An Extreme Learning Machine-Based Method for Computational PDEs in Higher Dimensions

no code implementations • 13 Sep 2023 • Yiran Wang, Suchuan Dong

With the second method the high-dimensional PDE problem is reformulated through a constrained expression based on an Approximate variant of the Theory of Functional Connections (A-TFC), which avoids the exponential growth in the number of terms of TFC as the dimension increases.

Error Analysis of Physics-Informed Neural Networks for Approximating Dynamic PDEs of Second Order in Time

no code implementations • 22 Mar 2023 • Yanxia Qian, Yongchao Zhang, Yunqing Huang, Suchuan Dong

Our analyses show that, with feed-forward neural networks having two hidden layers and the $\tanh$ activation function, the PINN approximation errors for the solution field, its time derivative and its gradient field can be effectively bounded by the training loss and the number of training data points (quadrature points).

A Method for Computing Inverse Parametric PDE Problems with Random-Weight Neural Networks

no code implementations • 9 Oct 2022 • Suchuan Dong, Yiran Wang

The presented method has been compared with the physics-informed neural network method.

Numerical Computation of Partial Differential Equations by Hidden-Layer Concatenated Extreme Learning Machine

no code implementations • 24 Apr 2022 • Naxian Ni, Suchuan Dong

The HLConcELM method can produce highly accurate solutions to linear/nonlinear PDEs when the last hidden layer of the network is narrow and when it is wide.

Numerical Approximation of Partial Differential Equations by a Variable Projection Method with Artificial Neural Networks

no code implementations • 24 Jan 2022 • Suchuan Dong, Jielin Yang

For linear PDEs, enforcing the boundary/initial value problem on the collocation points leads to a separable nonlinear least squares problem about the network coefficients.

On Computing the Hyperparameter of Extreme Learning Machines: Algorithm and Application to Computational PDEs, and Comparison with Classical and High-Order Finite Elements

no code implementations • 27 Oct 2021 • Suchuan Dong, Jielin Yang

We consider the use of extreme learning machines (ELM) for computational partial differential equations (PDE).

A Modified Batch Intrinsic Plasticity Method for Pre-training the Random Coefficients of Extreme Learning Machines

no code implementations • 14 Mar 2021 • Suchuan Dong, Zongwei Li

In this paper we present a modified batch intrinsic plasticity (modBIP) method for pre-training the random coefficients in the ELM neural networks.

Local Extreme Learning Machines and Domain Decomposition for Solving Linear and Nonlinear Partial Differential Equations

no code implementations • 4 Dec 2020 • Suchuan Dong, Zongwei Li

The computational performance of the current method is on par with, and oftentimes exceeds, the FEM performance.

A Method for Representing Periodic Functions and Enforcing Exactly Periodic Boundary Conditions with Deep Neural Networks

no code implementations • 15 Jul 2020 • 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 neural networks (DNN).