Related papers: Inversion using a new low-dimensional representati…
We apply recent advances in machine learning and computer vision to a central problem in materials informatics: The statistical representation of microstructural images. We use activations in a pre-trained convolutional neural network to…
Selecting the appropriate dimensionality reduction (DR) technique and determining its optimal hyperparameter settings that maximize the accuracy of the output projections typically involves extensive trial and error, often resulting in…
Aircraft-based surveying to collect airborne electromagnetic data is a key method to image large swaths of the Earth's surface in pursuit of better knowledge of aquifer systems. Despite many years of advancements, 3D inversion still poses…
In groundwater hydrology, geophysical imaging holds considerable promise for improving parameter estimation, due to the generally high resolution and spatial coverage of geophysical data. However, inversion of geophysical data alone cannot…
The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…
Dimension reduction (DR) is commonly utilized to capture the intrinsic structure and transform high-dimensional data into low-dimensional space while retaining meaningful properties of the original data. It is used in various applications,…
We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution $\rho$ in $\mathbb{R}^D$, that is nearly supported on a $d$-dimensional set $\mathcal{M}$ - for example…
The health condition of components in civil infrastructures can be described by various discrete states according to their performance degradation. Inferring these states from measurable responses is typically an ill-posed inverse problem.…
Dimensionality reduction (DR) is a popular method for preparing and analyzing high-dimensional data. Reduced data representations are less computationally intensive and easier to manage and visualize, while retaining a significant…
To quantify uncertainties in inverse problems of partial differential equations (PDEs), we formulate them into statistical inference problems using Bayes' formula. Recently, well-justified infinite-dimensional Bayesian analysis methods have…
Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…
Tomographic image reconstruction is relevant for many medical imaging modalities including X-ray, ultrasound (US) computed tomography (CT) and photoacoustics, for which the access to full angular range tomographic projections might be not…
Estimating subsurface dielectric properties is essential for applications ranging from environmental surveys of soils to nondestructive evaluation of concrete in infrastructure. Conventional wave inversion methods typically assume few…
Seismic inverse modeling is a common method in reservoir prediction and it plays a vital role in the exploration and development of oil and gas. Conventional seismic inversion method is difficult to combine with complicated and abstract…
Modern deep learning models generalize remarkably well in-distribution, despite being overparametrized and trained with little to no explicit regularization. Instead, current theory credits implicit regularization imposed by the choice of…
The data-based discovery of effective, coarse-grained (CG) models of high-dimensional dynamical systems presents a unique challenge in computational physics and particularly in the context of multiscale problems. The present paper offers a…
Deep Neural Networks (DNNs) demonstrate remarkable capabilities in learning complex hierarchical data representations, but the nature of these representations remains largely unknown. Existing global explainability methods, such as Network…
Recently, multiple formulations of vision problems as probabilistic inversions of generative models based on computer graphics have been proposed. However, applications to 3D perception from natural images have focused on low-dimensional…
Seismic datasets contain valuable information that originate from areas of interest in the subsurface; such seismic reflections are however inevitably contaminated by other events created by waves reverberating in the overburden.…
Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic…