Registered Data

[CT090]

[01159] A multiscale framework for rigid bodies in Stokes flow with applications to nanocellulose

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : The dynamics of rod-like nanocellulose chrystals in an aqueous suspension is modelled with the rigid multiblob method for Stokes flow, with particle interactions from an accurate potential obtained from molecular dynamics data fed to a neural network. Tools to control the error from the hydrodynamic interactions and from discretising the overdamped Langevin equation, describing the Brownian motion of the particles, enable predictions of physical properties difficult to measure in the lab.
  • Classification : 65C30, Boundary integral equations;
  • Author(s) :
    • Anna Broms (KTH Royal Institute of Technology)
    • Anna-Karin Tornberg (KTH Royal Institute of Technology)
    • Mattias Sandberg (KTH Royal Institute of Technology)

[02305] Simulating First Passage Times for Ito Diffusions

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : We are interested in the mechanism of olfactory receptor neuron responses in moths. A neuron's processing of information is represented by spike trains, collections of spikes, short and precisely shaped electrical impulses. Mathematically, these can be modeled as the first passage times of solutions to certain stochastic differential equations, describing the membrane voltage, to a threshold. Classical numerical methods like the Euler-Maruyama method and the Milstein scheme approximate hitting times as a ‘by-product’ and are not very good if we perform them on a large interval of time. For that reason, we study an algorithm that simulates the exact discretized grid of a class of stochastic differential equations. It uses an acceptance-rejection scheme for the simulation of that grid at random time intervals; later, the whole path can be completed independently of the target process by interpolation of the Brownian or Bessel bridge. This method is very effective in the sense that it neither simulates the whole path nor focuses on a fixed time interval. We further examine the different numerical methods with the help of an example.
  • Classification : 65C30, 60H99, 92-10, First Passage Times, Exact Simulations, Applications in Neuroscience
  • Author(s) :
    • Evelyn Buckwar (Johannes Kepler University)
    • Devika Khurana (Johannes Kepler University)

[02361] A unified framework for convergence analysis of stochastic gradient algorithms with momentum: a linear two-step approach

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : From the viewpoint of weak approximation, the stochastic gradient algorithm and stochastic differential equation are closely related. In this talk, we develop a systematic framework for the convergence of stochastic gradient descent with momentum by exploring the stationary distribution of a linear two-step method applied to stochastic differential equations. Then we prove the convergence of two stochastic linear two-step methods, which are associated with the stochastic heavy ball method and Nesterov's accelerated gradient method.
  • Classification : 65C30, 60H35
  • Author(s) :
    • Qian Guo (Shanghai Normal University)
    • Fangfang Ma (Shanghai Normal University)

[02532] Stochastic pseudo-symplectic explicit Runge-Kutta methods for Hamiltonian Systems

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : We propose a systematic approach, based on colored trees and B-series, to construct explicit Runge-Kutta pseudo-symplectic schemes for stochastic Hamiltonian systems in the sense of Stratonovich. Numerical experiments are presented to verify our theoretical analysis and illustrate the long-term accuracy of these methods. Overall, these schemes offer a good compromise between computational time and accuracy, because they are more accurate than the explicit Itô-Taylor approximation methods and less computationally expensive than the implicit symplectic schemes.
  • Classification : 65C30, 60H35
  • Author(s) :
    • cristina adela anton (MacEwan University)

[02215] Solving Fokker-Planck Equation in High Dimensions via Milestoning

  • Session Date & Time : 2D (Aug.22, 15:30-17:10)
  • Type : Contributed Talk
  • Abstract : We propose a novel method for solving Fokker-Planck-type equations via the Feynman-Kac formula, closely related to rare events sampling. A family of trajectories is maintained between each pair of milestones while new samples are drawn based on an importance-sampling principle. We also show a probabilistic estimate of the sampling error which explains why, so-called, milestoning can significantly speed up molecular dynamics simulations.
  • Classification : 65C35, 65C30, 60H35
  • Author(s) :
    • Ziheng Chen (University of Texas at Austin)
    • Bjorn Engquist (University of Texas at Austin)