Conditioned Neural ODE Models and Applications to Stiff Reaction Systems
In this work, a data-driven reduced order modelling methodology was developed for simultaneous stiffness and dimension reduction of dynamical systems. A nonlinear bottleneck compression model is first trained on existing data, minimizing a combined penalty term including the reconstruction accuracy and a finite-difference formulation of the condition number metric. This produces a reversible reduced order mapping of the original stiff system to a set of minimum dimensionality, nonstiff dynamics. In combination with a neural ODE dynamics model, this combined set of models is denoted the reduced order neural ODE model (RONODE). The RONODE method allows efficient simulation of dynamic systems using rapid explicit integration algorithms that were not previously feasible for stiff dynamics. The Robertson equations, a stiff ODE benchmark problem, and two additional hydrocarbon combustion problems using the GRI 3.0 reaction mechanism with 53 species and 325 reactions were used as test cases. This is the first time a stiff reaction system of this scale has been successfully solved using a purely data-driven methodology.