In this article the procedure and method for the ice accretion prediction for different airfoils using artificial neural networks (ANNs) are discussed. A dataset for the neural network is based on the numerical experiment results—obtained through iceFoam solver—with four airfoils (NACA0012, General Aviation, Business Jet, and Commercial Transport). Input data for neural networks include airfoil and ice geometries, transformed into a set of parameters using a parabolic coordinate system and Fourier series expansion. Besides input features include physical parameters of flow (velocity, temperature, droplets diameter, liquid water content, time of ice accretion) and angle of attack. The novelty of this work is in that the neural network dataset includes various airfoils and the data augmentation technique being a combination of all time slices. Several artificial neural networks (ANNs), fully connected networks (FCNNs), and convolutional networks (CNNs) were trained to predict airfoil ice shapes. Two different loss functions were considered. In order to improve performance of models, batch normalization and dropout layers were used. The most accurate results of ice shape prediction were obtained using CNN and FCNN that applied batch normalization and dropout layers to output neurons of each layer.

The modified rheological Vinogradov-Pokrovskii model is applied to solve the problem of the mathematical modeling of three-dimensional flow of a nonlinear viscoelastic fluid in a plane-parallel...

A mathematical model of the self-heating of dispersed solid mixtures is considered taking into account the boundary kinetics of formation of the intermediate product phase. It is shown that...

Mathematical models of non-small-cell lung cancer are powerful tools that use clinical and experimental data to describe various aspects of tumorigenesis. The developed algorithms capture phenotypic changes in the tumor and predict changes in tumor behavior, drug resistance, and clinical outcomes of anti-cancer therapy. The aim of this study was to propose a mathematical model that predicts the changes in the cellular composition of patient-derived tumor organoids over time with a perspective of translation of these results to the parental tumor, and therefore to possible clinical course and outcomes for the patient. Using the data on specific biomarkers of cancer cells (PD-L1), tumor-associated macrophages (CD206), natural killer cells (CD8), and fibroblasts (αSMA) as input, we proposed a model that accurately predicts the cellular composition of patient-derived tumor organoids at a desired time point. Combining the obtained results with “omics” approaches will improve our understanding of the nature of non-small-cell lung cancer. Moreover, their implementation into clinical practice will facilitate a decision-making process on treatment strategy and develop a new personalized approach in anti-cancer therapy.