Locally Imposing Function for Generalized Constraint Neural Networks - A Study on Equality Constraints

摘要

This work is a further study on the Generalized Constraint Neural Network(GCNN) model [1], [2]. Two challenges are encountered in the study, that is, toembed any type of prior information and to select its imposing schemes. Thework focuses on the second challenge and studies a new constraint imposingscheme for equality constraints. A new method called locally imposing function(LIF) is proposed to provide a local correction to the GCNN predictionfunction, which therefore falls within Locally Imposing Scheme (LIS). Incomparison, the conventional Lagrange multiplier method is considered asGlobally Imposing Scheme (GIS) because its added constraint term exhibits aglobal impact to its objective function. Two advantages are gained from LISover GIS. First, LIS enables constraints to fire locally and explicitly in thedomain only where they need on the prediction function. Second, constraints canbe implemented within a network setting directly. We attempt to interpretseveral constraint methods graphically from a viewpoint of the localityprinciple. Numerical examples confirm the advantages of the proposed method. Insolving boundary value problems with Dirichlet and Neumann constraints, theGCNN model with LIF is possible to achieve an exact satisfaction of theconstraints.