82 citations · 926 across the 70 of their papers we have counts for
10 papers · 1 filter
BIMC: The Bayesian Inverse Monte Carlo method for goal-oriented uncertainty quantification. Part II
Siddhant Wahal, George Biros
In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The a…
BIMC: The Bayesian Inverse Monte Carlo method for goal-oriented uncertainty quantification. Part I
Siddhant Wahal, George Biros
We consider the problem of estimating rare event probabilities, focusing on systems whose evolution is governed by differential equations with uncertain input parameters. If the sy…
Fast Approximation of the Gauss-Newton Hessian Matrix for the Multilayer Perceptron
Chao Chen, Severin Reiz, Chenhan Yu +2
We introduce a fast algorithm for entry-wise evaluation of the Gauss-Newton Hessian (GNH) matrix for the fully-connected feed-forward neural network. The algorithm has a precomputa…
Stable shapes of three-dimensional vesicles in unconfined and confined Poiseuille flow
Dhwanit Agarwal, George Biros
We use numerical simulations to study the dynamics of three dimensional vesicles in unconfined and confined Poiseuille flow. Previous numerical studies have shown that when the flu…
Image-Driven Biophysical Tumor Growth Model Calibration
Klaudius Scheufele, Shashank Subramanian, Andreas Mang +2
We present a novel formulation for the calibration of a biophysical tumor growth model from a single-time snapshot, MRI scan of a glioblastoma patient. Tumor growth models are typi…
Where did the tumor start? An inverse solver with sparse localization for tumor growth models
Shashank Subramanian, Klaudius Scheufele, Miriam Mehl +1
We present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth…
ANODEV2: A Coupled Neural ODE Evolution Framework
Tianjun Zhang, Zhewei Yao, Amir Gholami +4
It has been observed that residual networks can be viewed as the explicit Euler discretization of an Ordinary Differential Equation (ODE). This observation motivated the introducti…
Machine learning acceleration of simulations of Stokesian suspensions
Gokberk Kabacaoglu, George Biros
Particulate Stokesian flows describe the hydrodynamics of rigid or deformable particles in Stokes flows. Due to highly nonlinear fluid-structure interaction dynamics, moving interf…
ANODE: Unconditionally Accurate Memory-Efficient Gradients for Neural ODEs
Amir Gholami, Kurt Keutzer, George Biros
Residual neural networks can be viewed as the forward Euler discretization of an Ordinary Differential Equation (ODE) with a unit time step. This has recently motivated researchers…
A domain decomposition preconditioning for the integral equation formulation of the inverse scattering problem
Carlos Borges, George Biros
We propose domain decomposition preconditioners for the solution of an integral equation formulation of forward and inverse acoustic scattering problems with point scatterers. We s…