About the Project

MONET (Moment-sum-of-squares Optimization for NETwork dynamics) is a 36-month (2026-2028) collaborative project funded by the ANR (France) and DFG (Germany) under the PRCI instrument.

Context: Predicting and controlling dynamical systems is crucial for energy grids, gas pipelines, and traffic networks. However, achieving global optimality for these nonlinear systems is challenging due to their high dimensionality.

Goal: The overarching goal of MONET is to unlock the full potential of the Moment-SOS hierarchy to compute global performance bounds for networks of hyperbolic PDEs. We aim to exploit the sparse couplings in networks to break through existing scalability barriers.

Key Objectives

• O1: Generalize the moment-SOS hierarchy for scalar conservation laws to handle variable boundary conditions.
• O2: Create a novel hierarchy specifically adapted for networks of hyperbolic PDEs.
• O3: Introduce computational enhancements (space-time decomposition, interpolation bases).
• O4: Deliver open-source software and benchmark examples (e.g., gas networks).

Coordinated by Didier Henrion (LAAS-CNRS) and Giovanni Fantuzzi (FAU).

This work was supported by the French National Research Agency (ANR) under project MONET with reference ANR-25-CE48-6598-01 and by the Deutsche Forschungsgemeinschaft (DFG).