Comet.ml

... and friends

Adam Getchell & Scott Kirkland

University of California, Davis

Data Science Initiative

GitHub for Machine Learning

Demo

https://www.comet.ml/acgetchell/iris

Numerical Quantum Gravity

... in 3 easy steps

Path Integral

\langle B|T|A\rangle=\int\mathcal{D}[g]e^{iI_{EH}}
⟨B∣T∣A⟩=∫D[g]eiIEH\langle B|T|A\rangle=\int\mathcal{D}[g]e^{iI_{EH}}
I_{EH}=\frac{1}{16\pi G_{N}}\int d^{4}x\sqrt{-g}(R-2\Lambda)
IEH=116πGN∫d4x−g(R−2Λ) I_{EH}=\frac{1}{16\pi G_{N}}\int d^{4}x\sqrt{-g}(R-2\Lambda)

Equations of Motion

\partial S = 0 \rightarrow R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=8\pi G_{N}T_{\mu\nu}
∂S=0→Rμν−12Rgμν=8πGNTμν\partial S = 0 \rightarrow R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=8\pi G_{N}T_{\mu\nu}

Ricci scalar

Cosmological constant

Ricci tensor

Ricci scalar

Stress-Energy tensor

Transition probability amplitude

Foliation

I_{R}=\frac{1}{8\pi G_{N}}\left(\sum\limits_{hinges}A_{h}\delta_{h}-\Lambda\sum\limits_{simplices}V_{s}\right)
IR=18πGN(∑hingesAhδh−Λ∑simplicesVs)I_{R}=\frac{1}{8\pi G_{N}}\left(\sum\limits_{hinges}A_{h}\delta_{h}-\Lambda\sum\limits_{simplices}V_{s}\right)

Metropolis-Hastings

\langle B|T|A\rangle=\sum\limits_{triangulations}\frac{1}{C(T)}e^{-I_{R}(T)}
⟨B∣T∣A⟩=∑triangulations1C(T)e−IR(T)\langle B|T|A\rangle=\sum\limits_{triangulations}\frac{1}{C(T)}e^{-I_{R}(T)}

Inequivalent Triangulations

Partition Function

Wick rotation

  1. Pick an ergodic (Pachner) move
  2. Make that move with a probability of a1a2, where:
a_{1}=\frac{move[i]}{\sum\limits_{i}move[i]}
a1=move[i]∑imove[i]a_{1}=\frac{move[i]}{\sum\limits_{i}move[i]}
a_{2}=e^{\Delta S}
a2=eΔSa_{2}=e^{\Delta S}

Fast foliated Delaunay Triangulations in CGAL

256 timeslices, 222,132 vertices,  2,873,253 faces, 1,436,257 simplices

Creation time: 284.596s

(MacBook Pro Retina, Mid 2012)

Demo

https://www.comet.ml/acgetchell/cdt-plusplus
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