Fast and Scalable Inference of Dynamical Systems via Integral Matching

We present a novel approach to identifying parameters of nonlinear Ordinary Differential Equations (ODEs). This method, which is based on collocation methods, enables the direct identification of parameters from time series data by matching the integral of the dynamic with an interpolation of the trajectory. This method is distinct from existing literature in that it does not require ODE solvers or an estimate of the time derivative. Furthermore, batching strategies, such as time subintervals and component of the state, are proposed to improve scalability, thus providing a fast and highly parallel method to evaluate gradients, and a faster convergence than adjoint methods. The effectiveness of the method is demonstrated on chaotic systems, with speed-ups of three orders of magnitude compared to adjoint methods, and its robustness to observational noise and data availability is assessed.