Theory revision in equation discovery

Abstract

State of the art equation discovery systems start the discovery process from scratch, rather than from an initial hypothesis in the space of equations. On the other hand, theory revision systems start from a given theory as an initial hypothesis and use new examples to improve its quality. Two quality criteria are usually used in theory revision systems. The first is the accuracy of the theory on new examples and the second is the minimality of change of the original theory. In this paper, we formulate the problem of theory revision in the context of equation discovery. Moreover, we propose a theory revision method suitable for use withth e equation discovery system Lagramge. The accuracy of the revised theory and the minimality of theory change are considered. The use of the method is illustrated on the problem of improving an existing equation based model of the net production of carbon in the Earth ecosystem. Experiments show that small changes in the model parameters and structure considerably improve the accuracy of the model.