Related papers: Multiscale virtual particle based elastic network …
We present a Virtual Element Method (VEM) for possibly nonlinear elastic and inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is based on a low-order approximation of the displacement field, as well as…
We propose a physics informed, neural network-based elasto-viscoplasticity (NN-EVP) constitutive modeling framework for predicting the flow response in metals as a function of underlying grain size. The developed NN-EVP algorithm is based…
Discrete mesoscale network models, in which explicitly modeled polymer chains are replaced by implicit pairwise potentials, are capable of predicting the macroscale mechanical response of polymeric materials such as elastomers and gels,…
The Poisson-Nernst-Planck (PNP) system is a standard model for describing ion transport. In many applications, e.g., ions in biological tissues, the presence of thin boundary layers poses both modelling and computational challenges. In this…
In this work, we review the framework of the Virtual Element Method (VEM) for a model in magneto-hydrodynamics (MHD), that incorporates a coupling between electromagnetics and fluid flow, and allows us to construct novel discretizations for…
In this paper, an enhanced Virtual Element Method (VEM) formulation is proposed for plane elasticity. It is based on the improvement of the strain representation within the element, without altering the degree of the displacement…
Large datasets often contain multiple distinct feature sets, or views, that offer complementary information that can be exploited by multi-view learning methods to improve results. We investigate anatomical multi-view data, where each brain…
We explore the recently-proposed Virtual Element Method (VEM) for numerical solution of boundary value problems on arbitrary polyhedral meshes. More specifically, we focus on the elasticity equations in three-dimensions and elaborate upon…
Deep neural networks (DNN) have been used successfully in many scientific problems for their high prediction accuracy, but their application to genetic studies remains challenging due to their poor interpretability. In this paper, we…
Expectation maximisation (EM) is an unsupervised learning method for estimating the parameters of a finite mixture distribution. It works by introducing "hidden" or "latent" variables via Baum's auxiliary function $Q$ that allow the joint…
We characterize different cell states, related to cancer and ageing phenotypes, by a measure of entropy of network ensembles, integrating gene expression values and protein interaction networks. The entropy measure estimates the parameter…
State Space Models (SSMs), especially Mamba, have shown great promise in medical image segmentation due to their ability to model long-range dependencies with linear computational complexity. However, accurate medical image segmentation…
Bridging the gap between atomistic detail and continuum mechanics is a central challenge in modeling biological membranes, particularly for mesoscopic phenomena spanning large length and time scales. In this work, we introduce a new,…
We introduce a novel Multimodal Neural Operator (MNO) architecture designed to learn solution operators for multi-parameter nonlinear boundary value problems (BVPs). Traditional neural operators primarily map either the PDE coefficients or…
Energy-based models (EBMs) are a simple yet powerful framework for generative modeling. They are based on a trainable energy function which defines an associated Gibbs measure, and they can be trained and sampled from via well-established…
Continuous monitoring and in-situ assessment of microvascular connectivity have significant implications for culturing vascularized organoids and optimizing the therapeutic strategies. However, commonly used methods for vascular…
Molecular Communications (MC) is an emerging research paradigm that utilizes molecules to transmit information, with promising applications in biomedicine such as targeted drug delivery or tumor detection. It is also envisioned as a key…
Inferring biophysical parameters and hidden state variables from partial and noisy observations is a fundamental challenge in computational neuroscience. This problem is particularly difficult for fast - slow spiking and bursting models,…
A refined a priori error analysis of the lowest order (linear) Virtual Element Method (VEM) is developed for approximating a model two dimensional Poisson problem. A set of new geometric assumptions is proposed on shape regularity of…
The Deep Material Network (DMN) has emerged as a powerful framework for multiscale materials modeling, enabling efficient and accurate prediction of material behavior across different length scales. Unlike conventional data-driven…