB/s) & (GFlop/s) & (GFlop/s) \\
|
||||
\hline
|
||||
\textsc{EPYC} 7513 & $2\times 128$ & $2 \times 32)$ & 4 & 2.6 & 409.6 & 2~662 & 1~576 \\
|
||||
Xeon Gold 6130 & $2\times 22$ & $2 \times 16)$ & 8 & 2.1 & 256.0 & 2~150 & 667 \\ % 239.891
|
||||
ARM Q80 & $32$ & $80$ & 2 & 2.8 & 204.8 & 1~792 & 547 \\ % 292.492
|
||||
& & (MB) & & (GHz) & (GB/s) & (GFlop/s) & (GFlop/s) \\
|
||||
\hline
|
||||
\textsc{EPYC} 7513 & $2 \times 32$ & $2\times 128$ & 4 & 2.6 & 409.6 & 2~662 & 1~576 \\
|
||||
Xeon Gold 6130 & $2 \times 16$ & $2\times 22$ & 8 & 2.1 & 256.0 & 2~150 & 667 \\ % 239.891
|
||||
ARM Q80 & $80$ & $32$ & 2 & 2.8 & 204.8 & 1~792 & 547 \\ % 292.492
|
||||
\end{tabular}
|
||||
\end{ruledtabular}
|
||||
\caption{\label{tab:flops} Average performance of the code measured as the number of double precision (DP) floating-point operations per second (Flop/s) on different machines.}
|
||||
|
Loading…
Reference in New Issue
Block a user