Reaction Coordinates and the Transition-Vector Approximation to the IRC

2008 ◽  
Vol 4 (6) ◽  
pp. 920-928 ◽  
Author(s):  
Willem-Jan van Zeist ◽  
Anton H. Koers ◽  
Lando P. Wolters ◽  
F. Matthias Bickelhaupt
Keyword(s):  
Reaction Coordinates ◽  
Vector Approximation ◽  
Transition Vector

An Eight-Node Hexahedral Finite Element with Rotational DOFs for Elastoplastic Applications

2019 ◽  
Vol 11 (1) ◽  
pp. 54-66
Author(s):  
Ayoub Ayadi ◽  
Kamel Meftah ◽  
Lakhdar Sedira ◽  
Hossam Djahara
Keyword(s):  
Mathematical Model ◽  
Finite Element ◽  
Plastic Zone ◽  
Displacement Vector ◽  
Small Strain ◽  
Benchmark Problems ◽  
Plasticity Model ◽  
Vector Approximation ◽  
Calculation Code

Abstract In this paper, the earlier formulation of the eight-node hexahedral SFR8 element is extended in order to analyze material nonlinearities. This element stems from the so-called Space Fiber Rotation (SFR) concept which considers virtual rotations of a nodal fiber within the element that enhances the displacement vector approximation. The resulting mathematical model of the proposed SFR8 element and the classical associative plasticity model are implemented into a Fortran calculation code to account for small strain elastoplastic problems. The performance of this element is assessed by means of a set of nonlinear benchmark problems in which the development of the plastic zone has been investigated. The accuracy of the obtained results is principally evaluated with some reference solutions.

Rare event simulation

2017 ◽  
Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley
Keyword(s):  
Rare Event ◽  
Path Sampling ◽  
Rapid Progress ◽  
Computationally Efficient ◽  
Transition Path ◽  
Transition Path Sampling ◽  
Event Simulation ◽  
Reaction Coordinates ◽  
Simulation Techniques ◽  
Transition Interface

The development of techniques to simulate infrequent events has been an area of rapid progress in recent years. In this chapter, we shall discuss some of the simulation techniques developed to study the dynamics of rare events. A basic summary of the statistical mechanics of barrier crossing is followed by a discussion of approaches based on the identification of reaction coordinates, and those which seek to avoid prior assumptions about the transition path. The demanding technique of transition path sampling is introduced and forward flux sampling and transition interface sampling are considered as rigorous but computationally efficient approaches.

scholarly journals Dimensionality Reduction of Complex Metastable Systems via Kernel Embeddings of Transition Manifolds

2020 ◽  
Vol 31 (1) ◽  
Author(s):  
Andreas Bittracher ◽  
Stefan Klus ◽  
Boumediene Hamzi ◽  
Péter Koltai ◽  
Christof Schütte
Keyword(s):  
Stochastic Systems ◽  
Reproducing Kernel ◽  
Learning Algorithm ◽  
Reproducing Kernel Hilbert Space ◽  
Mathematical Framework ◽  
Reaction Coordinates ◽  
Effective Dynamics ◽  
Distortion Bounds ◽  
Low Dimensional ◽  
Metastable Systems

AbstractWe present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework for the computation of optimal reaction coordinates of such systems that is based on learning a parameterization of a low-dimensional transition manifold in a certain function space. In this article, we enhance this approach by embedding and learning this transition manifold in a reproducing kernel Hilbert space, exploiting the favorable properties of kernel embeddings. Under mild assumptions on the kernel, the manifold structure is shown to be preserved under the embedding, and distortion bounds can be derived. This leads to a more robust and more efficient algorithm compared to the previous parameterization approaches.

scholarly journals Thinking Globally, Acting Locally: Distantly Supervised Global-to-Local Knowledge Selection for Background Based Conversation

2020 ◽  
Vol 34 (05) ◽  
pp. 8697-8704
Author(s):  
Pengjie Ren ◽  
Zhumin Chen ◽  
Christof Monz ◽  
Jun Ma ◽  
Maarten De Rijke
Keyword(s):  
Local Knowledge ◽  
State Of The Art ◽  
Background Knowledge ◽  
Global Perspective ◽  
Conversational Context ◽  
Human Evaluation ◽  
Text Fragment ◽  
Selection For ◽  
High Degree ◽  
Transition Vector

Background Based Conversation (BBCs) have been introduced to help conversational systems avoid generating overly generic responses. In a BBC, the conversation is grounded in a knowledge source. A key challenge in BBCs is Knowledge Selection (KS): given a conversational context, try to find the appropriate background knowledge (a text fragment containing related facts or comments, etc.) based on which to generate the next response. Previous work addresses KS by employing attention and/or pointer mechanisms. These mechanisms use a local perspective, i.e., they select a token at a time based solely on the current decoding state. We argue for the adoption of a global perspective, i.e., pre-selecting some text fragments from the background knowledge that could help determine the topic of the next response. We enhance KS in BBCs by introducing a Global-to-Local Knowledge Selection (GLKS) mechanism. Given a conversational context and background knowledge, we first learn a topic transition vector to encode the most likely text fragments to be used in the next response, which is then used to guide the local KS at each decoding timestamp. In order to effectively learn the topic transition vector, we propose a distantly supervised learning schema. Experimental results show that the GLKS model significantly outperforms state-of-the-art methods in terms of both automatic and human evaluation. More importantly, GLKS achieves this without requiring any extra annotations, which demonstrates its high degree of scalability.

scholarly journals Meta-Descent for Online, Continual Prediction

2019 ◽  
Vol 33 ◽  
pp. 3943-3950
Author(s):  
Andrew Jacobsen ◽  
Matthew Schlegel ◽  
Cameron Linke ◽  
Thomas Degris ◽  
Adam White ◽  
...  
Keyword(s):  
Gradient Descent ◽  
Large Scale ◽  
Time Series Prediction ◽  
Real Data ◽  
Second Order ◽  
Stochastic Gradient Descent ◽  
Step Size ◽  
Vector Approximation ◽  
Prediction Problems ◽  
Stationary Problems

This paper investigates different vector step-size adaptation approaches for non-stationary online, continual prediction problems. Vanilla stochastic gradient descent can be considerably improved by scaling the update with a vector of appropriately chosen step-sizes. Many methods, including AdaGrad, RMSProp, and AMSGrad, keep statistics about the learning process to approximate a second order update—a vector approximation of the inverse Hessian. Another family of approaches use meta-gradient descent to adapt the stepsize parameters to minimize prediction error. These metadescent strategies are promising for non-stationary problems, but have not been as extensively explored as quasi-second order methods. We first derive a general, incremental metadescent algorithm, called AdaGain, designed to be applicable to a much broader range of algorithms, including those with semi-gradient updates or even those with accelerations, such as RMSProp. We provide an empirical comparison of methods from both families. We conclude that methods from both families can perform well, but in non-stationary prediction problems the meta-descent methods exhibit advantages. Our method is particularly robust across several prediction problems, and is competitive with the state-of-the-art method on a large-scale, time-series prediction problem on real data from a mobile robot.

scholarly journals Fiedler Vector Approximation via Interacting RandomWalks

2020 ◽  
Vol 48 (1) ◽  
pp. 101-102
Author(s):  
Vishwaraj Doshi ◽  
Do Young Eun
Keyword(s):  
Fiedler Vector ◽  
Vector Approximation

scholarly journals Data-driven computation of molecular reaction coordinates

2018 ◽  
Vol 149 (15) ◽  
pp. 154103 ◽  
Author(s):  
Andreas Bittracher ◽  
Ralf Banisch ◽  
Christof Schütte
Keyword(s):  
Data Driven ◽  
Reaction Coordinates ◽  
Molecular Reaction
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