12 citations · 28 across the 15 of their papers we have counts for
18 papers
Pontryagin-Based Solver with Smoothed Hamiltonian, Adaptive , and PA-Bundle Refinement
Salim Ksous, Sebastian Lalvay Segovia, Mattias Sandberg +3
We present a Pontryagin-based numerical solver for deterministic optimal control problems in Bolza form. The solver regularizes the generally nonsmooth Hamiltonian using a log-sum-…
Convergence for adaptive resampling of random Fourier features
Xin Huang, Aku Kammonen, Anamika Pandey +4
The machine learning random Fourier feature method for data in high dimension is computationally and theoretically attractive since the optimization is based on a convex standard l…
Convergence rates for random feature neural network approximation in molecular dynamics
Xin Huang, Petr Plechac, Mattias Sandberg +1
Random feature neural network approximations of the potential in Hamiltonian systems yield approximations of molecular dynamics correlation observables that have the expected error…
Path integral molecular dynamics approximations of quantum canonical observables
Xin Huang, Petr Plechac, Mattias Sandberg +1
Mean-field molecular dynamics based on path integrals is used to approximate canonical quantum observables for particle systems consisting of nuclei and electrons. A computational…
A Locally Corrected Multiblob Method with Hydrodynamically Matched Grids for the Stokes Mobility Problem
Anna Broms, Mattias Sandberg, Anna-Karin Tornberg
Inexpensive numerical methods are key to enable simulations of systems of a large number of particles of different shapes in Stokes flow. Several approximate methods have been intr…
Canonical mean-field molecular dynamics derived from quantum mechanics
Xin Huang, Petr Plechac, Mattias Sandberg +1
Canonical quantum correlation observables can be approximated by classical molecular dynamics. In the case of low temperature the ab initio molecular dynamics potential energy is b…
Smaller generalization error derived for a deep residual neural network compared to shallow networks
Aku Kammonen, Jonas Kiessling, Petr Plecháč +3
Estimates of the generalization error are proved for a residual neural network with random Fourier features layers $\bar z_{\ell+1}=\bar z_\ell + \mathrm{Re}\sum_{k=1}^K\bar b_…
Adaptive random Fourier features with Metropolis sampling
Aku Kammonen, Jonas Kiessling, Petr Plecháč +2
The supervised learning problem to determine a neural network approximation with one hidden layer is studied…
The classical limit of quantum observables in the conservation laws of fluid dynamics
Petr Plecháč, Mattias Sandberg, Anders Szepessy
In the classical work by Irving and Zwanzig [Irving J.H. and Zwanzig R.W., J. Chem. Phys. 19 (1951), 1173-1180 ] it has been shown that quantum observables for macroscopic density,…
Canonical quantum observables for molecular systems approximated by ab initio molecular dynamics
Aku Kammonen, Petr Plechac, Mattias Sandberg +1
It is known that ab initio molecular dynamics based on the electron ground state eigenvalue can be used to approximate quantum observables in the canonical ensemble when the temper…
Computable error estimates for finite element approximations of elliptic partial differential equations with rough stochastic data
Eric Joseph Hall, Håkon Hoel, Mattias Sandberg +2
We derive computable error estimates for finite element approximations of linear elliptic partial differential equations (PDE) with rough stochastic coefficients. In this setting,…
An adaptive mass algorithm for Car-Parrinello and Ehrenfest ab initio molecular dynamics
Ashraful Kadir, Mattias Sandberg, Anders Szepessy
Ehrenfest and Car-Parrinello molecular dynamics are computational alternatives to approximate Born-Oppenheimer molecular dynamics without solving the electron eigenvalue problem at…
An a posteriori error estimate for Symplectic Euler approximation of optimal control problems
Jesper Karlsson, Stig Larsson, Mattias Sandberg +2
This work focuses on numerical solutions of optimal control problems. A time discretization error representation is derived for the approximation of the associated value function.…
Computational error estimates for Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces
Christian Bayer, Hakon Hoel, Ashraful Kadir +3
The difference of the values of observables for the time-independent Schroedinger equation, with matrix valued potentials, and the values of observables for ab initio Born-Oppenhei…
How accurate is molecular dynamics?
Christian Bayer, Håkon Hoel, Petr Plecháč +2
Born-Oppenheimer dynamics is shown to provide an accurate approximation of time-independent Schrödinger observables for a molecular system with an electron spectral gap, in the lim…
The Forward Euler Scheme for Nonconvex Lipschitz Differential Inclusions Converges with Rate One
Mattias Sandberg
In a previous paper it was shown that the Forward Euler method applied to differential inclusions where the right-hand side is a Lipschitz continuous set-valued function with unifo…
Extended Applicability of the Symplectic Pontryagin Method
Mattias Sandberg
The Symplectic Pontryagin method was introduced in a previous paper. This work shows that this method is applicable under less restrictive assumptions. Existence of solutions to th…
Convergence rates for an optimally controlled Ginzburg-Landau equation
Mattias Sandberg
An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the…