Krzysztof M. Graczyk

Krzysztof M. Graczyk, Beata E. Kowal, Artur M. Ankowski et al.

Transfer learning (TL) allows a deep neural network (DNN) trained on one type of data to be adapted for new problems with limited information. We propose to use the TL technique in physics. The DNN learns the details of one process, and after fine-tuning, it makes predictions for related processes. We consider the DNNs, trained on inclusive electron-carbon scattering data, and show that after fine-tuning, they accurately predict cross sections for electron interactions with nuclear targets ranging from helium-3 to iron.

Krzysztof M. Graczyk, Dawid Strzelczyk, Maciej Matyka

We adopt convolutional neural networks (CNN) to predict the basic properties of the porous media. Two different media types are considered: one mimics the sand packings, and the other mimics the systems derived from the extracellular space of biological tissues. The Lattice Boltzmann Method is used to obtain the labeled data necessary for performing supervised learning. We distinguish two tasks. In the first, networks based on the analysis of the system's geometry predict porosity and effective diffusion coefficient. In the second, networks reconstruct the concentration map. In the first task, we propose two types of CNN models: the C-Net and the encoder part of the U-Net. Both networks are modified by adding a self-normalization module [Graczyk \textit{et al.}, Sci Rep 12, 10583 (2022)]. The models predict with reasonable accuracy but only within the data type, they are trained on. For instance, the model trained on sand packings-like samples overshoots or undershoots for biological-like samples. In the second task, we propose the usage of the U-Net architecture. It accurately reconstructs the concentration fields. In contrast to the first task, the network trained on one data type works well for the other. For instance, the model trained on sand packings-like samples works perfectly on biological-like samples. Eventually, for both types of the data, we fit exponents in the Archie's law to find tortuosity that is used to describe the dependence of the effective diffusion on porosity.

Krzysztof M. Graczyk, Jaroslaw Pawlowski, Sylwia Majchrowska et al.

The statistical properties of the density map (DM) approach to counting microbiological objects on images are studied in detail. The DM is given by U$^2$-Net. Two statistical methods for deep neural networks are utilized: the bootstrap and the Monte Carlo (MC) dropout. The detailed analysis of the uncertainties for the DM predictions leads to a deeper understanding of the DM model's deficiencies. Based on our investigation, we propose a self-normalization module in the network. The improved network model, called \textit{Self-Normalized Density Map} (SNDM), can correct its output density map by itself to accurately predict the total number of objects in the image. The SNDM architecture outperforms the original model. Moreover, both statistical frameworks -- bootstrap and MC dropout -- have consistent statistical results for SNDM, which were not observed in the original model. The SNDM efficiency is comparable with the detector-base models, such as Faster and Cascade R-CNN detectors.

Krzysztof M. Graczyk, Kornel Witkowski

We present the application of the physics-informed neural network (PINN) approach in Bayesian formulation. We have adopted the Bayesian neural network framework to obtain posterior densities from Laplace approximation. For each model or fit, the evidence is computed, which is a measure that classifies the hypothesis. The optimal solution is the one with the highest value of evidence. We have proposed a modification of the Bayesian algorithm to obtain hyperparameters of the model. We have shown that within the Bayesian framework, one can obtain the relative weights between the boundary and equation contributions to the total loss. Presented method leads to predictions comparable to those obtained by sampling from the posterior distribution within the Hybrid Monte Carlo algorithm (HMC). We have solved heat, wave, and Burger's equations, and the results obtained are in agreement with the exact solutions, demonstrating the effectiveness of our approach. In Burger's equation problem, we have demonstrated that the framework can combine information from differential equations and potential measurements. All solutions are provided with uncertainties (induced by the model's parameter dependence) computed within the Bayesian framework.

Jose L. Bonilla, Krzysztof M. Graczyk, Artur M. Ankowski et al.

We propose a new approach to simulate neutrino scattering events as an alternative to the standard Monte Carlo generator approach. Generative adversarial neural network (GAN) models are developed to simulate charged current neutrino-carbon collisions in the few-GeV energy range. We consider a simplified framework to generate muon kinematic variables, specifically its energy and scattering angle. GAN models are trained on simulation data from \nuwro{} Monte Carlo event generator. Two GAN models have been obtained: one simulating quasielastic neutrino-nucleus scatterings and another simulating all interactions at given neutrino energy. The models work for neutrino energy ranging from 300 MeV to 10 GeV. The performance of both models has been assessed using two statistical metrics. It is shown that both GAN models successfully reproduce the distribution of muon kinematics.

Beata E. Kowal, Krzysztof M. Graczyk, Artur M. Ankowski et al.

Employing the neural network framework, we obtain empirical fits to the electron-scattering cross sections for carbon over a broad kinematic region, extending from the quasielastic peak through resonance excitation to the onset of deep-inelastic scattering. We consider two different methods of obtaining such model-independent parametrizations and the corresponding uncertainties: based on the bootstrap approach and the Monte Carlo dropout approach. In our analysis, the $χ^2$ defines the loss function, including point-to-point and normalization uncertainties for each independent set of measurements. Our statistical approaches lead to fits of comparable quality and similar uncertainties of the order of $7$%. To test these models, we compare their predictions to test datasets excluded from the training process and theoretical predictions obtained within the spectral function approach. The predictions of both models agree with experimental measurements and theoretical calculations. We also perform a comparison to a dataset lying beyond the covered kinematic region, and find that the bootstrap approach shows better interpolation and extrapolation abilities than the one based on the dropout algorithm.

Jose L. Bonilla, Krzysztof M. Graczyk, Artur M. Ankowski et al.

We utilize transfer learning to extrapolate the physics knowledge encoded in a Generative Adversarial Network (GAN) model trained on synthetic charged-current (CC) neutrino-carbon inclusive scattering data. This base model is adapted to generate CC inclusive scattering events (lepton kinematics only) for neutrino-argon and antineutrino-carbon interactions. Furthermore, we assess the effectiveness of transfer learning in re-optimizing a custom model when new data comes from a different neutrino-nucleus interaction model. Our results demonstrate that transfer learning significantly outperforms training generative models from scratch. To study this, we consider two training data sets: one with 10,000 and another with 100,000 events. The models obtained via transfer learning perform well even with smaller training data. The proposed method provides a promising approach for constructing neutrino scattering event generators in scenarios where experimental data is sparse.

Beata E. Kowal, Krzysztof M. Graczyk, Artur M. Ankowski et al.

We present an updated deep neural network model for inclusive electron-carbon scattering. Using the bootstrap model [Phys.Rev.C 110 (2024) 2, 025501] as a prior, we incorporate recent experimental data, as well as older measurements in the deep inelastic scattering region, to derive a re-optimized posterior model. We examine the impact of these new inputs on model predictions and associated uncertainties. Finally, we evaluate the resulting cross-section predictions in the kinematic range relevant to the Hyper-Kamiokande and DUNE experiments.

Krzysztof M. Graczyk, Maciej Matyka

Convolutional neural networks (CNN) are utilized to encode the relation between initial configurations of obstacles and three fundamental quantities in porous media: porosity ($\varphi$), permeability $k$, and tortuosity ($T$). The two-dimensional systems with obstacles are considered. The fluid flow through a porous medium is simulated with the lattice Boltzmann method. It is demonstrated that the CNNs are able to predict the porosity, permeability, and tortuosity with good accuracy. With the usage of the CNN models, the relation between $T$ and $\varphi$ has been reproduced and compared with the empirical estimate. The analysis has been performed for the systems with $\varphi \in (0.37,0.99)$ which covers five orders of magnitude span for permeability $k \in (0.78, 2.1\times 10^5)$ and tortuosity $T \in (1.03,2.74)$.