Slides Template

Sam Foreman
foremans@anl.gov

Argonne National Laboratory

2023-09-07

Slide Template
(feel free to make your own!)

 
Sam Foreman
saforem2/slides-template

2023-08-21 @ Nobel Prize Award Ceremony

Ongoing Work & Collaborations

Cool Callouts

Climate Modeling

Lattice QCD

saforem2/slides-template

Quarto + Reveal.js

  • Quarto Guide
    • Comprehensive guide to using Quarto
    • Start with the tutorial if you’re new to Quarto

Executable Code

import numpy as np
import matplotlib.pyplot as plt

from slides import set_plot_style

set_plot_style()

r = np.arange(0, 2, 0.01)
theta = 2 * np.pi * r
fig, ax = plt.subplots(
  subplot_kw={
    'projection': 'polar'
  }
)
ax.plot(theta, r)
ax.set_rticks([0.5, 1.0, 1.5, 2.])
ax.grid(True)
plt.show()

slides.set_plot_style()

Tabsets

Content for Tab A

Content for Tab B

Overview

  1. Background: {MCMC,HMC}
  2. L2HMC: Generalizing MD
  3. References
  4. Extras

Markov Chain Monte Carlo (MCMC)

Goal

Generate independent samples \{x_{i}\}, such that1 \{x_{i}\} \sim p(x) \propto e^{-S(x)} where S(x) is the action (or potential energy)

  • Want to calculate observables \mathcal{O}:
    \left\langle \mathcal{O}\right\rangle \propto \int \left[\mathcal{D}x\right]\hspace{4pt} {\mathcal{O}(x)\, p(x)}

If these were independent, we could approximate: \left\langle\mathcal{O}\right\rangle \simeq \frac{1}{N}\sum^{N}_{n=1}\mathcal{O}(x_{n})
\sigma_{\mathcal{O}}^{2} = \frac{1}{N}\mathrm{Var}{\left[\mathcal{O} (x) \right]}\Longrightarrow \sigma_{\mathcal{O}} \propto \frac{1}{\sqrt{N}}

saforem2/lattice23