Machine-learning-based neutrino-event generation constrained by experimental measurements

Jose Luis Bonilla; Krzysztof M. Graczyk; Rwik Dharmapal Banerjee; Beata E. Kowal; Hemant Prasad; Jan T. Sobczyk

hep-phOct 14, 2026

Machine-learning-based neutrino-event generation constrained by experimental measurements

Authors: Jose Luis Bonilla, Krzysztof M. Graczyk, Rwik Dharmapal Banerjee, Beata E. Kowal, Hemant Prasad, Jan T. Sobczyk

Organizations: Institute of Theoretical Physics, University of Wrocław, plac Maxa Borna 9, 50-204, Wrocław, Poland

Abstract

We present a generative surrogate for charged-current $ν_μ$ -nucleus scattering that can be calibrated to measured differential cross sections without event-level experimental samples. Starting from a theoretical interaction model, we fine-tune the surrogate to a MicroBooNE measurement and show that this also improves the description of observables not used in the fit. The calibrated model can also be applied to measurements from different neutrino fluxes without retuning, while retaining event-level predictions of outgoing-muon kinematics. Our results show that experimental cross sections can directly constrain generative event models while preserving their applicability across different observables and beam configurations.

Figures & tables

Figure 1: Training scheme: (a) The

\sigma

-DNN and GAN are pretrained on NuWro. (b) Fine-tuning alternates adversarial regularization using the data-informed reservoir with a differentiable full-covariance fit to the forward-smeared MicroBooNE measurement. The latter updates

G

and the

\sigma

-DNN.

	$\chi_{v}^{2}$ /n	$\chi_{c}^{2}$ /n
$\sigma$ -DNN ${}_{\text{B}}$ , GAN ${}_{\text{B}}$	461.7/138	460.3/138
$\sigma$ -DNN ${}_{\text{B}}$ , GAN ${}_{\text{T}}$	435.6/138	268.4/138
$\sigma$ -DNN ${}_{\text{T}}$ , GAN ${}_{\text{B}}$	152.0/138	500.1/138
$\sigma$ -DNN ${}_{\text{T}}$ , GAN ${}_{\text{T}}$	110.5/138	220.3/138

Table 1: The values of

\chi^{2}_{v}

and

\chi^{2}_{c}

over the number of bins (n) for four configurations of the models: base (subscript B) and fine-tuned (subscript T)

\sigma

-DNN and GAN models. Computed for samples of 1 million events.

Figure 2: Base and tuned models compared with the MicroBooNE double-differential cross-section measurement [ 23 ] for various

E_{\nu}

ranges. Grey vertical dashed lines separate different

E_{\nu}

regions, from left to right:

[0.2,0.705]

[0.705,1.05]

[1.05,1.57]

, and

[1.57,4]

GeV.

Figure 3: Event distribution at

E_{\nu}=3

GeV generated by the fine-tuned GAN with and without the reservoir sub-step.

Figure 4: Base and fine-tuned models compared to the MicroBooNE measurement [ 24 ] :

\sigma/\langle E_{\nu}\rangle

(left),

d\sigma/dE_{\mu}

(center) and

d\sigma/dE_{\text{had}}

(right).

Figure 5: Base model, tuned model, and the MicroBooNE data [ 25 , 26 ] for

d\sigma/d\cos\theta

, not used in the training.

Figure 6: Base model, tuned model, and ArgoNeuT data [ 27 , 28 ] for

d\sigma/dp_{\mu}

distribution. The shaded area shows the

p_{\mu}

range of the training MicroBooNE data.

Figure S1: Training scheme. (a) The

\sigma

-DNN and the conditional GAN (

G

D

) are first trained on NuWro. (b) Fine-tuning combines (1) adversarial regularization using the data-informed reservoir and (2) a differentiable full-covariance fit in the measurement space. The discriminator is updated on every reservoir batch, while every fifth discriminator update is followed by an adversarial update of

G

and by the

\chi_{c}^{2}

update of

G

and the

\sigma

-DNN. Sampling of

E_{\nu}

from

\Phi\hat{\sigma}

carries no gradient.

Figure S2: Cross section predicted by NuWro and by the base neural network. Predictions were made on the energies sampled for training ( NuWro ) and points in the middle of the energies of the tables (DNN).

Figure S3: The output of each block of

G

and

D

is used as an input to all subsequent blocks; all inputs to a block are averaged before it is processed.

Figure S4: One-million-event reservoir used to fine-tune the GAN. The reservoir is constructed by resampling truth-level NuWro events according to flux-weighted target occupancies inferred from the MicroBooNE measurement. The visible bin structures reflect the experimental binning.

Figure S5: Left: A representation of a flux

\Phi

bin of width

\Delta E_{\nu}

divided into sub-bins of flux

\Phi^{\prime}

of width

\Delta E^{\prime}_{\nu}

. Right: Measurement bins of width

\Delta E^{\prime\prime}_{\nu,\omega}

that may contain several

\Phi

bins or fractions, but always entire

\Phi^{\prime}

bins.

Figure S6: Left: double differential cross section as a function of

E_{\nu}

from the base DNN models, using exact event counts to create histograms, and the result using the differentiable histogram approximation, with a batch of 4000 events. Right: same data as left, but smeared with the matrix

A_{c}

Figure S7: Base and tuned models compared with MicroBooNE two-dimensional differential cross-section data in

E_{\nu}

Bins [ 23 ] on the left, and the (MC

-

Data)

/

Unc ratio on the right. The black plot in the ratio figure shows Data

-|

Data

|

to highlight the negative cross-section values found in the experimental measurement, and the gray bands show the measurement uncertainties. Grey vertical dashed lines show the different

E_{\nu}

regions.

	$\sigma(E_{\nu})$		$d\sigma/dE_{\mu}$		$d\sigma/dE_{\text{had}}$
	$\chi^{2}_{c}$ /n	$\chi^{2}_{v}$ /n	$\chi^{2}_{c}$ /n	$\chi^{2}_{v}$ /n	$\chi^{2}_{c}$ /n	$\chi^{2}_{v}$ /n
Base	58.1/10	54.2/10	29.1/11	69.1/11	17.1/8	41.3/8
Tuned	44.2/10	0.5/10	12.7/11	6.4/11	4.4/8	6.0/8

Table S1:

\chi_{c}^{2}

and

\chi_{v}^{2}

over the number of bins of the base and tuned DNN models for

\sigma(E_{\nu})

d\sigma/dE_{\mu}

, and

d\sigma/dE_{\text{had}}

Figure S8: Base model, tuned model, and MicroBooNE data [ 25 , 26 ] for

d^{2}\sigma/dE_{\mu}d\cos\theta

(left) and

d\sigma/d\cos\theta

(right).

	$d^{2}\sigma/dE_{\mu}d\cos\theta$		$d\sigma/d\cos\theta$
	$\chi^{2}_{c}$ /n	$\chi^{2}_{v}$ /n	$\chi^{2}_{c}$ /n	$\chi^{2}_{v}$ /n
Base	257.0/69	554.7/69	291.5/17	2991.7/17
Tuned	109.2/69	87.9/69	6.8/17	4.8/17

Table S2: Same as Table S1 but for

d^{2}\sigma/dE_{\mu}d\cos\theta

and

d\sigma/d\cos\theta

Figure S9: Base model, tuned model, and ArgoNeuT data [ 27 , 28 ] . Left:

d\sigma/d\theta

. Right:

d\sigma/dp_{\mu}

. Results for neutrinos in the NuMI neutrino beam. The shaded areas on the right-side plot show the

p_{\mu}

range of the training MicroBooNE data.

	$\chi^{2}_{v}$ /n
	$d\sigma/d\theta$	$d\sigma/dp_{\mu}$
Base	13.2/14	6.1/11
Tuned	11.4/14	6.0/11

Table S3: Comparison of MicroBooNE-tuned DNN to ArgoNeuT measurement of muon neutrino

\nu_{\mu}

on NuMI neutrino beam.

	$\chi^{2}_{v}$ /n
	$d\sigma/d\theta$	$d\sigma/dp_{\mu}$
Base	9.1/18	9.6/20
Tuned	9.6/18	9.1/20

Table S4: Comparison of MicroBooNE-tuned DNN to ArgoNeuT measurement of muon neutrino

\nu_{\mu}

on NuMI anti-neutrino

\bar{\nu}_{\mu}

beam.

Figure S10: Base model, tuned model, and ArgoNeuT data [ 27 , 28 ] . Left:

d\sigma/d\theta

. Right:

d\sigma/dp_{\mu}

. Results for neutrinos on the NuMI antineutrino beam. The shaded areas on the right-side plots show the

p_{\mu}

range of the training MicroBooNE data.

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