Related papers: Relationships between full-space and subspace quad…
Direct numerical simulation of dynamical systems is of fundamental importance in studying a wide range of complex physical phenomena. However, the ever-increasing need for accuracy leads to extremely large-scale dynamical systems whose…
We construct a class of super-reflexive complementably minimal spaces, and study uniformly convex distortions of the norm on Hilbert space by using methods of complex interpolation.
Multi-material design optimization problems can, after discretization, be solved by the iterative solution of simpler sub-problems which approximate the original problem at an expansion point to first order. In particular, models…
Subspace designs are a (large) collection of high-dimensional subspaces $\{H_i\}$ of $\F_q^m$ such that for any low-dimensional subspace $W$, only a small number of subspaces from the collection have non-trivial intersection with $W$; more…
This paper improves the algorithms based on supporting halfspaces and quadratic programming for convex set intersection problems in our earlier paper in several directions. First, we give conditions so that much smaller quadratic programs…
We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be expressed as a convex combination of certain interpolants when…
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,…
We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…
Using the adjoint action of the infinitesimal translations (with respect to some (in)dependant variables) on specific finite-dimensional subspaces of the space of generalized symmetries of some system of partial differential equations, we…
We generalize the two dimensional mixed finite elements of Arbogast and Correa [T. Arbogast and M. R. Correa, SIAM J. Numer. Anal., 54 (2016), pp. 3332--3356] defined on quadrilaterals to three dimensional cuboidal hexahedra. The…
Given a set of points \F in a high dimensional space, the problem of finding a union of subspaces \cup_i V_i\subset \R^N that best explains the data \F increases dramatically with the dimension of \R^N. In this article, we study a class of…
The fast Fourier transform (FFT) based matrix-free ansatz interpolatory approximations of periodic functions are fundamental for efficient realization in several applications.In this work we design, analyze, and implement similar…
Driven by increased complexity of dynamical systems, the solution of system of differential equations through numerical simulation in optimization problems has become computationally expensive. This paper provides a smart data driven…
We consider Hamiltonians associated with 3 dimensional conformally flat spaces, possessing 2, 3 and 4 dimensional isometry algebras. We use the conformal algebra to build additional {\em quadratic} first integrals, thus constructing a large…
The Subspace Theorem is a powerful tool in number theory. It has appeared in various forms and been adapted and improved over time. It's applications include diophantine approximation, results about integral points on algebraic curves and…
One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric…
Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from…
There are 13 equivalence classes of 2D second order quantum and classical superintegrable systems with nontrivial potential, each associated with a quadratic algebra of hidden symmetries. We study the finite and infinite irreducible…
Model merging combines fine-tuned checkpoints into a single multi-task model without retraining. Existing methods - such as task arithmetic, model soups, TIES, and DARE - are computationally efficient and empirically successful, but rely on…
Surrogate models are used for global approximation of responses generated by expensive computer experiments like CFD applications. In this paper, we make use of structural similarities which are shared by a class of related problems. We…