Related papers: Computational modelling and data-driven homogenisa…
Gaussian process regression (GPR) has been a well-known machine learning method for various applications such as uncertainty quantifications (UQ). However, GPR is inherently a data-driven method, which requires sufficiently large dataset.…
The mechanical properties of periodic microstructures are pivotal in various engineering applications. Homogenization theory is a powerful tool for predicting these properties by averaging the behavior of complex microstructures over a…
Spherical symmetry is ubiquitous in nature. It's therefore unfortunate that spherical system simulations are so hard, and require complete spheres with millions of interacting particles. Here we introduce an approach to model spherical…
Exploiting the variational interpretation of kernel interpolation we exhibit a direct connection between interpolation and regression, where interpolation appears as a limiting case of regression. By applying this framework to point clouds…
Compressing neural nets is an active research problem, given the large size of state-of-the-art nets for tasks such as object recognition, and the computational limits imposed by mobile devices. We give a general formulation of model…
Data-driven modeling approaches can produce fast surrogates to study large-scale physics problems. Among them, graph neural networks (GNNs) that operate on mesh-based data are desirable because they possess inductive biases that promote…
The homogenized stiffnesses of a corrugated plate are calculated by solving the periodicity cell problem of the homogenization theory by using two-steps dimension reduction procedure. The three-dimensional periodicity cell problem first…
The article addresses the mathematical modeling of the folding of a thin elastic sheet along a prescribed curved arc. A rigorous model reduction from a general hyperelastic material description is carried out under appropriate scaling…
A finite element simulation of the mechanical behaviour of woven textile materials at the scale of individual fibers is proposed in this paper. The aim of the simulation is to understand and identify phenomena involved at different scales…
The revolutionary advancements in metal additive manufacturing have enabled the production of alloy-based lattice structures with complex geometrical features and high resolutions. This has encouraged the development of nonlinear material…
This work presents a shear elastoplasticity model for textile fabrics within the theoretical framework of anisotropic Kirchhoff-Love shells with bending of embedded fibers proposed by Duong et al. (2023). The plasticity model aims at…
Membranes holomorphically embedded in flat noncompact space are constructed in terms of the degrees of freedom of an infinite collection of 0-branes. To each holomorphic curve we associate infinite-dimensional matrices which are static…
Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…
Nonlinear bending phenomena of thin elastic structures arise in various modern and classical applications. Characterizing low energy states of elastic rods has been investigated by Bernoulli in 1738 and related models are used to determine…
Knitted fabrics exhibit high flexibility due to their periodic loop structures formed by bent yarns. Under compressive loading, they develop three-dimensional (3D) wrinkling patterns that reflect nonlinear interactions between yarn…
We present a hybrid numerical approach to simulate quantum many body problems on two spatial dimensional quantum lattice models via the non-Abelian ab initio version of the density matrix renormalization group method on state-of-the-art…
Recent advances in optimization methods used for training convolutional neural networks (CNNs) with kernels, which are normalized according to particular constraints, have shown remarkable success. This work introduces an approach for…
A polymer network can imbibe water, forming an aggregate called hydrogel, and undergo large and inhomogeneous deformation with external mechanical constraint. Due to the large deformation, nonlinearity plays a crucial role, which also…
In this study, we utilize genetic algorithms to develop a realistic implicit solvent ultra-coarse-grained (PC) membrane model comprising only three interaction sites. The key philosophy of the ultra-CG membrane model SMARTINI3 is its…
Exotic behaviour of mechanical metamaterials often relies on an internal transformation of the underlying microstructure triggered by its local instabilities, rearrangements, and rotations. Depending on the presence and magnitude of such a…