Refine
Document Type
Language
- English (2)
Has Fulltext
- yes (2)
Is part of the Bibliography
- yes (2)
Keywords
- Diffusion (2) (remove)
Institute
Open Access
- Open Access (2) (remove)
Lithium-ion batteries exhibit slow voltage dynamics on the minute time scale that are usually associated with transport processes. We present a novel modelling approach toward these dynamics by combining physical and data-driven models into a Grey-box model. We use neural networks, in particular neural ordinary differential equations. The physical structure of the Grey-box model is borrowed from the Fickian diffusion law, where the transport domain is discretized using finite volumes. Within this physical structure, unknown parameters (diffusion coefficient, diffusion length, discretization) and dependencies (state of charge, lithium concentration) are replaced by neural networks and learnable parameters. We perform model-to-model comparisons, using as training data (a) a Fickian diffusion process, (b) a Warburg element, and (c) a resistor-capacitor circuit. Voltage dynamics during constant-current operation and pulse tests as well as electrochemical impedance spectra are simulated. The slow dynamics of all three physical models in the order of ten to 30 min are well captured by the Grey-box model, demonstrating the flexibility of the present approach.
Diffusion plays a decisive role in brain function. In treating brain disorders, where diffusion is often compromised, understanding the transport of molecules can be essential to effective drug delivery. It became apparent that the classical laws of diffusion, cast in the framework of porous media theory, can deliver an accurate quantitative description of the way that molecules are transported through the brain tissue.