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

Adaptive optimizers can reduce to normalized steepest descent (NSD) when only adapting to the current gradient, suggesting a close connection between the two algorithmic families. A key distinction between their analyses, however, lies in…

Solid-state electrolytes are essential in the development of all-solid-state batteries. While density functional theory (DFT)-based nudged elastic band (NEB) and ab initio molecular dynamics (AIMD) methods provide fundamental insights on…

The nudged elastic band (NEB) method is one of the most widely used techniques for determining minimum-energy reaction pathways and activation barriers between known initial and final states. However, conventional implementations face steep…

Monitoring the integrity of elastic structures using ultrasonic waves requires the efficient identification of material parameters from measured surface displacements. The displacement field is governed by Cauchy's equation of motion, i.e.,…

This paper presents a theoretical overview of a Neural Contraction Metric (NCM): a neural network model of an optimal contraction metric and corresponding differential Lyapunov function, the existence of which is a necessary and sufficient…

Wavelet phase is a critical parameter in seismic processing, where zero-phase wavelets are essential for maximizing temporal resolution and ensuring accurate interpretation of subsurface structures. In practice, however, the seismic wavelet…

Ion transport, often described by the Poisson--Nernst--Planck (PNP) equations, is ubiquitous in electrochemical devices and many biological processes of significance. In this work, we develop conservative, positivity-preserving, energy…

Structural identification and damage detection can be generalized as the simultaneous estimation of input forces, physical parameters, and dynamical states. Although Kalman-type filters are efficient tools to address this problem, the…

We develop a mixed formulation for incompressible hyper-elastodynamics based on a continuum modeling framework recently developed and smooth generalizations of the Taylor-Hood element based on non-uniform rational B-splines (NURBS). This…

Bulk thermal conductivity estimates based on predictions from non-equilibrium molecular dynamics (NEMD) using the so-called direct method are known to be severely under-predicted since finite simulation length-scales are unable to mimic…

Minimum energy paths for transitions such as atomic and/or spin rearrangements in thermalized systems are the transition paths of largest statistical weight. Such paths are frequently calculated using the nudged elastic band method, where…

Data sparsity is a common issue to train machine learning tools such as neural networks for engineering and scientific applications, where experiments and simulations are expensive. Recently physics-constrained neural networks (PCNNs) were…

Edge computing environments impose strict constraints on energy consumption and latency, making the deployment of deep neural networks a significant challenge. Therefore, smart and adaptive inference strategies that dynamically balance…

This paper presents an approach to trajectory-centric learning control based on contraction metrics and disturbance estimation for nonlinear systems subject to matched uncertainties. The approach uses deep neural networks to learn uncertain…

A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on shape…

Recently, adaptive control systems with relaxed persistent excitation (PE) conditions have been proposed to guarantee true parameter convergence and improve the transient response. However, in some cases, sufficient control performance and…

In this paper, we study several important geometric optimization problems arising in machine learning. First, we revisit the Minimum Enclosing Ball (MEB) problem in Euclidean space $\mathbb{R}^d$. The problem has been extensively studied…

Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these…

The Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions (PNP-FBV) describe ion transport with Faradaic reactions and have applications in a wide variety of fields. Using an adaptive time-stepper based…

EEG decoding systems based on deep neural networks have been widely used in decision making of brain computer interfaces (BCI). Their predictions, however, can be unreliable given the significant variance and noise in EEG signals. Previous…