arXiv subjects

Rafał Topolnicki

Publications and source records attributed to Rafał Topolnicki.

6 recordsLinked to original sources

arXiv2026

Direction-aware topological descriptors for elastic stiffness tensor prediction in porous materials

Classical topological descriptors used in topological data analysis (TDA) are invariant under permutations of spatial axes and therefore cannot represent the loading direction, which is essential for modeling anisotropic mechanical response. Here, this limitation is addressed by introducing a direction-aware TDA framework in which the loading axis is explicitly embedded into filtration functions used to compute both persistent homology and Euler characteristic profile descriptors. We apply this framework to predict the full elastic stiffness tensor of porous microstructures using non-directional as well as direction-aware descriptors of the structures as well as convolutional neural networks trained directly on the voxelized structure. We show that the performance of all those are comparable on the diagonal uniaxial, Poisson, and shear components. However for the twelve off-diagonal, normal shear coupling components - which govern elastic anisotropy and are the hardest to predict - only direction-aware topology retains meaningful predictive power, with all baselines, non-directional descriptors and the CNN collapsing to near-chance accuracy. When used as inputs to gradient-boosted tree models, the proposed descriptors match or exceed the accuracy of the convolutional neural network specifically on these hardest-to-predict coupling terms, despite relying on a compact, physically interpretable representation that is orders of magnitude smaller than the raw voxel grid. Overall, the results establish direction-aware TDA as a practical route for linking porous microstructure to the full anisotropic elastic response, capturing coupling terms that conventional descriptors and end-to-end deep learning models fail to resolve.

physics.comp-ph↗

arXiv2026

Transferable 3D Convolutional Neural Networks for Elastic Constants Prediction in Nanoporous Metals

The topology of nanoporous metals is crucial for determining their mechanical response. In this work, we generated 6,000 gold and 422 silver nanoporous structures and calculated three components of elastic modulus with Molecular Dynamics simulations, resulting in 19,263 data points. This study compared two distinct approaches of predicting elastic modulus: a Fully-Connected neural network trained on precomputed topological descriptors, and several 3D Convolutional neural network architectures adapted from computer vision. The 3D CNNs outperformed the descriptor-based baseline model ($R^2 = 0.704$), with to-performing DenseNet-201 architecture achieving $R^2 = 0.955$. Additionally, the effects of training grid resolution, dataset size, and descriptor integration into a model were investigated. We further demonstrated model robustness through Transfer learning: a pretrained model was fine-tuned on a much smaller dataset of denser gold structures and the dataset of denser silver structures. Finally, the trained model was employed to evaluate the mechanical properties of 100,000 stochastic nanoporous gold structures and identify the Pareto optimal designs.

cond-mat.mtrl-sci↗

arXiv2026

Physics-informed convolutional neural networks for fluid flow through porous media

Accurate simulation of fluid flow in porous media is challenging due to complex pore-space geometries and the computational cost of solving the Navier-Stokes equations. This difficulty is particularly important when repeated simulations are required, as standard numerical solvers may converge slowly in intricate porous domains. We present a neural-network-based framework for predicting pore-scale velocity fields directly from sample geometry. The method uses a convolutional encoder-decoder architecture with skip connections to preserve spatial detail while extracting multi-scale features. Physical consistency is encouraged through a custom loss function combining velocity reconstruction with incompressibility, no-flow conditions inside solids, periodicity constraints, and agreement with the global tortuosity index. We analyze the influence of the corresponding loss weights and quantify the contribution of individual loss components to prediction accuracy. Several CNN backbones are evaluated to identify architectures providing accurate and robust predictions. The generalization ability of the trained model is tested on samples outside the training distribution, including changes in obstacle geometry, boundary conditions, porosity, and realistic porous structures. Finally, we demonstrate a practical use of the predicted velocity fields as initial conditions for Lattice-Boltzmann simulations. This warm-start strategy accelerates solver convergence, reducing the number of iterations in over 90% of tested cases.

cs.LG↗

arXiv2026

Reducing Estimation Uncertainty Using Normalizing Flows and Stratification

Estimating the expectation of a real-valued function of a random variable from sample data is a critical aspect of statistical analysis, with far-reaching implications in various applications. Current methodologies typically assume (semi-)parametric distributions such as Gaussian or mixed Gaussian, leading to significant estimation uncertainty if these assumptions do not hold. We propose a flow-based model, integrated with stratified sampling, that leverages a parametrized neural network to offer greater flexibility in modeling unknown data distributions, thereby mitigating this limitation. Our model shows a marked reduction in estimation uncertainty across multiple datasets, including high-dimensional (30 and 128) ones, outperforming crude Monte Carlo estimators and Gaussian mixture models. Reproducible code is available at https://github.com/rnoxy/flowstrat.

cs.LG↗

arXiv2025

Estimation of conditional inequality curves and measures via estimating the conditional quantile function

The classical concept of inequality curves and measures is extended to conditional inequality curves and measures and a curve of conditional inequality measures is introduced. This extension provides a more nuanced analysis of inequality in relation to covariates. In particular, this enables comparison of inequalities between subpopulations, conditioned on certain values of covariates. To estimate the curves and measures, a novel method for estimating the conditional quantile function is proposed. The method incorporates a modified quantile regression framework that employs isotonic regression to ensure that there is no quantile crossing. The consistency of the proposed estimators is proved while their finite sample performance is evaluated through simulation studies and compared with existing quantile regression approaches. Finally, practical application is demonstrated by analysing salary inequality across different employee age groups, highlighting the potential of conditional inequality measures in empirical research. The code used to prepare the results presented in this article is available in a dedicated GitHub repository.

math.ST↗

arXiv2023

Topology-Driven Goodness-of-Fit Tests in Arbitrary Dimensions

This paper adopts a tool from computational topology, the Euler characteristic curve (ECC) of a sample, to perform one- and two-sample goodness of fit tests. We call our procedure TopoTests. The presented tests work for samples of arbitrary dimension, having comparable power to the state-of-the-art tests in the one-dimensional case. It is demonstrated that the type I error of TopoTests can be controlled and their type II error vanishes exponentially with increasing sample size. Extensive numerical simulations of TopoTests are conducted to demonstrate their power for samples of various sizes.

stat.ME↗