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

Hidden physics models: Machine learning of nonlinear partial differential equations

While there is currently a lot of enthusiasm about “big data”, useful data is usually “small” and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by tim...

Learning of a single-hidden layer feedforward neural network using an optimized extreme learning machine

This paper proposes a learning framework for single-hidden layer feedforward neural networks (SLFN) called optimized extreme learning machine (O-ELM). In O-ELM, the structure and the parameters of the SLFN are determined using an optimization method. The output weights, like in the batch ELM, are obtained by a least squares algorithm, but using Tikhonov’s regularization in order to improve the ...

Numerical Solution of Partial Differential Equations

Preface These lecture notes are intended to supplement a one-semester graduate-level engineering course at The George Washington University in numerical methods for the solution of partial differential equations. Both finite difference and finite element methods are included. The main prerequisite is a standard undergraduate calculus sequence including ordinary differential equations. In genera...

Numerical Solution of Partial Differential Equations

Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this book, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents Preface to the first edition page viii Preface to the second edition xi 1 Introduction 1 2 Parabolic equations in one space v...

Numerical Solution of Nonlinear Partial Differential Equations