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Deterministic particle flows for constraining stochastic nonlinear systems [article]

Dimitra Maoutsa, Manfred Opper
2021 arXiv   pre-print
Applied to several biologically inspired models, we show that our method provides the necessary optimal controls in settings with terminal-, transient-, or generalised collective-state constraints and  ...  Existing methods for identifying the necessary dynamical adjustments resort either to space discretising solutions of ensuing partial differential equations, or to iterative stochastic path sampling schemes  ...  A second class of methods optimises the interventions directly in iterative schemes.  ... 
arXiv:2112.05735v1 fatcat:syidouw7yzdejj27pboif4nofa

ACCELERATING GENERALIZED ITERATIVE SCALING BASED ON STAGGERED AITKEN METHOD FOR ON-LINE CONDITIONAL RANDOM FIELDS

HEE-DEOK YANG, HEUNG-IL SUK, SEONG-WHAN LEE
2012 International Journal of Wavelets, Multiresolution and Information Processing  
of other stochastic optimization methods, and illustrate experimental results with two public datasets.  ...  Bordes et al. 1 developed a variant of the second-order SGD, which iterates as fast as the first-order SGD but needs less iteration.  ...  The SGD-QN iterates as fast as a first-order SGD but can achieve a similar performance with less iterations. 1 As shown in Eq. (2.4), the second-order SGD uses the inverse of the objective function's  ... 
doi:10.1142/s0219691312500592 fatcat:6rb66orfivcxvd47xu2rktkmxe

Efficient Relaxed Gradient Support Pursuit for Sparsity Constrained Non-convex Optimization [article]

Fanhua Shang, Bingkun Wei, Hongying Liu, Yuanyuan Liu, Jiacheng Zhuo
2019 arXiv   pre-print
Inspired by GraSP, this paper proposes a new general relaxed gradient support pursuit (RGraSP) framework, in which the sub-algorithm only requires to satisfy a slack descent condition.  ...  Most existing deterministic optimization methods (e.g., GraSP) are not suitable for large-scale and high-dimensional problems, and thus stochastic optimization methods with hard thresholding (e.g., SVRGHT  ...  Besides these methods, there are still several stochastic firstor second-order nonconvex optimization algorithms, such as ASBCDHT [Chen and Gu, 2016] , HSG-HT , FNHTP [Chen and Gu, 2017] and SL-BFGS  ... 
arXiv:1912.00858v1 fatcat:oycupdhrjreobfpfvvfcuba6ce

A dynamic stochastic forcing method as a wall-layer model for large-eddy simulation

Anthony Keating, Ugo Piomelli
2006 Journal of turbulence  
The present work presents a dynamic stochastic forcing method, that, when coupled with the detached-eddy simulation methodology, significantly speeds up this transition resulting in more accurate predictions  ...  The method is shown to be equally effective in a periodic and in a spatially developing flow.  ...  In the momentum equation, the wall-normal diffusion was advanced implicitly using a second-order Crank-Nicolson method, while the other terms were advanced explicitly using a second-order Adams-Bashforth  ... 
doi:10.1080/14685240612331392460 fatcat:epq35aldjjatlp746jxaaur3oy

Multiscale Hy3S: hybrid stochastic simulation for supercomputers

Howard Salis, Vassilios Sotiropoulos, Yiannis N Kaznessis
2006 BMC Bioinformatics  
perturbations in both the number of molecules of species and reaction kinetic parameters; combinatorial variation of both initial conditions and kinetic parameters to enable sensitivity analysis; use  ...  However, the computational cost of the original stochastic simulation algorithm can be high, motivating the use of hybrid stochastic methods.  ...  Kinetic parameters or initial conditions may be varied from a start to end value with any number of either linear or logarithmic steps.  ... 
doi:10.1186/1471-2105-7-93 pmid:16504125 pmcid:PMC1421438 fatcat:5won4hnxejgktdiuo7qvot6jhm

Page 302 of SPE Reservoir Evaluation & Engineering Vol. 3, Issue 4 [page]

2000 SPE Reservoir Evaluation & Engineering  
The advantages of the method are speed and global condition- ing. It can be applied in any number of dimensions.  ...  .: *‘Stochastic Modeling of Seafloor Mor- phology: Inversion of Sea Beam Data for Second-Order Statistics,”’ J. Geophys.  ... 

Combining Adversarial Guarantees and Stochastic Fast Rates in Online Learning [article]

Wouter M. Koolen and Peter Grünwald and Tim van Erven
2016 arXiv   pre-print
We prove that these algorithms attain fast rates in their respective settings both in expectation and with high probability.  ...  We quantify the friendliness of stochastic environments by means of the well-known Bernstein (a.k.a. generalized Tsybakov margin) condition.  ...  The following result shows that second-order methods automatically adapt to the Bernstein condition. (Proof sketch in Section 4.) Theorem 3.  ... 
arXiv:1605.06439v1 fatcat:utni7muta5d6tipmgqzh7o7mre

Comparative Study of the Path Integration Method and the Stochastic Averaging Method for Nonlinear Roll Motion in Random Beam Seas

Wei Chai, Leo Dostal, Arvid Naess, Bernt J. Leira
2017 Procedia Engineering  
In this work, the path integration method and the energy-based stochastic averaging method are introduced in order to study the stochastic responses of ship roll motion in random beam seas.  ...  Abstract In this work, the path integration method and the energy-based stochastic averaging method are introduced in order to study the stochastic responses of ship roll motion in random beam seas.  ...  In this work, a second-order linear is applied in order to approximate the desired spectrum, Smm(ω).  ... 
doi:10.1016/j.proeng.2017.09.220 fatcat:23qubiroujfczgajcmiebthmpy

Fast Black-box Variational Inference through Stochastic Trust-Region Optimization [article]

Jeffrey Regier and Michael I. Jordan and Jon McAuliffe
2017 arXiv   pre-print
We introduce TrustVI, a fast second-order algorithm for black-box variational inference based on trust-region optimization and the reparameterization trick.  ...  The former is based on stochastic first-order optimization. The latter uses second-order information, but lacks convergence guarantees.  ...  Conclusions For variational inference, it is no longer necessary to pick between slow stochastic first-order optimization (e.g., ADVI) and fast-but-restrictive deterministic second-order optimization.  ... 
arXiv:1706.02375v2 fatcat:c4bysldalbdpplwzmy6ye5eaeu

Elimination of fast variables in chemical Langevin equations

Yueheng Lan, Timothy C. Elston, Garegin A. Papoian
2008 Journal of Chemical Physics  
Previous work in this area has focused on direct treatment of the master equation. However, eliminating fast variables in the chemical Langevin equation is also an important problem.  ...  Internal and external fluctuations are ubiquitous in cellular signaling processes.  ...  Within each time interval, we used a second-order stochastic integrator to update m as in the previous example.  ... 
doi:10.1063/1.3027499 pmid:19063552 pmcid:PMC2674792 fatcat:3hflsewaqfdw3mwzbegdgwinxe

ASPDC: Accelerated SPDC Regularized Empirical Risk Minimization for Ill-Conditioned Problems in Large-Scale Machine Learning

Haobang Liang, Hao Cai, Hejun Wu, Fanhua Shang, James Cheng, Xiying Li
2022 Electronics  
Our proposed ASPDC methods achieve a good balance between low per-iteration computation complexity and fast convergence speed, even when the condition number becomes very large.  ...  The large condition number causes ill-conditioned problems, which usually requires many more iterations before convergence and longer per-iteration times in data training for machine learning.  ...  General optimization methods to the RERM problem using gradients are categorized into two types, namely, first-order and second-order.  ... 
doi:10.3390/electronics11152382 fatcat:jnxrtaxo5rfrtn7kmosivr6msi

Stochastic Simulation of Chemical Kinetics

Daniel T. Gillespie
2007 Annual review of physical chemistry (Print)  
Stochastic chemical kinetics describes the time evolution of a wellstirred chemically reacting system in a way that takes into account the fact that molecules come in whole numbers and exhibit some degree  ...  After reviewing the supporting theory of stochastic chemical kinetics, I discuss some recent advances in methods for using that theory to make numerical simulations.  ...  The logarithmic direct method is not susceptible to this problem because it does not depend on any ordering scheme for the reaction indices; indeed, with the logarithmic direct method, the ordering could  ... 
doi:10.1146/annurev.physchem.58.032806.104637 pmid:17037977 fatcat:syonvd5tbnep7mvynnf2d3och4

Stochastic Second-Order Method for Large-Scale Nonconvex Sparse Learning Models

Hongchang Gao, Heng Huang
2018 Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence  
In this paper, we propose a linearly convergent stochastic second-order method to optimize this nonconvex problem for large-scale datasets.  ...  The proposed method incorporates second-order information to improve the convergence speed.  ...  For instance, when the condition number of the objective function in Eq. (1) is extremely large, the first-order method will converge very slowly.  ... 
doi:10.24963/ijcai.2018/294 dblp:conf/ijcai/GaoH18a fatcat:ujo5pw33hrdutk3cl6xem3pxfa

Page 7215 of Mathematical Reviews Vol. , Issue 87m [page]

1987 Mathematical Reviews  
The definition of the proposed conditional mean squared error is motivated by considering the stationary first-order autoregressive model in detail.  ...  Given a time series Z,,---,Zjy, the number of higher order crossings of order k, denoted by D,,n, is defined as the number of occurrences of x{*) # x), t = 2,---,N.  ... 

Moment estimation for chemically reacting systems by extended Kalman filtering

J. Ruess, A. Milias-Argeitis, S. Summers, J. Lygeros
2011 Journal of Chemical Physics  
future research is the derivation of observability conditions based on the structure of the system.  ...  The method is based on closing the moment dynamics by replacing the moments of order n + 1 by estimates calculated from a small number of stochastic simulation runs.  ...  In Figure 2 , the number of SSA trajectories is plotted against the logarithm of the L 2 -error of filter (blue) and SSA on its own (green).  ... 
doi:10.1063/1.3654135 pmid:22047267 fatcat:iwz26oag2beyxpzuvchsii3hya
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