Registered Data

[CT090]

  • Session Time & Room
    • CT090 (1/1) : 2D @E506 [Chair: cristina adela anton]
  • Classification
    • CT090 (1/1) : Probabilistic methods, stochastic differential equations (65C) / Numerical methods for partial differential equations, boundary value problems (65N)

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

  • Session Time & Room : 2D (Aug.22, 15:30-17:10) @E506
  • 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
  • Format : Talk at Waseda University
  • Author(s) :
    • cristina adela anton (MacEwan University)

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

  • Session Time & Room : 2D (Aug.22, 15:30-17:10) @E506
  • 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
  • Format : Online Talk on Zoom
  • Author(s) :
    • Qian Guo (Shanghai Normal University)
    • Fangfang Ma (Shanghai Normal University)

[01104] Generation of $hp$-FEM Massive Databases for Deep Learning Inversion

  • Session Time & Room : 2D (Aug.22, 15:30-17:10) @E506
  • Type : Contributed Talk
  • Abstract : Deep Neural Networks are employed in many geophysical applications to characterize the Earth’s subsurface. However, they often need to solve hundreds of thousands of complex and expensive forward problems to produce the training dataset. This work presents a robust approach to producing massive databases at a reduced computational cost. In particular, we build a single $hp$-adapted mesh that accurately solves many FEM problems for any combination of parameters within a given range.
  • Classification : 65N30, Finite Element Method, Deep Neural Networks, Goal-Oriented Adaptivity
  • Format : Talk at Waseda University
  • Author(s) :
    • Julen Alvarez-Aramberri (University of the Basque Country (UPV/EHU))
    • Vincent Darrigrand (CNRS-IRIT, Toulouse)
    • Felipe Vinicio Caro (Basque Center for Applied Mathematics (BCAM), University of the Basque Country (UPV/EHU))
    • David Pardo (University of the Basque Country (UPV-EHU), Basque Center for Applied Mathematics (BCAM), Ikerbasque)

[02305] Simulating First Passage Times for Ito Diffusions

  • Session Time & Room : 2D (Aug.22, 15:30-17:10) @E506
  • 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
  • Format : Talk at Waseda University
  • Author(s) :
    • Evelyn Buckwar (Johannes Kepler University)
    • Devika Khurana (Johannes Kepler University)

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

  • Session Time & Room : 2D (Aug.22, 15:30-17:10) @E506
  • 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
  • Format : Talk at Waseda University
  • Author(s) :
    • Ziheng Chen (University of Texas at Austin)
    • Bjorn Engquist (University of Texas at Austin)