Related papers: An asymptotically compatible bond-based peridynami…
This paper proposes a ridgeless kernel method for solving infinite-horizon, deterministic, continuous-time models in economic dynamics, formulated as systems of differential-algebraic equations with asymptotic boundary conditions (e.g.,…
Modeling dislocations is an inherently multiscale problem as one needs to simultaneously describe the high stress fields near the dislocation cores, which depend on atomistic length scales, and a surface boundary value problem which depends…
The Gaussian kernel is one of the most important kernels, applicable to many research fields, including scientific computing and data science. In this paper, we present asymptotic analysis of the Gaussian kernel matrix in high dimension…
This work presents a generalized boundary integral method for elliptic equations on surfaces, encompassing both boundary value and interface problems. The method is kernel-free, implying that the explicit analytical expression of the kernel…
This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…
We implement a computational periporomechanics model for simulating localized failure in unsaturated porous media. The coupled periporomechanics model is based on the peridynamic state concept and the effective force state concept. The…
Gaussian processes are machine learning models capable of learning unknown functions in a way that represents uncertainty, thereby facilitating construction of optimal decision-making systems. Motivated by a desire to deploy Gaussian…
In this work, we propose a novel clothed human reconstruction method called GaussianBody, based on 3D Gaussian Splatting. Compared with the costly neural radiance based models, 3D Gaussian Splatting has recently demonstrated great…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…
In this paper, we propose a novel one-dimensional (1D) discrete differential geometry (DDG)-based numerical method for geometrically nonlinear mechanics analysis (e.g., buckling and snapping) of axisymmetric shell structures. Our numerical…
Peridynamics (PD) is a non-local continuum formulation. The original version of PD was restricted to bond-based interactions. Bond-based PD is geometrically exact and its kinematics are similar to classical continuum mechanics (CCM).…
This work introduces the causal bootstrap, a framework for bounding smeared spectral observables from finite non-perturbative Euclidean data. The method optimizes over the convex set of positive spectral densities compatible with the data…
Modeling complex rigid motion across large spatiotemporal spans remains an unresolved challenge in dynamic reconstruction. Existing paradigms are mainly confined to short-term, small-scale deformation and offer limited consideration for…
In the present work, a rate-dependent cohesive zone model for the fracture of polymeric interfaces is presented. Inverse calibration of parameters for such complex models through trial and error is computationally tedious due to the large…
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.…
We introduce an accurate and efficient method for a class of nonlocal potential evaluations with free boundary condition, including the 3D/2D Coulomb, 2D Poisson and 3D dipolar potentials. Our method is based on a Gaussian-sum approximation…
Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference,…
In this article, using kernel convolution of order based dependent Dirichlet process (Griffin and Steel (2006)) we construct a nonstationary, nonseparable, nonparametric space-time process, which, as we show, satisfies desirable properties,…
This paper introduces a new type of probabilistic semiparametric model that takes advantage of data binning to reduce the computational cost of kernel density estimation in nonparametric distributions. Two new conditional probability…
The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel…