QuantImPy: Minkowski functionals and functions with Python

Boelens, Arnout

doi:10.1016/j.softx.2021.100823

Cited by 16 publications

(7 citation statements)

References 17 publications

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“…We introduce geometrical and statistical descriptors to characterize the morphological evolution. The Minkowski functionals are a set of mathematical measures for analyzing the morphology and topology in a system [ 47 , 48 , 49 , 63 ]. Among the three geometrical characteristics, i.e., area fraction, boundary length, and domain connectivity, the connectivity correlates with pattern complexity, and we choose it as one of the crucial measures during phase separation.…”

Section: Methods and Analysismentioning

confidence: 99%

Connecting Structural Characteristics and Material Properties in Phase-Separating Polymer Solutions: Phase-Field Modeling and Physics-Informed Neural Networks

Lin,

Chen,

2023

Polymers

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The formed morphology during phase separation is crucial for determining the properties of the resulting product, e.g., a functional membrane. However, an accurate morphology prediction is challenging due to the inherent complexity of molecular interactions. In this study, the phase separation of a two-dimensional model polymer solution is investigated. The spinodal decomposition during the formation of polymer-rich domains is described by the Cahn–Hilliard equation incorporating the Flory–Huggins free energy description between the polymer and solvent. We circumvent the heavy burden of precise morphology prediction through two aspects. First, we systematically analyze the degree of impact of the parameters (initial polymer volume fraction, polymer mobility, degree of polymerization, surface tension parameter, and Flory–Huggins interaction parameter) in a phase-separating system on morphological evolution characterized by geometrical fingerprints to determine the most influential factor. The sensitivity analysis provides an estimate for the error tolerance of each parameter in determining the transition time, the spinodal decomposition length, and the domain growth rate. Secondly, we devise a set of physics-informed neural networks (PINN) comprising two coupled feedforward neural networks to represent the phase-field equations and inversely discover the value of the embedded parameter for a given morphological evolution. Among the five parameters considered, the polymer–solvent affinity is key in determining the phase transition time and the growth law of the polymer-rich domains. We demonstrate that the unknown parameter can be accurately determined by renormalizing the PINN-predicted parameter by the change of characteristic domain size in time. Our results suggest that certain degrees of error are tolerable and do not significantly affect the morphology properties during the domain growth. Moreover, reliable inverse prediction of the unknown parameter can be pursued by merely two separate snapshots during morphological evolution. The latter largely reduces the computational load in the standard data-driven predictive methods, and the approach may prove beneficial to the inverse design for specific needs.

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Section: Methods and Analysismentioning

confidence: 99%

Connecting Structural Characteristics and Material Properties in Phase-Separating Polymer Solutions: Phase-Field Modeling and Physics-Informed Neural Networks

Lin,

Chen,

2023

Polymers

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“…For 2D images, the three measures M i are the area (A in Equation 1) which implies porosity, contour length of the boundaries between pores and solids (L in Equation 2), and Euler characteristic (Equation 3), an indicator of connectedness (topology) of a system. We use QuantImPy, an opensource Python package to perform Minkowski functionals calculation (Boelens & Tchelepi, 2021).…”

Section: Minkowski Functionalsmentioning

confidence: 99%

AI-Based Digital Rocks Augmentation and Assessment Metrics

Liu,

Chang,

Prodanović

et al. 2024

Preprint

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Reliable uncertainty model calculation in subsurface engineering from pore- and grain-scale to field-scale relies on sufficient data, but subsurface dataset acquisition remains a challenge, particularly in domains where data collection is expensive or time-consuming, such as Computed Topography (CT) imaging for digital rock images. While AI-based data augmentation may assist the model training, it still requires many training images as well as the quality assessment of generated data. Yet, most data quantitative metrics flatten spatial data into vectors; therefore, removing the essential spatial relationships within the data. We evaluate topology-based metrics for quality assessment of AI-based image augmentation, coupled with digital rocks augmentation practice using the Single image Generative Adversarial Network (SinGAN) for binarized (segmented) images. Compared to most traditional dimensionality reduction methods that process images into a flattened vector, we propose topological image analysis for dimensionality reduction while preserving the essential geometric and topological features of the high-dimensional data. To demonstrate our proposed approach, we evaluate the generated images starting from four distinct digital rock samples, sorted sandstone, synthetic sphere pack, limestone, and poorly sorted sandstone, using Minkowski functionals, image graph network-based measures, graph Laplacian-based measures, local trend maps, and a homogeneity-heterogeneity classifier. Our workflow suggests that AI-based digital rock augmentation, combined with topological dimensionality reduction offers a powerful tool for enhanced quality assessment and diagnostic of digital rock augmentation and improved interpretation to support decision-making.

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“…We show in the third, fourth, and fifth rows of Figure 3 the Minkowski functional statistics for our data. We compute these statistics using the Python package QuantImPy (Boelens & Tchelepi 2021). The area 0  just gives another perspective of the previous distributions of pixels, as it directly relates to the cumulative distribution of pixel values.…”

Section: Quantitative Assessmentmentioning

confidence: 99%

Generative Models of Multichannel Data from a Single Example—Application to Dust Emission

Blancard

Allys

Auclair

et al. 2023

ApJ

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The quest for primordial B-modes in the cosmic microwave background has emphasized the need for refined models of the Galactic dust foreground. Here we aim at building a realistic statistical model of the multifrequency dust emission from a single example. We introduce a generic methodology relying on microcanonical gradient descent models conditioned by an extended family of wavelet phase harmonic (WPH) statistics. To tackle the multichannel aspect of the data, we define cross-WPH statistics, quantifying non-Gaussian correlations between maps. Our data-driven methodology could apply to various contexts, and we have updated the software PyWPH, on which this work relies, accordingly. Applying this to dust emission maps built from a magnetohydrodynamics simulation, we construct and assess two generative models: (1) a (I, E, B) multi-observable input, and (2) a { I ν } ν multifrequency input. The samples exhibit consistent features compared to the original maps. A statistical analysis of model 1 shows that the power spectra, distributions of pixels, and Minkowski functionals are captured to a good extent. We analyze model 2 by fitting the spectral energy distribution (SED) of both the synthetic and original maps with a modified blackbody (MBB) law. The maps are equally well fitted, and a comparison of the MBB parameters shows that our model succeeds in capturing the spatial variations of the SED from the data. Besides the perspectives of this work for dust emission modeling, the introduction of cross-WPH statistics opens a new avenue to characterize non-Gaussian interactions across different maps, which we believe will be fruitful for astrophysics.

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QuantImPy: Minkowski functionals and functions with Python

Cited by 16 publications

References 17 publications

Connecting Structural Characteristics and Material Properties in Phase-Separating Polymer Solutions: Phase-Field Modeling and Physics-Informed Neural Networks

Connecting Structural Characteristics and Material Properties in Phase-Separating Polymer Solutions: Phase-Field Modeling and Physics-Informed Neural Networks

AI-Based Digital Rocks Augmentation and Assessment Metrics

Generative Models of Multichannel Data from a Single Example—Application to Dust Emission

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