## Abstract

Time-resolved photoelectron spectroscopy provides a versatile tool for investigating electron dynamics in gaseous, liquid, and solid samples on sub-femtosecond time scales. The extraction of information from spectrograms recorded with the attosecond streak camera remains a difficult challenge. Common algorithms are highly specialized and typically computationally heavy. In this work, we apply deep neural networks to map from streaking traces to near-infrared pulses as well as electron wavepackets and extensively benchmark our results on simulated data. Additionally, we illustrate domain-shift to real-world data. We also attempt to quantify the model predictive uncertainty. Our deep neural networks display competitive retrieval quality and superior tolerance against noisy data conditions, while reducing the computational time by orders of magnitude.

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### Data availability

Data underlying the results presented in this paper as well as the source code and trained neural networks may be obtained from the authors upon reasonable request.

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### Equations (11)

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(1)
$${S}_{\mathrm{W}\mathrm{P}\mathrm{A}}({E}_{f},\tau )={\left|\u0237{\int}_{-\mathrm{\infty}}^{\mathrm{\infty}}dt\phantom{\rule{thinmathspace}{0ex}}\chi (t+\tau ){\mathrm{e}}^{\u0237({E}_{f}+{I}_{p})t}{\mathrm{e}}^{\u0237{\mathrm{\Phi}}_{V}({E}_{f},t)}\right|}^{2},$$
(2)
$${\mathrm{\Phi}}_{V}(E,t)=-{\int}_{t}^{\mathrm{\infty}}d{t}^{\prime}\phantom{\rule{thinmathspace}{0ex}}(\sqrt{2E}{A}_{\mathrm{N}\mathrm{I}\mathrm{R}}({t}^{\prime})+\frac{1}{2}{A}_{\mathrm{N}\mathrm{I}\mathrm{R}}^{2}({t}^{\prime})),$$
(3)
$$\stackrel{~}{\chi}(E)=\sqrt{{I}_{\mathrm{W}\mathrm{P}}(E)}\phantom{\rule{thinmathspace}{0ex}}{\mathrm{e}}^{\u0237{\varphi}_{\mathrm{W}\mathrm{P}}(E)},$$
(4)
$${S}_{\mathrm{C}\mathrm{M}\mathrm{A}}({E}_{f},\tau )\propto {\left|{\mathcal{F}}^{-1}[\chi (t+\tau )\stackrel{~}{G}(t)]\right|}^{2},$$
(5)
$$\mathrm{S}\mathrm{N}\mathrm{R}=10{\mathrm{log}}_{10}\left[\frac{\sum _{i}\sum _{j}S[i,j]}{\sum _{i}\sum _{j}|S[i,j]-{S}^{\prime}[i,j]|}\right],$$
(6)
$$\mathcal{J}\left(\overrightarrow{\theta}\right)=\frac{1}{N}\sum _{n=0}^{N-1}\mathcal{L}({y}^{(n)},f({x}^{(n)};\overrightarrow{\theta})),$$
(7)
$${\mathcal{L}}_{A}({\overrightarrow{A}}_{\mathrm{N}\mathrm{I}\mathrm{R}},{\hat{\overrightarrow{A}}}_{\mathrm{N}\mathrm{I}\mathrm{R}})=\frac{\Vert {\overrightarrow{A}}_{\mathrm{N}\mathrm{I}\mathrm{R}}-{\hat{\overrightarrow{A}}}_{\mathrm{N}\mathrm{I}\mathrm{R}}{\Vert}_{2}}{\Vert {\overrightarrow{A}}_{\mathrm{N}\mathrm{I}\mathrm{R}}{\Vert}_{2}}\phantom{\rule{thinmathspace}{0ex}}.$$
(8)
$${\mathcal{L}}_{\varphi}({\overrightarrow{\varphi}}_{\mathrm{W}\mathrm{P}},{\hat{\overrightarrow{\varphi}}}_{\mathrm{W}\mathrm{P}})=\sum _{i=0}^{I-1}[w[i]{({\varphi}_{\mathrm{W}\mathrm{P}}[i]-{\hat{\varphi}}_{\mathrm{W}\mathrm{P}}[i])}^{2}+\eta {({I}_{\mathrm{W}\mathrm{P}}[i]-{\hat{I}}_{\mathrm{W}\mathrm{P}}[i])}^{2}]\phantom{\rule{thinmathspace}{0ex}}.$$
(9)
$$w[i]=1({I}_{\mathrm{W}\mathrm{P}}[i]>{t}_{h}),$$
(10)
$${\mathcal{Q}}_{\varphi}({\overrightarrow{\varphi}}_{\mathrm{W}\mathrm{P}},{\hat{\overrightarrow{\varphi}}}_{\mathrm{W}\mathrm{P}})={\left[\frac{\sum _{i}w[i]{({\varphi}_{\mathrm{W}\mathrm{P}}[i]-{\hat{\varphi}}_{\mathrm{W}\mathrm{P}}[i])}^{2}}{\sum _{i}w[i]}\right]}^{\frac{1}{2}}\phantom{\rule{thinmathspace}{0ex}}.$$
(11)
$${\mathcal{Q}}_{S}(S,\hat{S})={\left[\frac{\sum _{i}\sum _{j}{(S[i,j]-\hat{S}[i,j])}^{2}}{\sum _{i}\sum _{j}{(S[i,j])}^{2}}\right]}^{\frac{1}{2}}\phantom{\rule{thinmathspace}{0ex}}.$$