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Ill-posed inverse problems are ubiquitous in applications. Under- standing of algorithms for their solution has been greatly enhanced by a deep understanding of the linear inverse problem. In the applied communities ensemble-based filtering…
We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…
Slater determinants have underpinned quantum chemistry for nearly a century, yet their full potential has remained challenging to exploit. In this work, we show that a variational wavefunction composed of a few hundred optimized…
We propose a new space-variant anisotropic regularisation term for variational image restoration, based on the statistical assumption that the gradients of the target image distribute locally according to a bivariate generalised Gaussian…
Compact and accurate wave functions can be constructed by quantum Monte Carlo methods. Typically, these wave functions consist of a sum of a small number of Slater determinants multiplied by a Jastrow factor. In this paper we study the…
Variance reduction is a family of powerful mechanisms for stochastic optimization that appears to be helpful in many machine learning tasks. It is based on estimating the exact gradient with some recursive sequences. Previously, many papers…
This paper aims at developing new shape functions adapted to smooth vanishing coefficients for scalar wave equation. It proposes the numerical analysis of their interpolation properties. The interpolation is local but high order convergence…
A system of high-order adaptive multiresolution wavelet collocation upwind schemes are developed for the solution of hyperbolic conservation laws. A couple of asymmetrical wavelet bases with interpolation property are built to realize the…
We present here a new approach to determine an accurate variational wavefunction for general quantum antiferromagnets, completely defined by the requirement to reproduce the simple and well known spin-wave expansion. By this wavefunction,…
We extend the standard notion of self-concordance to non-convex optimization and develop a family of second-order algorithms with global convergence guarantees. In particular, two function classes -- \textit{weakly self-concordant}…
A Gutzwiller-type variational wave function is proposed for the neutron resonance mode in the cuprate superconductors. An efficient re-weighting technique is devised to perform variational Monte Carlo simulation on the proposed wave…
Maximally localized Wannier functions are widely used in electronic structure theory for analyses of bonding, electric polarization, orbital magnetization, and for interpolation. The state of the art method for their construction is based…
Although the linear method is one of the most robust algorithms for optimizing non-linearly parametrized wavefunctions in variational Monte Carlo, it suffers from a memory bottleneck due to the fact at each optimization step a generalized…
The paper is devoted to a comprehensive study of composite models in variational analysis and optimization the importance of which for numerous theoretical, algorithmic, and applied issues of operations research is difficult to overstate.…
State and parameter estimation, along with fault detection, are three crucial estimation problems within the control systems community. Although different approaches have been proposed for each type of problem, the modulating function…
Finding a succinct representation to describe the ground state of a disordered interacting system could be very helpful in understanding the interplay between the interactions that is manifested in a quantum phase transition. In this work…
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte-Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial…
This paper is devoted to studying the first-order variational analysis of non-convex and non-differentiable functions that may not be subdifferentially regular. To achieve this goal, we entirely rely on two concepts of directional…
Variational quantum eigensolver (VQE), aiming at determining the ground state energy of a quantum system described by a Hamiltonian on noisy intermediate scale quantum (NISQ) devices, is among the most significant applications of…
This work investigates Kolmogorov-Arnold network-based wavefunction ansatz as viable representations for quantum Monte Carlo simulations. Through systematic analysis of one-dimensional model systems, we evaluate their computational…