This paper introduces a neural network approach for solving two-dimensional traveltime tomography(TT)problems based on the eikonal equation.The mathematical problem of TT is to recover the slowness field of a medium b...This paper introduces a neural network approach for solving two-dimensional traveltime tomography(TT)problems based on the eikonal equation.The mathematical problem of TT is to recover the slowness field of a medium based on the boundary measurement of the traveltimes of waves going through the medium.This inverse map is high-dimensional and nonlinear.For the circular tomography geometry,a perturbative analysis shows that the forward map can be approximated by a vectorized convolution operator in the angular direction.Motivated by this and filtered backprojection,we propose an effective neural network architecture for the inverse map using the recently proposed BCR-Net,with weights learned from training datasets.Numerical results demonstrate the efficiency of the proposed neural networks.展开更多
This note introduces the double flip move to accelerate the Swendsen-Wang algorithm for Ising models with mixed boundary conditions below the critical temperature.The double flip move consists of a geometric flip of t...This note introduces the double flip move to accelerate the Swendsen-Wang algorithm for Ising models with mixed boundary conditions below the critical temperature.The double flip move consists of a geometric flip of the spin lattice followed by a spin value flip.Both symmetric and approximately symmetric models are considered.We prove the detailed balance of the double flip move and demonstrate its empirical efficiency in mixing.展开更多
This note introduces a method for sampling Ising models with mixed boundary conditions.As an application of annealed importance sampling and the Swendsen-Wang algorithm,the method adopts a sequence of intermediate dis...This note introduces a method for sampling Ising models with mixed boundary conditions.As an application of annealed importance sampling and the Swendsen-Wang algorithm,the method adopts a sequence of intermediate distributions that keeps the temperature fixed but turns on the boundary condition gradually.The numerical results show that the variance of the sample weights is relatively small.展开更多
Numerical Methods for Partial Differential Equations Numerical methods for partial differential equation have experienced steady developments in the past several decades.Most of the remaining challenges fall into two ...Numerical Methods for Partial Differential Equations Numerical methods for partial differential equation have experienced steady developments in the past several decades.Most of the remaining challenges fall into two categories,both of which are associated with the curse of the dimensionality.In the first category,the function of the partial differential equation is high dimensional,with examples from many-body quantum nieclianics,molecular dynamics.展开更多
A new understanding of adversarial examples and adversarial robustness is proposedby decoupling the data generator and the label generator (which we call the teacher). Inour framework, adversarial robustness is a cond...A new understanding of adversarial examples and adversarial robustness is proposedby decoupling the data generator and the label generator (which we call the teacher). Inour framework, adversarial robustness is a conditional concept—the student model is notabsolutely robust, but robust with respect to the teacher. Based on the new understanding, we claim that adversarial examples exist because the student cannot obtain sufficientinformation of the teacher from the training data. Various ways of achieving robustness iscompared. Theoretical and numerical evidence shows that to efficiently attain robustness,a teacher that actively provides its information to the student may be necessary.展开更多
基金partially supported by the U.S.Department of Energy,Office of Science,Office of Advanced Scientific Computing Research,Scientific Discovery through Advanced Computing(SciDAC)programpartially supported by the National Science Foundation under award DMS-1818449.
文摘This paper introduces a neural network approach for solving two-dimensional traveltime tomography(TT)problems based on the eikonal equation.The mathematical problem of TT is to recover the slowness field of a medium based on the boundary measurement of the traveltimes of waves going through the medium.This inverse map is high-dimensional and nonlinear.For the circular tomography geometry,a perturbative analysis shows that the forward map can be approximated by a vectorized convolution operator in the angular direction.Motivated by this and filtered backprojection,we propose an effective neural network architecture for the inverse map using the recently proposed BCR-Net,with weights learned from training datasets.Numerical results demonstrate the efficiency of the proposed neural networks.
文摘This note introduces the double flip move to accelerate the Swendsen-Wang algorithm for Ising models with mixed boundary conditions below the critical temperature.The double flip move consists of a geometric flip of the spin lattice followed by a spin value flip.Both symmetric and approximately symmetric models are considered.We prove the detailed balance of the double flip move and demonstrate its empirical efficiency in mixing.
文摘This note introduces a method for sampling Ising models with mixed boundary conditions.As an application of annealed importance sampling and the Swendsen-Wang algorithm,the method adopts a sequence of intermediate distributions that keeps the temperature fixed but turns on the boundary condition gradually.The numerical results show that the variance of the sample weights is relatively small.
文摘Numerical Methods for Partial Differential Equations Numerical methods for partial differential equation have experienced steady developments in the past several decades.Most of the remaining challenges fall into two categories,both of which are associated with the curse of the dimensionality.In the first category,the function of the partial differential equation is high dimensional,with examples from many-body quantum nieclianics,molecular dynamics.
文摘A new understanding of adversarial examples and adversarial robustness is proposedby decoupling the data generator and the label generator (which we call the teacher). Inour framework, adversarial robustness is a conditional concept—the student model is notabsolutely robust, but robust with respect to the teacher. Based on the new understanding, we claim that adversarial examples exist because the student cannot obtain sufficientinformation of the teacher from the training data. Various ways of achieving robustness iscompared. Theoretical and numerical evidence shows that to efficiently attain robustness,a teacher that actively provides its information to the student may be necessary.
