Sketching the temperature history of geological samples: analyses of diffusion profiles using multilayer perceptrons

A method using multilayer perceptrons for analysing diffusion profiles and sketching the temperature history of geological samples is explored. Users of this method can intuitively test and compare results thinking in terms of analytical solutions of the diffusion equation whilst the bulk of the work is made computationally. Being neither completely analytical nor numerical, the method is a hybrid and represents an ideal man-machine interaction. The approach presented in this paper should be preferred when the retrieval of the diffusion coefficients from concentration profiles using dimensionless parameters is not possible and/or there is more than one unknown parameter in the analytical solution of the diffusion equation. Its versatility is a key factor for extending the potential of Dodson’s formulation. The case of a species produced by a radiogenic source and diffusing in a cooling system is therefore discussed. Both the classical change of variable for diffusion coefficients depending on time and an alternative approach decomposing the overall effect of diffusion into a sum of effects due to smaller events could be used to tackle this problem. As multilayer perceptrons can approximate any function, none of the assumptions originally stated by Dodson are necessary.