Understanding dynamics in complex systems is challenging because there are many degrees of freedom, and those that are most important for describing events of interest are often not obvious. The leading eigenfunctions of the transition operator are useful for visualization, and they can provide an efficient basis for computing statistics, such as the likelihood and average time of events (predictions). Here, we develop inexact iterative linear algebra methods for computing these eigenfunctions (spectral estimation) and making predictions from a dataset of short trajectories sampled at finite intervals. We demonstrate the methods on a low-dimensional model that facilitates visualization and a high-dimensional model of a biomolecular system. Implications for the prediction problem in reinforcement learning are discussed.
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC10328561 | PMC |
| http://dx.doi.org/10.1063/5.0151309 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
High-order methods beyond the classical complexity bounds: inexact high-order proximal-point methods.
Math Program
January 2024
Center for Operations Research and Econometrics (CORE) and Department of Mathematical Engineering (INMA), Catholic University of Louvain (UCL), 34voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium.
We introduce a (BiOPT) framework for minimizing the sum of two convex functions, where one of them is smooth enough. The BiOPT framework offers three levels of freedom: (i) choosing the order of the proximal term; (ii) designing an inexact th-order proximal-point method in the upper level; (iii) solving the auxiliary problem with a lower-level non-Euclidean method in the lower level. We here regularize the objective by a th-order proximal term (for arbitrary integer ) and then develop the generic inexact high-order proximal-point scheme and its acceleration using the standard estimating sequence technique at the upper level.
View Article and Find Full Text PDFEfficient Shift-and-Invert Preconditioning for Multi-GPU Accelerated Density Functional Calculations.
J Chem Theory Comput
September 2024
Department of Chemistry, Inha University, 100 Inha-ro, Incheon, Michuhol-gu 22212, Republic of Korea.
To accelerate the iterative diagonalization of electronic structure calculations, we propose a new inexact shift-and-invert (ISI) preconditioning method. The key idea is to improve shift values in the ISI preconditioning to be closer to the exact eigenvalues, leading to a significant boost in the convergence speed of the iterative diagonalization. Furthermore, we adopted a preconditioned conjugate gradient solver to rapidly evaluate an inversion process.
View Article and Find Full Text PDFMUSIC: Accelerated Convergence for Distributed Optimization With Inexact and Exact Methods.
IEEE Trans Neural Netw Learn Syst
March 2024
Gradient-type distributed optimization methods have blossomed into one of the most important tools for solving a minimization learning task over a networked agent system. However, only one gradient update per iteration makes it difficult to achieve a substantive acceleration of convergence. In this article, we propose an accelerated framework named multiupdates single-combination (MUSIC) allowing each agent to perform multiple local updates and a single combination in each iteration.
View Article and Find Full Text PDFComments and CorrectionsConvergence Analysis on Trace Ratio Linear Discriminant Analysis Algorithms.
IEEE Trans Neural Netw Learn Syst
February 2024
Linear discriminant analysis (LDA) may yield an inexact solution by transforming a trace ratio problem into a corresponding ratio trace problem. Most recently, optimal dimensionality LDA (ODLDA) and trace ratio LDA (TRLDA) have been developed to overcome this problem. As one of the greatest contributions, the two methods design efficient iterative algorithms to derive an optimal solution.
View Article and Find Full Text PDFAn Inexact Sequential Quadratic Programming Method for Learning and Control of Recurrent Neural Networks.
IEEE Trans Neural Netw Learn Syst
January 2024
This article considers the two-stage approach to solving a partially observable Markov decision process (POMDP): the identification stage and the (optimal) control stage. We present an inexact sequential quadratic programming framework for recurrent neural network learning (iSQPRL) for solving the identification stage of the POMDP, in which the true system is approximated by a recurrent neural network (RNN) with dynamically consistent overshooting (DCRNN). We formulate the learning problem as a constrained optimization problem and study the quadratic programming (QP) subproblem with a convergence analysis under a restarted Krylov-subspace iterative scheme that implicitly exploits the structure of the associated Karush-Kuhn-Tucker (KKT) subsystem.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!