Constraint Reasoning for Differential Models

Comparing the major features of biophysical inadequacy was related with the representation of differential equations. System dynamics is often modeled with the expressive power of the existing interval constraints framework. It is clear that the most important model was through differential equations but there was no way of expressing a differential equation as a constraint and integrate it within the constraints framework. Consequently, the goal of this work is focused on the integration of ordinary differential equations within the interval constraints framework, which for this purpose is extended with the new formalism of Constraint Satisfaction Differential Problems. Such framework allows the specification of ordinary differential equations, together with related information, by means of constraints, and provides efficient propagation techniques for pruning the domains of their variables. This enabled the integration of all such information in a single constraint whose variables may subsequently be used in other constraints of the model. The specific method used for pruning its variable domains can then be combined with the pruning methods associated with the other constraints in an overall propagation algorithm for reducing the bounds of all model variables.
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