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Gaussian processes offers a convenient way to perform nonparametric reconstructions of observational data assuming only a kernel which describes the covariance between neighbouring points in a data set. We approach the ambiguity in the…
A novel methodology is presented for reconstructing the Eulerian number density field of dispersed gas-droplet flows modelled using the Fully Lagrangian Approach (FLA). In this work, the nonparametric framework of kernel regression is used…
Advances in hyperspectral imaging modes including electron energy loss spectroscopy (EELS) in scanning transmission electron microscopy (STEM) bring forth the challenges of exploratory and subsequently physics-based analysis of…
A method to reconstruct fields, source strengths and physical parameters based on Gaussian process regression is presented for the case where data are known to fulfill a given linear differential equation with localized sources. The…
Flow of cerebrospinal fluid in perivascular spaces is a key mechanism underlying brain transport and clearance. In this paper, we present a mathematical and numerical formalism for reduced models of pulsatile viscous fluid flow in networks…
The paper presents a Graph Attention Convolutional Network (GACN) for flow reconstruction from very sparse data in time-varying geometries. The model incorporates a feature propagation algorithm as a preprocessing step to handle extremely…
We introduce new Gaussian Process (GP) high-order approximations to linear operations that are frequently used in various numerical methods. Our method employs the kernel-based GP regression modeling, a non-parametric Bayesian approach to…
Recent cosmological observations have achieved high-precision measurements of the Universe's expansion history, prompting the use of nonparametric methods such as Gaussian processes (GP) regression. We apply GP regression for reconstructing…
In nonparametric regression, it is common for the inputs to fall in a restricted subset of Euclidean space. Typical kernel-based methods that do not take into account the intrinsic geometry of the domain across which observations are…
Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…
Anatomical trees play an important role in clinical diagnosis and treatment planning. Yet, accurately representing these structures poses significant challenges owing to their intricate and varied topology and geometry. Most existing…
Supervised learning has recently garnered significant attention in the field of computational physics due to its ability to effectively extract complex patterns for tasks like solving partial differential equations, or predicting material…
Gaussian process (GP) regression is a popular surrogate modeling tool for computer simulations in engineering and scientific domains. However, it often struggles with high computational costs and low prediction accuracy when the simulation…
We introduce a novel approach for the reconstruction of tubular shapes from skeletal representations. Our method processes all skeletal points as a whole, eliminating the need for splitting input structure into multiple segments. We…
Many applications in speech, robotics, finance, and biology deal with sequential data, where ordering matters and recurrent structures are common. However, this structure cannot be easily captured by standard kernel functions. To model such…
Blood vessel segmentation and -tracing are essential tasks in many medical imaging applications. Although numerous methods exist, the prevailing segment-then-fix paradigm is fundamentally limited regarding its suitability for modeling the…
Gaussian processes are flexible function approximators, with inductive biases controlled by a covariance kernel. Learning the kernel is the key to representation learning and strong predictive performance. In this paper, we develop…
This paper introduces algorithms to select/design kernels in Gaussian process regression/kriging surrogate modeling techniques. We adopt the setting of kernel method solutions in ad hoc functional spaces, namely Reproducing Kernel Hilbert…
We present a multivariate Gaussian process regression approach for parameter field reconstruction based on the field's measurements collected at two different scales, the coarse and fine scales. The proposed approach treats the parameter…
We present a nonlinear Bayesian tomographic framework for Doppler spectral imaging that enables simultaneous reconstruction of emissivity, ion temperature, and flow velocity from line-integrated spectra. The method employs nonlinear…