A Constrained Backpropagation Approach for the Adaptive Solution of Partial Differential Equations - Rudd, Keith; Muro, Gianluca Di; Ferrari, Silvia (IEEE transaction on neural networks and learning systems, 2014)
Keywords: 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