Related papers: Greedy Emulators for Nuclear Two-Body Scattering
Nonlinear kernels can be approximated using finite-dimensional feature maps for efficient risk minimization. Due to the inherent trade-off between the dimension of the (mapped) feature space and the approximation accuracy, the key problem…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
Fitting a theoretical model to experimental data in a Bayesian manner using Markov chain Monte Carlo typically requires one to evaluate the model thousands (or millions) of times. When the model is a slow-to-compute physics simulation,…
Quantifying uncertainties in physical or engineering systems often requires a large number of simulations of the underlying computer models that are computationally intensive. Emulators or surrogate models are often used to accelerate the…
Greedy-GQ is an off-policy two timescale algorithm for optimal control in reinforcement learning. This paper develops the first finite-sample analysis for the Greedy-GQ algorithm with linear function approximation under Markovian noise. Our…
The Reduced Basis Method (RBM) is a model reduction technique used to solve parametric PDEs that relies upon a basis set of solutions to the PDE at specific parameter values. To generate this reduced basis, the set of a small number of…
Background: Uncertainty quantification for nuclear theories has gained a more prominent role in the field, with more and more groups attempting to understand the uncertainties on their calculations. However, recent studies have shown that…
In this paper we consider the problem of computing the stationary distribution of nearly completely decomposable Markov processes, a well-established area in the classical theory of Markov processes with broad applications in the design,…
We use asymptotically optimal \emph{adaptive} numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method (RBM). The resulting discretizations for each snapshot…
Kernel-based methods provide flexible and accurate algorithms for the reconstruction of functions from meshless samples. A major question in the use of such methods is the influence of the samples locations on the behavior of the…
A method using an expansion of the four-body Yakubovsky wave function components onto the basis of the Faddeev-equation solutions for the two-cluster sub-Hamiltonian eigenfunctions is exploited for computations of low-energy scattering…
Neutron and x-ray scattering experiments traditionally rely upon histogrammed data sets, which are analysed using least-squares curve fitting of multiple probability distribution components to quantify separately the various scientific…
In this paper, we extend the reduced-basis methods developed earlier for wave equations to goal-oriented wave equations with affine parameter dependence. The essential new ingredient is the dual (or adjoint) problem and the use of its…
Adaptive finite element methods are a powerful tool to obtain numerical simulation results in a reasonable time. Due to complex chemical and mechanical couplings in lithium-ion batteries, numerical simulations are very helpful to…
In this work, we apply multi-goal oriented error estimation to the finite element method. In particular, we use the dual weighted residual method and apply it to a model problem. This model problem consist of locally different coercive…
Methods for solving PDEs using neural networks have recently become a very important topic. We provide an a priori error analysis for such methods which is based on the $\mathcal{K}_1(\mathbb{D})$-norm of the solution. We show that the…
Compound resonances in nucleon-nucleus scattering are related to the discrete spectrum of the target. Such resonances can be studied in a unified and general framework by a scattering model that uses sturmian expansions of postulated…
The globalised cascaded scattering matrix technique is a well proven, practical method that can be used to simulate large accelerating RF structures in which realistic fabrication errors to be incorporated in an efficient manner without the…
It is known that greedy methods perform well for maximizing monotone submodular functions. At the same time, such methods perform poorly in the face of non-monotonicity. In this paper, we show - arguably, surprisingly - that invoking the…
We present a generative reduced basis (RB) approach to construct reduced order models for parametrized partial differential equations. Central to this approach is the construction of generative RB spaces that provide rapidly convergent…