A Constrained Backpropagation Approach for the Adaptive Solution of Partial Differential Equations

• Published in: IEEE transaction on neural networks and learning systems Vol. 25; no. 3; pp. 571 - 584
• Main Authors: Rudd, Keith, Muro, Gianluca Di, Ferrari, Silvia
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2014; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive algorithm; Applied sciences; Approximation; Artificial intelligence; Artificial neural networks; artificial neural networks (ANNs); Back propagation; Boundaries; Computer science; control theory; systems; Connectionism. Neural networks; Constraints; Equations; Exact sciences and technology; Jacobian matrices; Linear programming; Mathematical analysis; Mathematics; Neural networks; Nonlinearity; Optimization; Partial differential equations; partial differential equations (PDEs); Sciences and techniques of general use; scientific computing; Training; Backpropagation; Dimensionality; artificial neural networks (ANNs); Adaptive algorithm; Initial condition; scientific computing; Elimination; Constraint satisfaction; Neural network; Boundary condition; Adaptive method; Partial differential equation; Penalty method; Constrained optimization; Backpropagation algorithm; Parabolic equation; Lagrange multiplier; Elliptic equation; Scientific computation; partial differential equations (PDEs); Non linear effect; Mathematical programming

This paper presents a constrained backpropagation (CPROP) methodology for solving nonlinear elliptic and parabolic partial differential equations (PDEs) adaptively, subject to changes in the PDE parameters or external forcing. Unlike existing methods based on penalty functions or Lagrange multiplier...