Related papers: On immersed boundary kernel functions: a constrain…
We investigate a simple objective for nonlinear instrumental variable (IV) regression based on a kernelized conditional moment restriction (CMR) known as a maximum moment restriction (MMR). The MMR objective is formulated by maximizing the…
Invariant risk minimization (IRM) has recently emerged as a promising alternative for domain generalization. Nevertheless, the loss function is difficult to optimize for nonlinear classifiers and the original optimization objective could…
Approximations of the Dirac delta distribution are commonly used to create sequences of smooth functions approximating nonsmooth (generalized) functions, via convolution. In this work, we show a priori rates of convergence of this…
Isogeometric analysis was proposed to bridge the gap between computer-aided design and numerical discretization. However, standard multi-patch isogeometric analysis mandates conformal discretizations across patch interfaces, posing…
We implemented a coarse-graining procedure to construct mesoscopic models of complex molecules. The final aim is to obtain better results on properties depending on slow modes of the molecules. Therefore the number of particles considered…
Learning a distance metric from the given training samples plays a crucial role in many machine learning tasks, and various models and optimization algorithms have been proposed in the past decade. In this paper, we generalize several…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
We employ a fast and accurate algorithm to treat dielectric interfaces within molecular dynamics simulations and demonstrate the importance of dielectric boundary forces (DBFs) in two systems of interests in soft-condensed matter science.…
Gaussian Process (GP) regression is a powerful nonparametric Bayesian framework, but its performance depends critically on the choice of covariance kernel. Selecting an appropriate kernel is therefore central to model quality, yet remains…
We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more specifically non-uniform rational B-splines (NURBS). This new…
Asymmetric kernels naturally exist in real life, e.g., for conditional probability and directed graphs. However, most of the existing kernel-based learning methods require kernels to be symmetric, which prevents the use of asymmetric…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
Physics-informed machine learning combines the expressiveness of data-based approaches with the interpretability of physical models. In this context, we consider a general regression problem where the empirical risk is regularized by a…
In this work, based on the moving-least-squares immersed boundary method, we proposed a new technique to improve the calculation of the volume force representing the body boundary. For boundary with simple geometry, we theoretically analyse…
In this work we present a novel optimization strategy for image reconstruction tasks under analysis-based image regularization, which promotes sparse and/or low-rank solutions in some learned transform domain. We parameterize such…
Point set is a flexible and lightweight representation widely used for 3D deep learning. However, their discrete nature prevents them from representing continuous and fine geometry, posing a major issue for learning-based shape generation.…
We perform a stability analysis for a fluid-structure interaction problem in which a spherical elastic shell or membrane is immersed in a 3D viscous, incompressible fluid. The shell is an idealised structure having zero thickness, and has…
We introduce the implicitly constrained least squares (ICLS) classifier, a novel semi-supervised version of the least squares classifier. This classifier minimizes the squared loss on the labeled data among the set of parameters implied by…
The immersed boundary (IB) method has become a leading approach in cardiac fluid-structure interaction (FSI) modeling due to its ability to handle large deformations and complex geometries without requiring mesh regeneration. However, the…
This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order…