Solving Large Dynamical Systems by Constraint Sampling

The ability to conduct fast and reliable simulations of dynamic systems is of special interest to many fields of operations. Such simulations can be very complex and, to be thorough, involve millions of variables, making it prohibitive in CPU time to run repeatedly for many different configurations. Reduced-Order Modeling (ROM) provides a concrete way to handle such complex simulations using a realistic amount of resources. However, when the original dynamical system is very large, the resulting reduced-order model, although much “thinner”, is still as tall as the original system, i.e., it has the same number of equations. In some extreme cases, the number of equations is prohibitive and cannot be loaded in memory. In this work, we combine traditional interval constraint solving techniques with a strategy to reduce the number of equations to consider. We describe our approach and report preliminary promising results.

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