19 papers · ranked by Valyu relevance
Patrick Dondl, Johannes Müller, Marius Zeinhofer
We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover nonlinear variational problems such as the p-Laplace equation or the Modica-Mortola energy with essential or natural boundary conditions. Under additional assumptions, we show that the convergence is uniform…
Danfeng Lou, Yong Chen, Qian Feng, Jinbiao Cai + 1 more
'Krzysztof Schabowicz'] A practical method to analyze the mechanical behavior of the asymmetric extradosed cable-stayed (AECS) bridge is provided in this paper. The work includes the analysis of the equivalent membrane tension of the cables, the ratio of side-span cable force to middle-span cable force, and the…
Vojin Jovanović, Sergiy Koshkin
We develop a general form of the Ritz method for trial functions that do not satisfy the essential boundary conditions. The idea is to treat the latter as variational constraints and remove them using the Lagrange multipliers. In multidimensional problems in addition to the trial functions boundary weight functions…
Zhongxiao Jia, Qingqing Zheng
We establish a general convergence theory of the Rayleigh–Ritz method and the refined Rayleigh–Ritz method for computing some simple eigenpair (λ∗, x∗) of a given analytic nonlinear eigenvalue problem (NEP). In terms of the deviation ε of x∗ from a given subspace W, we establish a priori convergence results on the Ritz…
Eric Hermes, Khachik Sargsyan, Habib Najm, Judit Zádor
We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, e.g. through the…
Rafael Florencio, Julio Guerrero
Recently, innovative adaptations of the Ritz Method incorporating deep learning have been developed, known as the Deep Ritz Method. This approach employs a neural network as the test function for variational problems. However, the neural network does not inherently satisfy the boundary conditions of the variational…
Elizabeta Šamec, Petra Gidak, Krešimir Fresl
Constrained form-finding results in a nonlinear system of equations unless a linear form-finding method (force density method) is iteratively applied until the given constraints are satisfied. Because the goal of this paper is to contribute to the further development of this method, a brief overview of the method and…
Clément Vella, Pierre Gosselet, Serge Prudhomme
We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based on the Hamiltonian formalism. The novelty of this work lies in the…
Zhongxiao Jia, Tianhang Liu
Under the hypothesis that the deviations of the desired eigenvectors of the matrix $A$ from the underlying subspace tend to zero, the Ritz vectors may not converge and have poor or little accuracy. This phenomenon is not unusual and particularly occurs when the associated Ritz values are close, which is independent of…
Ahmad Golbabai, Nima Safaei, Mahboubeh Molavi-Arabshahi, António Lopes + 2 more
'António Lopes' 'Alexandra M.S.F. Galhano' 'Carlo Cattani'] This paper introduces a direct method derived from the global radial basis function (RBF) interpolation over arbitrary collocation nodes occurring in variational problems involving functionals that depend on functions of a number of independent variables. This…
Daniel Peterseim, Jonas Püschel, Tatjana Stykel
This paper presents a novel Riemannian conjugate gradient method for the Kohn-Sham energy minimization problem in density functional theory (DFT), with a focus on non-metallic crystal systems. We introduce an energy-adaptive metric that preconditions the Kohn-Sham model, significantly enhancing optimization efficiency.…
Authors not listed
A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial…
Jie Liu, Fuzhang Wang, Sohail Nadeem, Abderrahim Wakif
The aim of this paper is to introduce a novel category of radial basis functions that incorporate smoothing techniques. Initially, we employ the power augmented and shape parameter schemes to create the radial basis functions. Subsequently, we apply the newly-constructed radial basis functions using the traditional…
Kai Luo, T. Wang, Xinguo Ren
in Kohn-Sham density functional theory for finite and extended systems Authors: ['Kai Luo' 'T. Wang' 'Xinguo Ren'] Direct minimization method on the complex Stiefel manifold in Kohn-Sham density functional theory is formulated to treat both finite and extended systems in a unified manner. This formulation is…
Marcin Wierzbiński, Alessandro Crimi
Lattice proteins are models resembling real proteins. They comprise an energy function and a set of conditions specifying the interaction between elements occupying adjacent lattice sites. In this paper we present an approach examining the behavior of chains of a large number of molecules. We investigate this by…
Authors not listed
Efficient and reliable identification of transition states (TS) is critical for reaction modelling. Among the approaches available, the combination of double-ended TS search with eigenvector-following, referred to as “hierarchical TS search”, is an effective tool to locate TSs starting from reactant and product…
Shawn C.C. Hsueh, Adekunle Aina, Steven S. Plotkin
Cyclic peptides naturally occur as antibiotics, fungicides, and immunosuppressants, and have been adapted for use as potential therapeutics. Scaffolded cyclic peptide antigens have many protein characteristics such as reduced toxicity, increased stability over linear peptides, and conformational selectivity, but with…
Ignac Ovari, Gabor Viczjan, Tamas Erdei, Barbara Takacs + 7 more
The receptorial responsiveness method (RRM) enables the estimation of a change in the concentration of a degradable agonist, near its receptor, by fitting its model to (at least) two concentration-effect (E/c) curves of a stable agonist of this receptor. One curve should be generated before this change in…
João Marcelo Lamim Ribeiro, Pratyush Tiwary
In this work we demonstrate how to leverage our recent iterative deep learning–all atom molecular dynamics (MD) technique “Reweighted autoencoded variational Bayes for enhanced sampling (RAVE)” (Ribeiro, Bravo, Wang, Tiwary, J. Chem. Phys. 149, 072301 (2018)) for sampling protein-ligand unbinding mechanisms and…