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We provide a method to identify system parameters of dynamical systems,called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings.In this setting, we are given a dataset of trajectories from a dynamical systemwith system parameter labels. Our goal is to identify system parameters of newtrajectories. The given trajectories may or may not encompass the full state ofthe system, and we may only observe a one-dimensional time series. In thelatter case, we reconstruct the full state by using delay embeddings, and undersufficient conditions, Taken's Embedding Theorem assures us the reconstructionis diffeomorphic to the original. This allows our method to work on timeseries. Our method works by first learning the velocity operator (as given orreconstructed) with a neural network having both state and system parameters asvariable inputs. Then on new trajectories we backpropagate prediction errors tothe system parameter inputs giving us a gradient. We then use gradient descentto infer the correct system parameter. We demonstrate the efficacy of ourapproach on many numerical examples: the Lorenz system, Lorenz96,Lotka-Volterra Predator-Prey, and the Compound Double Pendulum. We also applyour algorithm on a real-world dataset: propulsion of the Hall-effect Thruster(HET).

Parameter Inference of Time Series by Delay Embeddings and Learning Differentiable Operators