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| #import "../../../../lib.typ" as pop
#import "@preview/xarrow:0.3.0": xarrow
#set page("a1", margin: 2cm)
#pop.set-poster-layout(pop.layout-a1)
#pop.set-theme(pop.psi-ch)
#set text(font: "arial", size: pop.layout-a1.at("body-size"))
#let box-spacing = 1.2em
#set columns(gutter: box-spacing)
#set block(spacing: box-spacing)
#pop.update-poster-layout(spacing: box-spacing, heading-size: 30pt)
#pop.title-box(
[
#set text(fill: white)
#image("psi_scd_banner_white.png", width: 35%)
Predicting electronic screening for fast Koopmans spectral functionals
],
authors: [
#v(1cm)
#set text(fill: black)
Edward Linscott#super("1,2"),
Yannick Schubert#super("3"),
Sandra Luber#super("3"),
and Nicola Marzari#super("1,2,4")
],
institutes: [
#set text(fill: black, weight: "regular")
#super("1")Center for Scientific Computing, Theory and Data, Paul Scherrer Institute,
Switzerland
#super("2")National Centre for Computational Design and Discovery of Novel Materials
(MARVEL), Paul Scherrer Institute, Switzerland
#super("3")Department of Chemistry, University of Zurich, Switzerland
#super("4")Theory and Simulation of Materials, École Polytechnique Fédérale de Lausanne,
Switzerland"
],
background: box(image("pink-yellow.png", height: 16cm, width: 100%), inset: -2cm, outset: 0pt),
authors-size: 27pt,
institutes-size: 19pt,
)
#columns(2,[
#pop.column-box(heading: "Summary")[
- Koopmans functionals are powerful orbital-density-dependent functionals that predict spectral
properties as accurately as state-of-the-art GW@Dabo2010@Nguyen2018@Colonna2019@Linscott2023
- they rely on parameters to capture electronic screening
- we construct a ML framework to predict these parameters
- minimal training data is required to achieve desirable accuracy
]
#pop.column-box(heading: "1. What are screening parameters?")[
$
alpha_i = (angle.l n_i|epsilon^(-1) f_"Hxc"|n_i angle.r) / (angle.l n_i|f_"Hxc"|n_i angle.r)
$
- can be computed #emph[ab initio] @DeGennaro2022@Colonna2018@Colonna2022
- are the vast majority of Koopmans' computational cost
- must be accurate; if $psi_i (bold(r)) = sum_j U_(i j) phi_j (bold(r))$ then
#set text(size: 0.8em)
$
Delta epsilon_(i in"occ") =
sum_(j) alpha_j U_(i j)U_(j i)^dagger
(-E_"Hxc" [rho - n_j]+E_"Hxc" [rho] - integral d bold(r) v_"Hxc" [rho](bold(r)) n_j (bold(r)))
$
]
#pop.column-box(heading: "2. How can machine learning help?")[
#grid(columns: 8, column-gutter: 0.3em, row-gutter: 0.3em,
image("CsSnI3_disordered.png", width: 100%),
image("CsSnI3_disordered.png", width: 100%),
image("CsSnI3_disordered.png", width: 100%),
image("CsSnI3_disordered.png", width: 100%),
image("CsSnI3_disordered.png", width: 100%),
image("CsSnI3_disordered.png", width: 100%),
image("CsSnI3_disordered.png", width: 100%),
grid.cell(align: center + horizon, [...]),
grid.cell(inset: 0.2em, align: center, fill: rgb("#dc005a"), colspan: 3, text(fill: white, "train", size: 0.5em, weight: "bold")),
grid.cell(inset: 0.2em, align: center, fill: yellow, colspan: 5, text("predict", size: 0.5em, weight: "bold")),
)
#v(-0.5em)
_or_ train on a small cell and deploy on a larger cell (N.B. not a general-purpose model)
]
#pop.column-box(heading: "3. Our machine learning framework")[
$ rho_i (bold(r)) arrow.r p^i_(n_1 n_2 l k_1 k_2) arrow.r alpha_i $
#v(-0.5em)
*Descriptors* are power spectrum decompositions@Bartok2013@Himanen2020 of orbital densities
#set text(size: 0.8em)
#v(-1.5em)
$
p^i_(n_1 n_2 l,k_1 k_2) = pi sqrt(8 / (2l+1)) sum_m c_(n_1 l m,k_1)^(i *) c_(n_2 l m,k_2)^i
$
$
c^i_(n l m, k) & = integral dif bold(r) g_(n l) (r) Y_(l m)(theta,phi) n_i (
bold(r) - bold(R)_i
)
$
#set text(size: 1.25em)
*Network* is just ridge regression!
]
#pop.bibliography-box("docs/content/showcase/2025-PSI/references.bib", style: "docs/content/showcase/2025-PSI/brief.csl", body-size: 0.55em)
#colbreak()
#pop.column-box(heading: "4. Results")[
- accurate to $cal("O")$(10 meV) _cf._ typical $E_g$ accuracy of $cal("O")$(100 meV)
- speed-ups from $cal("O")$(10) to $cal("O")$(100) times!
- ridge-regression on one snapshot more accurate than oneshot
#grid(
columns: 2,
gutter: 0.2em,
[*Accuracy*], [*Speed-up*],
image("convergence_analysis_Eg_only.svg", width: 100%),
v(0.4em) + image("speedup.svg", width: 83%),
align(center, image("water_cls_calc_vs_pred_and_hist.svg", width: 98%)),
align(center, image("CsSnI3_calc_vs_pred_and_hist.svg", width: 98%)),
v(-25.8em) + text(size: 0.7em, "water"), v(-25.8em) + text(size: 0.7em, "CsSnI" + sub("3")) + v(25.1em),
[*Transferability*], [],
align(center, image("transferability_water.svg", width: 98%)),
align(center, image("transferability_cssni3.svg", width: 98%)),
)
#v(-0.5em)
]
#pop.column-box(heading: "5. Takeaways")[
- lightweight ML can predict Koopmans screening parameters
- more generally, predicting electronic response can be done efficiently with frozen-orbital approximations and ML
- try it now with `koopmans`! (`koopmans-functionals.org`)
]
])
#v(-1em)
#pop.bottom-box(
heading-box-args: (inset: 1cm, fill: rgb("#dc005a")),
logo: grid(columns: 2, align: horizon + center, column-gutter: 3em,
image("marvel_white_on_transparent.png", height: 2em),
image("snf_white_on_transparent.png", height: 2em),
),
)[
#box(height: 2em)[#set text(size: 27pt, fill: white, weight: "bold")
#align(horizon)[For more details, see Schubert _et al._, npj Computational Materials (2024)]]
]
|