pres_intel/scemama.org

#+TITLE: Library development within TREX
#+DATE: 12/03/2021
#+AUTHOR: Anthony Scemama

#+LaTeX_HEADER: \institute{Lab. Chimie et Physique Quantiques, IRSAMC, UPS/CNRS, Toulouse (France)}
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#+BEAMER_THEME: trex
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#+LaTeX_HEADER: \usepackage{physics}
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#+startup: beamer
#+options: H:1 toc:nil

* Quantum chemistry
  
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  [[./dirac_4.jpg]]
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  [[./dirac2.png]]
   #+LATEX: \end{column}                                                                                  
   #+LATEX: \end{columns}                                                                                  

* Quantum chemistry
  
   #+LATEX: \begin{columns}
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   #+LATEX: \begin{exampleblock}{}
   - Describing matter with quantum mechanics (Schrödinger's equation)
   - Users: theoretical chemists and physicists
   #+LATEX: \end{exampleblock}
   #+LATEX: \end{column}                                                                                  
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   [[./Water.png]]
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   [[./casula.png]]
   #+LATEX: \end{column}
   #+LATEX: \begin{column}{0.6\textwidth}
   #+LATEX: \begin{exampleblock}{Implications for society}
   | - Health      | Drug design                       |
   | - Electronics | Nano- and micro-electronics       |
   | - Materials   | Carbon nanotubes, graphene, \dots |
   | - Catalysis   | Enzymatic reactions, petroleum    |
   #+LATEX: \end{exampleblock}
   #+LATEX: \end{column}
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* TREX: Targeting REal chemical accuracy at the EXascale

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   [[./Curve.png]]

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   #+LATEX: \begin{exampleblock}{Objective: Make codes ready for exascale}
    How: Instead of re-writing codes, provide libraries
    - One library for exchanging information between codes (*TREXIO*)
    - One library for high-performance (*QMCkl*)
   #+LATEX: \end{exampleblock}
   #+LATEX: \begin{exampleblock}{QMC: Quantum Monte Carlo methods}
    - Highly accurate
    - Massively parallelisable (multiple QMC trajectories)
    - CPU intensive
   #+LATEX: \end{exampleblock}
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* Quantum Monte Carlo (QMC)

#+BEGIN_SRC latex
\alert{Problem}: Stochastic resolution of the Schr\"odinger equation for $N$ electrons
\begin{eqnarray}
E &= &\frac{\int \dcoord \Phi(\coord) {\cal H} \Phi(\coord)}
                         {\int \dcoord \Phi(\coord) \Phi(\coord)} \nonumber \\
                  &\sim & \sum \frac{ {\cal H}\Psi(\coord )}{\Psi(\coord )}
                    \text{, sampled with } (\Psi \times \Phi)
\nonumber
\end{eqnarray}
\begin{columns}
\begin{column}{.5\textwidth}
\begin{itemize}
\item[$\cal H $: ] Hamiltonian operator
\item[$E$: ] Energy
\end{itemize}
\end{column}
\begin{column}{.4\textwidth}
\begin{itemize}
\item[$\coord $: ] Electron coordinates
\item[$\Phi $: ] Almost exact wave function
\item[$\Psi $: ] Trial wave function
\end{itemize}
\end{column}
\end{columns}
#+END_SRC

* Quantum Monte Carlo (QMC)

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    - Very low memory requirements (no integrals)
    - Distribute walkers on different cores or compute nodes
    - No blocking communication: near-ideal scaling
    - Difficulty: parallelize within a QMC trajectory
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   [[./Qmc.png]]
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* QMC kernel library (QMCkl)

** Computational kernels
  - QMCkl will contain the main kernels of QMC methods
  - Written together by QMC experts and HPC experts
  - Multiple high performance implementations of the kernels, tuned
    for different
    - architectures
    - problem sizes
    - requested accuracy (reduced precision)
  - The sequence of kernels will be scheduled with the StarPU runtime

  
* QMC kernel library (QMCkl)

** Two implementations
  - /Documentation/ : easy to read and understand, not necessarily efficient
  - /High performance/ : efficient, but not necessarily readable by physicists/chemists
  - Both /Documentation/ and /High performance/ have the same API.

** Advantages
   - The code can stay easy to understand by the physicists/chemists
     Performance-related aspects are delegated to the library
   - Changing architecture requires only linking with another 
     version of the library
   - Scientific code development does not break the performance
   - Better re-use of the optimization effort among the community

* Literate programming                                             :noexport:

  #+BEGIN_quote
  Literate programming is a programming paradigm introduced by Donald
  Knuth in which a computer program is given an explanation of its
  logic in a natural language, such as English, interspersed with
  snippets of macros and traditional source code, from which
  compilable source code can be generated. (Wikipedia)
  #+END_quote
  
* Documentation library                                            :noexport:
  Literate programming with org-mode:
  - Here, comments are more important than code
  - Can add graphics, \LaTeX formulas, tables, etc
  - Documentation always synchronized with the code
  - Some routines can be generated by embedded scripts
  - Most of the the first report was generated from the documentation
  - Kernels are implemented in Fortran for readability
  - The API is C-compatible: QMCkl appears like a C library
    $\Longrightarrow$ can be used in all other languages

* Design strategy

  1. Kernel extraction: QMC specialists agree on the 
     mathematical expression of the problem
  2. A mini-application is written to find the optimal data layout
     with HPC experts from real-size examples
  3. The kernel is written in the documentation library
  4. The documentation library is linked in a QMC code to check correctness
  5. HPC experts provide an HPC version of the kernel
  6. The HPC library is linked in the QMC codes of the CoE
     
* Our first application : 3-body Jastrow factor

#+LATEX: \newcommand{\Jeen}{J_{\text{een}}}
#+LATEX: \newcommand{\Nel}{N_{\text{elec}}}
#+LATEX: \newcommand{\Nat}{N_{\text{nucl}}}
#+LATEX: \newcommand{\Nord}{N_{\text{nord}}}
#+LATEX: \newcommand{\lmax}{p-k-2\delta_{k,0}}
#+LATEX: \newcommand{\br}{\mathbf{r}}
#+LATEX: \newcommand{\bR}{\mathbf{R}}
#+LATEX: \newcommand{\ttr}{\, \bar{\mathtt{r}}}
#+LATEX: \newcommand{\tR}{\, \bar{\mathtt{R}}}
#+LATEX: \newcommand{\tP}{\, \bar{\mathtt{P}}}

\[
  \Jeen (\br,\bR) = \sum_{\alpha=1}^{\Nat} \sum_{i=1}^{\Nel} \sum_{j=1}^{i-1}
\sum_{p=2}^{\Nord} \sum_{k=0}^{p-1}
\sum_{l=0}^{\lmax} c_{lkp\alpha}
\left( {r}_{ij} \right)^k
\left[ \left( {R}_{i\alpha} \right)^l + \left( {R}_{j\alpha} \right)^l \right]
\left( {R}_{i\,\alpha} \, {R}_{j\alpha} \right)^{(p-k-l)/2} 
\]

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   [[./speedup.pdf]]
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   - Gradient and Laplacian are also required
   - Up to $20\times$ faster than in the original code
   - $\sim 80\%$ of the AVX-512 peak is reached
   - Expressed with a DGEMM kernel $\Longrightarrow$ also efficient on GPU
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* Links

  - TREX web site : https://trex-coe.eu
  - QMCkl documentation : https://trex-coe.github.io/qmckl
  - QMCkl repository : https://github.com/trex-coe/qmckl

* Export                                                           :noexport:
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  #+RESULTS:
  : /home/scemama/TEX/ISC2021/scemama.pdf