ASMOD uses B-splines to represent general nonlinear and coupled dependencies in multivariable observation data (Kavli (1993), Weyer, E. and T. Kavli (1995,1997), Bridgett et al (1994)). B-splines are commonly used in computer graphics and CAD systems for representing three dimensional curves and surfaces with high accuracy. B-splines are also applicable for higher dimensional spaces and are therefore a suitable starting point for nonlinear and multivariable empirical modeling. However, by direct expansion of the standard spline representation to higher dimensions the number of parameters grows rapidly to impractical levels. Methods must thus be found to reduce the complexity of the models. The ASMOD algorithm represents one attempt to solve this problem by adapting the model structure to the dependencies, coupled or decoupled, that are observed in the data. The model complexity can then be dramatically reduced compared to using models of a general structure, and the model accuracy can be correspondingly improved since more accurate estimates can be obtained for the fewer parameters.

In the ASMOD algorithm the output variable is modeled as a sum of several sub-models, where each sub-model only depends on a small subset of the input variables. The decomposition of the high dimensional input space into low dimensional additive subspaces makes the model more transparent to the user. At the same time the complexity of the model is dramatically reduced. Data interpolation and extrapolation with B-splines have proven to be very well behaved, with no oscillatory behavior as commonly observed e.g. with polynomial fitting. There is a close link between ASMOD and a class fuzzy logic models (Kavli and Lines (1996), Bossley et al (1995)).

The ASMOD algorithm has proven to be able to find the underlying structure and give models of high accuracy in a large number of simulated and practical applications (Carlin et al (1994)).

1. Kavli, T. (1993). ASMOD-an algorithm for adaptive spline modelling of observation data, Int. Journal of Control, vol. 58, no. 4. pp. 947-967.
2. Weyer, E. and T. Kavli (1995), The ASMOD algorithm. Some new theoretical and experimental results. SINTEF report STF31 A95024. ISBN 82-595-8919-2
3. Weyer, E. and T. Kavli (1997), “Theoretical properties of the ASMOD algorithm for empirical modelling” International Journal of Control, Volume 67, Number 5, pp. 767 - 790
4. Bridgett, N.A., M. Brown, C.J. Harris and D.J. Mills (1994). “High dimensional approximation using an associative memory network”, IEE Control ‘94 Vol. 2, pp.1458-1465
5. Bossley, K.M., D.J. Mills, M. Brown and C.J. Harris (1995). “Construction and Design of Parsimonious Neurofuzzy Systems”,  In G. Irwin, K. Hunt and K. Warwick, editors. “Advances in Neural Networks for Control Systems. Advances in Industrial Control”, Springer Verlag, pp. 153 – 177.
6. Kavli, T. and G.T. Lines (1996) A unifying framework for mechanistic, fyzzy and data driven modelling, EUFIT’96, Achen, Gertmany, Sept. 2-5. pp. 752-756.
7. Carlin, M., T. Kavli, and B. Lillekjendlie (1994). ”A comparison of four methods for non_linear data modeling”.  Chemometrics and Intelligent Laboratory Systems Vol. 23, pp. 163 - 178

ASMOD is primarily an empirical technique for non-linear multivariate modeling from measured data, but it can be integrated into a unified modeling environment as illustrated here, making use of all three sources of information often available in a modeling task.