Related papers: AI-driven Bayesian inference of statistical micros…
We present a new Bayesian methodology to learn the unknown material density of a given sample by inverting its two-dimensional images that are taken with a Scanning Electron Microscope. An image results from a sequence of projections of the…
We derive exact expressions for effective elastodynamic properties of two-phase composites in the long-wavelength (quasistatic) regime via homogenized constitutive relations that are local in space. This is accomplished by extending the…
The quantitative characterization of the microstructure of random heterogeneous media in $d$-dimensional Euclidean space $\mathbb{R}^d$ via a variety of $n$-point correlation functions is of great importance, since the respective infinite…
The heterogeneous micromechanical properties of biological tissues have profound implications across diverse medical and engineering domains. However, identifying full-field heterogeneous elastic properties of soft materials using…
Effective learning of asymmetric and local features in images and other data observed on multi-dimensional grids is a challenging objective critical for a wide range of image processing applications involving biomedical and natural images.…
High dimensional and heterogeneous count data are collected in various applied fields. In this paper, we look closely at high-resolution sequencing data on the microbiome, which have enabled researchers to study the genomes of entire…
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…
Elastic geophysical properties (such as P- and S-wave velocities) are of great importance to various subsurface applications like CO$_2$ sequestration and energy exploration (e.g., hydrogen and geothermal). Elastic full waveform inversion…
Full-waveform inversion (FWI) is a powerful geophysical imaging technique that infers high-resolution subsurface physical parameters by solving a non-convex optimization problem. However, due to limitations in observation, e.g., limited…
Physical imaging is a foundational characterization method in areas from condensed matter physics and chemistry to astronomy and spans length scales from atomic to universe. Images encapsulate crucial data regarding atomic bonding,…
Quantifying the relationship between geometric descriptors of microstructure and effective properties like permeability is essential for understanding and improving the behavior of porous materials. In this paper, we employ a previously…
The 3D microstructure of porous media, such as electrodes in lithium-ion batteries or fiber-based materials, significantly impacts the resulting macroscopic properties, including effective diffusivity or permeability. Consequently,…
Full waveform inversion (FWI) can be expressed in a Bayesian framework, where the associated uncertainties are captured by the posterior probability distribution (PPD). In practice, solving Bayesian FWI with sampling-based methods such as…
Semi-structured regression models enable the joint modeling of interpretable structured and complex unstructured feature effects. The structured model part is inspired by statistical models and can be used to infer the input-output…
Estimation of spatially-varying parameters for computationally expensive forward models governed by partial differential equations is addressed. A novel multiscale Bayesian inference approach is introduced based on deep probabilistic…
Material indentation studies, in which a probe is brought into controlled physical contact with an experimental sample, have long been a primary means by which scientists characterize the mechanical properties of materials. More recently,…
Seismic full-waveform inversion (FWI) uses full seismic records to estimate subsurface velocity structure. This requires a highly nonlinear and nonunique inverse problem to be solved, and Bayesian methods have been used to quantify…
Microstructured materials, such as architected metamaterials and phononic crystals, exhibit complex wave propagation phenomena due to their internal structure. While full-scale numerical simulations can capture these effects, they are…
Microstructure reconstruction, a major component of inverse computational materials engineering, is currently advancing at an unprecedented rate. While various training-based and training-free approaches are developed, the majority of…
Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…