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

arXiv: https://arxiv.org/abs/2203.06269 · HTML: https://mlsanity.com/paper/2203.06269/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 32 references that are in the map.
- First posted on arXiv 11 Mar 2022.

## Builds on (most cited first, 6 of 6)

- [ROCKET: Exceptionally fast and accurate time series classification using random convolutional kernels](https://mlsanity.com/paper/1910.13051/) (2019)
- [MINIROCKET: A Very Fast (Almost) Deterministic Transform for Time Series Classification](https://mlsanity.com/paper/2012.08791/) (2020)
- [Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems](https://mlsanity.com/paper/1801.01236/) (2018)
- [Optimal Transport for Parameter Identification of Chaotic Dynamics via Invariant Measures](https://mlsanity.com/paper/2104.15138/) (2021)
- [System Identification Through Lipschitz Regularized Deep Neural Networks](https://mlsanity.com/paper/2009.03288/) (2020)
- [A Neural Network Ensemble Approach to System Identification](https://mlsanity.com/paper/2110.08382/) (2021)

## Built on by (most cited first, 1 of 1)

- [SPADE4: Sparsity and Delay Embedding based Forecasting of Epidemics](https://mlsanity.com/paper/2211.08277/) (2022)

## Abstract (arXiv)

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 system with system parameter labels. Our goal is to identify system parameters of new trajectories. The given trajectories may or may not encompass the full state of the system, and we may only observe a one-dimensional time series. In the latter case, we reconstruct the full state by using delay embeddings, and under sufficient conditions, Taken's Embedding Theorem assures us the reconstruction is diffeomorphic to the original. This allows our method to work on time series. Our method works by first learning the velocity operator (as given or reconstructed) with a neural network having both state and system parameters as variable inputs. Then on new trajectories we backpropagate prediction errors to the system parameter inputs giving us a gradient. We then use gradient descent to infer the correct system parameter. We demonstrate the efficacy of our approach on many numerical examples: the Lorenz system, Lorenz96, Lotka-Volterra Predator-Prey, and the Compound Double Pendulum. We also apply our algorithm on a real-world dataset: propulsion of the Hall-effect Thruster (HET).