175 citations · 196 across the 5 of their papers we have counts for
5 papers
Learning the Exact Time Integration Algorithm for Initial Value Problems by Randomized Neural Networks
Suchuan Dong, Naxian Ni
We present a method leveraging extreme learning machine (ELM) type randomized neural networks (NNs) for learning the exact time integration algorithm for initial value problems (IV…
Numerical Computation of Partial Differential Equations by Hidden-Layer Concatenated Extreme Learning Machine
Naxian Ni, Suchuan Dong
The extreme learning machine (ELM) method can yield highly accurate solutions to linear/nonlinear partial differential equations (PDEs), but requires the last hidden layer of the n…
A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networks
Suchuan Dong, Naxian Ni
We present a simple and effective method for representing periodic functions and enforcing exactly the periodic boundary conditions for solving differential equations with deep neu…
An Energy-Stable Scheme for Incompressible Navier-Stokes Equations with Periodically Updated Coefficient Matrix
L. Lin, N. Ni, Z. Yang +1
We present an energy-stable scheme for simulating the incompressible Navier-Stokes equations based on the generalized Positive Auxiliary Variable (gPAV) framework. In the gPAV-refo…
Energy-Stable Boundary Conditions Based on a Quadratic Form: Applications to Outflow/Open-Boundary Problems in Incompressible Flows
Naxian Ni, Zhiguo Yang, Suchuan Dong
We present a set of new energy-stable open boundary conditions for tackling the backflow instability in simulations of outflow/open boundary problems for incompressible flows. Thes…