Related papers: An enhanced parametric nonlinear reduced order mod…
Statistical applications often involve the calculation of intractable multidimensional integrals. The Laplace formula is widely used to approximate such integrals. However, in high-dimensional or small sample size problems, the shape of the…
Statistical identification of possibly non-fundamental SVARMA models requires structural errors: (i) to be an i.i.d process, (ii) to be mutually independent across components, and (iii) each of them must be non-Gaussian distributed. Hence,…
The paper introduces a reduced order model (ROM) for numerical integration of a dynamical system which depends on multiple parameters. The ROM is a projection of the dynamical system on a low dimensional space that is both problem-dependent…
It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…
In this article, we discuss new models for static nonlinear deformations via scale-invariant conformal energy functionals based on the linear distortion. In particular, we give examples to show that, despite equicontinuity estimates giving…
Methodologies for reducing the design-space dimensionality in shape optimization have been recently developed based on unsupervised machine learning methods. These methods provide reduced dimensionality representations of the design space,…
Neumann series underlie both Krylov methods and algebraic multigrid smoothers. A low-synch modified Gram-Schmidt (MGS)-GMRES algorithm is described that employs a Neumann series to accelerate the projection step. A corollary to the backward…
The industrial application motivating this work is the fatigue computation of aircraft engines' high-pressure turbine blades. The material model involves nonlinear elastoviscoplastic behavior laws, for which the parameters depend on the…
In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear dynamical systems whose nonlinear terms are polynomial…
This work proposes a model-reduction approach for the material point method on nonlinear manifolds. Our technique approximates the $\textit{kinematics}$ by approximating the deformation map using an implicit neural representation that…
In this paper, a novel surrogate model based on the Grassmannian diffusion maps (GDMaps) and utilizing geometric harmonics is developed for predicting the response of engineering systems and complex physical phenomena. The method utilizes…
Due to the substantial scale of Large Language Models (LLMs), the direct application of conventional compression methodologies proves impractical. The computational demands associated with even minimal gradient updates present challenges,…
We formulate a new projection-based reduced-ordered modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov-Galerkin (APG) method, is derived by decomposing the generalized…
Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral…
We present a general, constructive procedure to find the basis for tensors of arbitrary order subject to linear constraints by transforming the problem to that of finding the nullspace of a linear operator. The proposed method utilizes…
Some applied researchers hesitate to use nonparametric methods, worrying that they will lose power in small samples or overfit the data when simpler models are sufficient. We argue that at least some of these concerns are unfounded when…
Understanding structure-property relations is essential to optimally design materials for specific applications. Two-scale simulations are often employed to analyze the effect of the microstructure on a component's macroscopic properties.…
The stress fields of dislocations predicted by classical elasticity are known to be unrealistically large approaching the dislocation core, due to the singular nature of the theory. While in many cases this is remedied with the…
We propose a hybrid neural network and physics framework for reduced-order modeling of elastoplasticity and fracture. State-of-the-art scientific computing models like the Material Point Method (MPM) faithfully simulate large-deformation…
We present a formalism to compute Lagrangian displacement fields for a wide range of cosmologies in the context of perturbation theory up to third order. We emphasize the case of theories with scale dependent gravitational strengths, such…