Automatic-differentiated Physics-Informed Echo State Network (API-ESN)
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Abstract (arXiv)
We propose the Automatic-differentiated Physics-Informed Echo State Network (API-ESN). The network is constrained by the physical equations through the reservoir's exact time-derivative, which is computed by automatic differentiation. As compared to the original Physics-Informed Echo State Network, the accuracy of the time-derivative is increased by up to seven orders of magnitude. This increased accuracy is key in chaotic dynamical systems, where errors grows exponentially in time. The network is showcased in the reconstruction of unmeasured (hidden) states of a chaotic system. The API-ESN eliminates a source of error, which is present in existing physics-informed echo state networks, in the computation of the time-derivative. This opens up new possibilities for an accurate reconstruction of chaotic dynamical states.
Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). First posted on arXiv 28 Dec 2020.
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Citing papers per year: 2021: 2; 2022: 1; 2023: 3; 2024: 1; 2025: 0; 2026: 1.
8 papers.
- 2021Robust Optimization and Validation of Echo State Networks for learning chaotic dynamicscited by 27
- 2023Reconstruction, forecasting, and stability of chaotic dynamics from partial datacited by 7
- 2023Constraining Chaos: Enforcing dynamical invariants in the training of recurrent neural networkscited by 6
- 2021Gradient-free optimization of chaotic acoustics with reservoir computingcited by 4
- 2022Modelling spatiotemporal turbulent dynamics with the convolutional autoencoder echo state networkcited by 4
- 2023Physics-Informed Long Short-Term Memory for Forecasting and Reconstruction of Chaoscited by 3
- 2024Physics-informed nonlinear vector autoregressive models for the prediction of dynamical systemscited by 3
- 2026Quantum Reservoir Computing with Physics-Informed Correction for Reduced-Order PDE Forecastingcited by 0
- 2026Quantum Reservoir Computing with Physics-Informed Correction for Reduced-Order PDE Forecasting24 Aug 2026
- 2024Physics-informed nonlinear vector autoregressive models for the prediction of dynamical systems25 Jul 2024
- 2023Reconstruction, forecasting, and stability of chaotic dynamics from partial data24 May 2023
- 2023Constraining Chaos: Enforcing dynamical invariants in the training of recurrent neural networks24 Apr 2023
- 2023Physics-Informed Long Short-Term Memory for Forecasting and Reconstruction of Chaos3 Feb 2023
- 2022Modelling spatiotemporal turbulent dynamics with the convolutional autoencoder echo state network21 Nov 2022
- 2021Gradient-free optimization of chaotic acoustics with reservoir computing17 Jun 2021
- 2021Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics9 Feb 2021