The estimation of parameters in time-dependent transport problems: Dynamic programming and associative memories

Time-dependent radiation and energy transport problems are important in atmospheric science, medicine, biochemistry, and other areas. To determine external energy fields, direct problems (in which parameters are known) can be solved computationally by numerical integration followed by the numerical inversion of Laplace transforms. On the other hand, this paper treats inverse problems of estimating transport parameters on the basis of external observations of radiant intensity. These problems are approached using associative memory neural networks whose associated least squares problem is solved using a new dynamic programming algorithm. The quality of the estimates in the presence of noise in measurements is studied.