Neural networks trained by weight permutation are universal approximators.

The universal approximation property is fundamental to the success of neural networks, and has traditionally been achieved by training networks without any constraints on their parameters. However, recent experimental research proposed a novel permutation-based training method, which exhibited a desired classification performance without modifying the exact weight values. In this paper, we provide a theoretical guarantee of this permutation training method by proving its ability to guide a ReLU network to approximate one-dimensional continuous functions.

Mass conservative lattice Boltzmann scheme for a three-dimensional diffuse interface model with Peng-Robinson equation of state.

Peng-Robinson (P-R) equation of state (EOS) has been widely used in the petroleum industry for hydrocarbon fluids. In this work, a three-dimensional diffuse interface model with P-R EOS for two-phase fluid system is solved by the lattice Boltzmann (LB) method. In this diffuse interface model, an Allen-Cahn (A-C) type phase equation with strong nonlinear source term is derived.

The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number.

In this paper, numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problem is presented. To carry out such analysis, at each time step, we need to solve the incompressible Navier-Stokes equations on irregular domains twice, one for the primary variables; the other is for the sensitivity variables with homogeneous boundary conditions. The Navier-Stokes solver is the augmented immersed interface method for Navier-Stokes equations on irregular domains.

A FINITE ELEMENT METHOD FOR ELASTICITY INTERFACE PROBLEMS WITH LOCALLY MODIFIED TRIANGULATIONS.

A finite element method for elasticity systems with discontinuities in the coefficients and the flux across an arbitrary interface is proposed in this paper. The method is based on a Cartesian mesh with local modifications to the mesh. The total degrees of the freedom of the finite element method remains the same as that of the Cartesian mesh.