Related papers: Multiscale virtual particle based elastic network …
This paper devises a novel lowest-order conforming virtual element method (VEM) for planar linear elasticity with the pure displacement/traction boundary condition. The main trick is to view a generic polygon $K$ as a new one…
Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or…
McKean-Vlasov stochastic differential equations (MVSDEs) describe systems whose dynamics depend on both individual states and the population distribution, and they arise widely in neuroscience, finance, and epidemiology. In many…
Collective behaviors that emerge from interactions are fundamental to numerous biological systems. To learn such interacting forces from observations, we introduce a measure-valued neural network that infers measure-dependent interaction…
Score-based methods are powerful across machine learning, but they face a paradox: theoretically path-independent, yet practically path-dependent. We resolve this by proving that practical training objectives differ from the ideal,…
Modern scientific studies often collect data sets in the forms of tensors, which call for innovative statistical analysis methods. In particular, there is a pressing need for tensor clustering methods to understand the heterogeneity in the…
Multimodal probability distributions are common in both quantum and classical systems, yet modeling them remains challenging when the number of modes is large or unknown. Classical methods such as mixture-density networks (MDNs) scale…
Biopolymer gels, such as those made out of fibrin or collagen, are widely used in tissue engineering applications and biomedical research. Moreover, fibrin naturally assembles into gels in vivo during wound healing and thrombus formation.…
Machine-learning potentials (MLPs) have become important tools for modern molecular simulations. However, developing models that simultaneously achieve high accuracy and high computational efficiency remains a significant challenge. In this…
We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used to reduce the computational complexity of estimating the…
Ensembles of deep neural networks demonstrate improved performance over single models. For enhancing the diversity of ensemble members while keeping their performance, particle-based inference methods offer a promising approach from a…
The multinomial probit (MNP) model is widely used to analyze categorical outcomes due to its ability to capture flexible substitution patterns among alternatives. Conventional likelihood based and Markov chain Monte Carlo (MCMC) estimators…
Maximum entropy principle (MEP) offers an effective and unbiased approach to inferring unknown probability distributions when faced with incomplete information, while neural networks provide the flexibility to learn complex distributions…
In fields such as hydrology and climatology, modelling the entire distribution of positive data is essential, as stakeholders require insights into the full range of values, from low to extreme. Traditional approaches often segment the…
In this paper, we study the Bernstein polynomial model for estimating the multivariate distribution functions and densities with bounded support. As a mixture model of multivariate beta distributions, the maximum (approximate) likelihood…
The ability to understand and engineer molecular structures relies on having accurate descriptions of the energy as a function of atomic coordinates. Here we outline a new paradigm for deriving energy functions of hyperdimensional molecular…
In this paper, we propose an eXtended Virtual Element Method (X-VEM) for two-dimensional linear elastic fracture. This approach, which is an extension of the standard Virtual Element Method (VEM), facilitates mesh-independent modeling of…
Albeit worryingly underrated in the recent literature on machine learning in general (and, on deep learning in particular), multivariate density estimation is a fundamental task in many applications, at least implicitly, and still an open…
Bipartite graphs are ubiquitous across various scientific and engineering fields. Simultaneously grouping the two types of nodes in a bipartite graph via biclustering represents a fundamental challenge in network analysis for such graphs.…
The human microbiome plays an important role in human health and disease status. Next generating sequencing technologies allow for quantifying the composition of the human microbiome. Clustering these microbiome data can provide valuable…