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A smooth basis for atomistic machine learning

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Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis

Daniel Kressner

Novel memory-efficient Arnoldi algorithms for solving matrix polynomial eigenvalue problems are presented. More specifically, we consider the case of matrix polynomials expressed in the Chebyshev basis, which is often numerically more appropriate than the ...

Wiley-Blackwell2014

Nonbinary Associative Memory With Exponential Pattern Retrieval Capacity and Iterative Learning

Mohammad Amin Shokrollahi, Krishna Kumar, Amir Hesam Salavati

We consider the problem of neural association for a network of nonbinary neurons. Here, the task is to first memorize a set of patterns using a network of neurons whose states assume values from a finite number of integer levels. Later, the same network sh ...

Ieee-Inst Electrical Electronics Engineers Inc2014

Approximate dynamic programming via sum of squares programming

Maryam Kamgarpour, Tyler Summers

We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision variables. By rela ...

2013

The Chu Construction For Complete Atomistic Coatomistic Lattices

Gavin Jay Seal, Boris Ischi

The Chu construction is used to define a *-autonomous structure on a category of complete atomistic coatomistic lattices. This construction leads to a new tensor product that is compared with a certain number of other existing tensor products. ...

Univ Houston2013

An Error Analysis Of Galerkin Projection Methods For Linear Systems With Tensor Product Structure

Daniel Kressner, Christine Tobler

Recent results on the convergence of a Galerkin projection method for the Sylvester equation are extended to more general linear systems with tensor product structure. In the Hermitian positive definite case, explicit convergence bounds are derived for Gal ...

Society for Industrial and Applied Mathematics2013

A convex optimization approach for image recovery from nonlinear measurements in optical interferometry

Yves Wiaux, Rafael Eduardo Carrillo Rangel, Anna Auria Rasclosa

Image recovery in optical interferometry is an ill-posed nonlinear inverse problem arising from incomplete power spectrum and bi-spectrum measurements. We formulate a linear version of the problem for the order-3 tensor formed by the tensor product of the ...

2013

Electromagnetic modes of a disordered photonic crystal

Vincenzo Savona

We present a systematic numerical approach to compute the eigenmodes and the related eigenfrequencies of a disordered photonic crystal, characterized by small fluctuations of the otherwise periodic dielectric profile. The field eigenmodes are expanded on t ...

2011

Modeling Magma Dynamics with a Mixed Fourier Collocation - Discontinuous Galerkin Method

Jan Sickmann Hesthaven

A high-order discretization consisting of a tensor product of the Fourier collocation and discontinuous Galerkin methods is presented for numerical modeling of magma dynamics. The physical model is an advection-reaction type system consisting of two hyperb ...

GLOBAL SCIENCE PRESS2011

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We propose a universal and efficient compressive sampling strategy based on the use of a spread spectrum technique. The method essentially consists in a random pre-modulation of the signal of interest followed by projections onto randomly selected vectors ...

2011

Quantum chemical methods are important tools for the predictions of electronic structure and energetics of molecules providing the interpretation of spectroscopic experiments and reaction mechanisms. In this thesis, density functional theory (DFT) and wave ...

EPFL2010