Parameter synthesis of polynomial dynamical systems
Résumé
Parametric dynamical systems emerge as a natural formalism for modeling natural and engineered systems ranging from biology, epidemiology, and medicine to cyber-physics. Parameter tuning is a complex task which, in many cases, is performed exploiting heavy simulations that have high computational complexity and do not ensure the correctness of the synthesized systems. In this manuscript, we consider the problem of parameter synthesis for discrete-time polynomial systems. We propose a formal method based on Bernstein coefficients that allows refining the set of parameters according to a temporal specification defined as a Signal Temporal Logic formula. We prove that the synthesized system is correct with respect to the specification and we demonstrate the scalability of the approach by implementing it in the C++ library Sapo, also available within a stand-alone application and as a web application. Finally, we illustrate the tool usage and the interface through a simple yet realistic epidemiological model and consider an intriguing application enhancing the accuracy of the verification of neural networks.
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