The method of Lagrange multipliers is utilized in the unsupervised training of a three-layer, single-output, feed-forward neural network for characterizing the dynamics of constrained physical systems. Training aims at minimizing the energy function that is obtained from the equations of state which are generated using the method of Lagrange multipliers. The approach is illustrated (1) to solve an inverse problem in nuclear reactor design, (2) to determine how competing biological entities organized (cells in a tissue, Eucalyptus trees), and (3) to solve an ill-posed differential equation.

• Received 10 March 1997

DOI:https://doi.org/10.1103/PhysRevE.57.R1247