Talk by Andrea Vandin: Language-based abstractions for dynamical systems

Speaker Andrea Vandin, IMT School for Advanced Studies Lucca, Italy, is giving a talk on a language-based approach to reduce ODEs.

Abstract: Ordinary differential equations (ODEs) are the primary means to modeling dynamical systems in a wide range of natural and engineering sciences. When the inherent complexity of the system under consideration is high, the number of equations required poses a serious detriment to our capability of performing effective analyses. This has motivated a large body of research, across many disciplines, into abstraction techniques that provide smaller ODE systems preserving the original dynamics in some appropriate sense.

In this talk I will present our novel computer-science perspective to this problem, borrowing ideas from the concurrency theory community. Akin to classical models of computation based on labelled transition systems, we recast the ODE reduction problem to that of finding appropriate equivalence relations over ODE variables. We study such "differential equivalences" for two basic intermediate languages, trading expressivity for efficiency:

(i) First, I will consider the language IDOL (Intermediate Drift-Oriented Language), which covers a general class of ODEs including the ODE semantics of existing stochastic process algebras. Computing the largest equivalences of IDOL terms can be done using a symbolic partition-refinement algorithm that exploits an encoding into a satisfiability modulo theories (SMT) problem.

(ii) Then, I will focus on ODEs with polynomial derivatives, which we characterise by a subset of the stochastic pi-calculus named reaction networks. The partition refinement for reaction networks is based on Paige and Tarjan’s seminal solution to the coarsest refinement problem. This gives an efficient algorithm that runs in polynomial time.

Using ERODE, our mature and user-friendly tool for the Evaluation and Reduction of ODEs, I will present numerical evidence of effective reductions in realistic models from the literature.