The authors of [1] suggest to apply the approach from [2]: to probabilistically predict Cell parameters by training a variational autoencoder (VAE) model after pre-training using the output of an electrochemical cell model. Pre-training on the electrochemical model output (i. e., a simulation output) essentially regularises the VAE model.

**Having a stochastic framework for estimating all parameters at once is essential because Li-ion cells have just one output signal: voltage.**

Even a Kalman Filter estimating all cell parameters at once will likely fail to discern the contributions of different cell parameters to saddle changes in the voltage response of the cell. This is because the classic Kalman Filter keeps only the latest estimated parameters as its state and doesn't consider the telemetry history holistically. For example, the changes in the Coulombic efficiency and in the Cell self-discharge rate lead to approximately the same effect unless we predict the parameters considering at least several charge/discharge cycles of different lengths.

An example of an electrical cell model which can be fed into the regularisation algorithm is Thevenin equivalent circuit model.

Open question: can the stochastic predictor use an LSTM network, as described in Online capacity estimation of lithium-ion batteries with deep long short-term memory networks?

See also:

- Estimator of cell parameters based on particle swarm optimisation
- Digital twin for battery systems: Cloud BMS with online SoC and SoH estimation

[1] The Application of Data-Driven Methods and Physics-Based Learning for Improving Battery Safety

[2] [Variational Auto-Regularized Alignment for Sim-to-Real Control](https://www.notion.so/Variational-Auto-Regularized-Alignment-for-Sim-to-Real-Control-2a5e545ed6674086970776cbe972997e)