Modern engineered systems and social organizations are complex structurally and temporally. As we move towards more autonomy of engineered systems, the “separation of concerns” strategy for design becomes more difficult to execute and the paradigm shifts to developing tools that deal with emergent properties of the system dynamics and are capable of handling a very large number of dynamically evolving states and possibly uncertain system constants. We present three mathematical tools that enable aspects of system engineering for such systems: 1) Operator-theory based visualization tools, 2) Koopman modes for efficient representation of system dynamics and 3) Fast sampling methods for uncertainty quantification and search. We also present a range of examples of applications of such tools in design, model validation and model reduction.
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