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In materials science, microstructures and their associated extrinsic properties are critical for engineering advanced structural and functional materials, yet their robust reconstruction and generation remain significant challenges. In this…
Inverse protein folding generates valid amino acid sequences that can fold into a desired protein structure, with recent deep-learning advances showing strong potential and competitive performance. However, challenges remain, such as…
A multi-reflection model of grating diffraction based on the simplified modal method is proposed. Simulation results for a guided mode resonance Brewster grating using our method and rigorous coupled wave analysis are presented to verify…
This article introduces a novel construction of the two-dimensional fractional Brownian motion (2D fBm) with dependent components. Unlike similar models discussed in the literature, our approach uniquely accommodates the full range of model…
Due to the high complexity and technical requirements of industrial production processes, surface defects will inevitably appear, which seriously affects the quality of products. Although existing lightweight detection networks are highly…
We present Bayesian Diffusion Models (BDM), a prediction algorithm that performs effective Bayesian inference by tightly coupling the top-down (prior) information with the bottom-up (data-driven) procedure via joint diffusion processes. We…
A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction.…
This note carries three purposes involving our latest advances on the radial basis function (RBF) approach. First, we will introduce a new scheme employing the boundary knot method (BKM) to nonlinear convection-diffusion problem. It is…
Masked diffusion models (MDMs), which leverage bidirectional attention and a denoising process, are narrowing the performance gap with autoregressive models (ARMs). However, their internal attention mechanisms remain under-explored. This…
In this study, we develop an interface-contact simulation framework based on physical criteria and machine-learning-assisted classification to describe coalescence and bouncing within a unified formulation. The framework realizes…
This paper develops a multifidelity method that enables estimation of failure probabilities for expensive-to-evaluate models via information fusion and importance sampling. The presented general fusion method combines multiple probability…
Neural radiance fields (NeRF) have gained prominence as a machine learning technique for representing 3D scenes and estimating the bidirectional reflectance distribution function (BRDF) from multiple images. However, most existing research…
We propose a generalization of the widely used fractional Brownian motion (FBM), memory-multi-FBM (MMFBM), to describe viscoelastic or persistent anomalous diffusion with time-dependent memory exponent $\alpha(t)$ in a changing environment.…
A new approach to Brownian motion of atomic clusters on solid surfaces is developed. The main topic discussed is the dependence of the diffusion coefficient on the fit between the surface static potential and the internal cluster…
We propose the first approach for multiple multivariate density-density regression (MDDR), making it possible to consider the regression of a multivariate density-valued response on multiple multivariate density-valued predictors. The core…
We introduce a Bayesian solution to the problem of inferring the density profile of strong gravitational lenses when the lens galaxy may contain multiple dark or faint substructures. The source and lens models are based on a superposition…
Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in [5]. In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation).…
Beamformers often trade off white noise gain against the ability to suppress interferers. With distributed microphone arrays, this trade-off becomes crucial as different arrays capture vastly different magnitude and phase differences for…
Capturing the shape and spatially-varying appearance (SVBRDF) of an object from images is a challenging task that has applications in both computer vision and graphics. Traditional optimization-based approaches often need a large number of…
Bayesian methods are appealing in their flexibility in modeling complex data and ability in capturing uncertainty in parameters. However, when Bayes' rule does not result in tractable closed-form, most approximate inference algorithms lack…