相关论文: Geometry-Preserving Nudged Elastic Band and Dimer …

Simulating interactions between non-spherical colloidal particles is computationally challenging due to the complex dependency of forces and energies on their geometry. We introduce and evaluate both descriptor-based and end-to-end models…

The analysis of structure-preserving numerical methods for the Poisson--Nernst--Planck (PNP) system has attracted growing interests in recent years. In this work, we provide an optimal rate convergence analysis and error estimate for finite…

Deep neural networks offer numerous potential applications across geoscience, for example, one could argue that they are the state-of-the-art method for predicting faults in seismic datasets. In quantitative reservoir characterization…

Robust optimization provides a principled framework for decision-making under uncertainty, with broad applications in finance, engineering, and operations research. In portfolio optimization, uncertainty in expected returns and covariances…

First-order optimization methods, such as SGD and Adam, are widely used for training large-scale deep neural networks due to their computational efficiency and robust performance. However, relying solely on gradient information, these…

The multi-direct-forcing immersed boundary method allows for a small velocity error of the no-slip condition in moving-particle problems but suffers from numerical instability if simulation parameters are not carefully chosen. This study…

Global existence for the nonisentropic compressible Euler equations with vacuum boundary for all adiabatic constants $\gamma > 1$ is shown through perturbations around a rich class of background nonisentropic affine motions. The notable…

We develop an entropy-stable high-order numerical method for the two-dimensional compressible Euler equations on general curvilinear meshes. The proposed approach is based on a nodal discontinuous Galerkin spectral element method (DGSEM)…

In this paper, a general stochastic optimization procedure is studied, unifying several variants of the stochastic gradient descent such as, among others, the stochastic heavy ball method, the Stochastic Nesterov Accelerated Gradient…

Recently Shah et al., 2020 pointed out the pitfalls of the simplicity bias - the tendency of gradient-based algorithms to learn simple models - which include the model's high sensitivity to small input perturbations, as well as sub-optimal…

Efficient algorithms for the calculation of minimum energy paths of magnetic transitions are implemented within the geodesic nudged elastic band (GNEB) approach. While an objective function is not available for GNEB and a traditional line…

This study investigates non-adiabatic wave dynamics in condensed media and the transition from adiabatic stability to spectral chaos. We introduce a dimensionless parameter, as a universal metric to quantify phase-mode redistribution at…

Unsupervised Anomaly Detection (UAD) is a key data mining problem owing to its wide real-world applications. Due to the complete absence of supervision signals, UAD methods rely on implicit assumptions about anomalous patterns (e.g.,…

This paper presents a new deep learning-based framework for robust nonlinear estimation and control using the concept of a Neural Contraction Metric (NCM). The NCM uses a deep long short-term memory recurrent neural network for a global…

A statistical method is presented to evaluate the uncertainty bands in the optical nucleus-nucleus potential and in differential cross sections. The starting point is the least square fit of a set of experimental values of elastic…

The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and…

With increasing computational demand, Neural-Network (NN) based models are being developed as pre-trained surrogates for different thermohydraulics phenomena. An area where this approach has shown promise is in developing higher-fidelity…

High-dimensional non-convex optimization problems in engineering design, control, and learning are often hindered by saddle points, flat plateaus, and strongly anisotropic curvature. This paper develops a unified, curvature-adaptive…

Numerical studies of ionic motion through solid electrolytes commonly involve static nudged-elastic band (NEB) methods or costly \emph{ab initio} molecular dynamics (AIMD). Building on a time-local model of current carrier-electrolyte…

In this work, we explore the application of Stabilization-Free Virtual Element Methods for Neumann boundary Optimal Control Problems in saddle point formulation. The method is proposed for arbitrary polynomial order of accuracy and general…