Software

Community detection from the observability Gramian of a network dynamical system. Computes linear, variational, and empirical Gramians from measured trajectories, clusters the normalized Gramian to recover the communities, and estimates their number from the largest eigenvalue gap. Includes the experiments on diffusion, Ornstein–Uhlenbeck, and Kuramoto dynamics over benchmark and real networks, including the IEEE 39-bus grid, with scripts that regenerate every figure of the Letter.

Variational observability Gramian (Var-Gram) for nonlinear systems, with the empirical Gramian and Lyapunov-exponent computations. The Var-Gram is demonstrated on combustion reaction networks (H₂O₂, 9 species; GRI-Mech 3.0, 53 species) modeled through Cantera, with implicit Runge–Kutta integration of the variational dynamics and a greedy sensor placement formulation that selects which species to measure.

Coupled overland flow and Green–Ampt infiltration represented as a differential-algebraic state-space model, with distribution-agnostic uncertainty propagation of uncertain paramerters to watershed states under partial gauging. Includes BDF and semi-implicit DAE solvers, Monte Carlo validation via Latin hypercube sampling, and the two test catchments from the paper: a synthetic V-tilted domain and the USDA-ARS Walnut Gulch experimental watershed.

Multi-species water quality sensor placement for drinking water distribution networks. Constructs state-averaged observability measures that retain submodularity across varying hydraulic and water quality scenarios, and selects sensor locations with a greedy algorithm while retaining provable approximation guarantees. Includes validation on EPANET benchmark networks.