# Physics-Informed Neural Network for Discovering Systems with Unmeasurable States with Application to Lithium-Ion Batteries

arXiv: https://arxiv.org/abs/2311.16374 · HTML: https://mlsanity.com/paper/2311.16374/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 32 references that are in the map.
- First posted on arXiv 27 Nov 2023.

## Builds on (most cited first, 4 of 4)

- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Understanding and mitigating gradient pathologies in physics-informed neural networks](https://mlsanity.com/paper/2001.04536/) (2020)
- [Recent Advances in Recurrent Neural Networks](https://mlsanity.com/paper/1801.01078/) (2017)
- [One-Shot Parameter Identification of the Thevenin's Model for Batteries: Methods and Validation](https://mlsanity.com/paper/2003.06504/) (2020)

## Abstract (arXiv)

Combining machine learning with physics is a trending approach for discovering unknown dynamics, and one of the most intensively studied frameworks is the physics-informed neural network (PINN). However, PINN often fails to optimize the network due to its difficulty in concurrently minimizing multiple losses originating from the system's governing equations. This problem can be more serious when the system's states are unmeasurable, like lithium-ion batteries (LiBs). In this work, we introduce a robust method for training PINN that uses fewer loss terms and thus constructs a less complex landscape for optimization. In particular, instead of having loss terms from each differential equation, this method embeds the dynamics into a loss function that quantifies the error between observed and predicted system outputs. This is accomplished by numerically integrating the predicted states from the neural network(NN) using known dynamics and transforming them to obtain a sequence of predicted outputs. Minimizing such a loss optimizes the NN to predict states consistent with observations given the physics. Further, the system's parameters can be added to the optimization targets. To demonstrate the ability of this method to perform various modeling and control tasks, we apply it to a battery model to concurrently estimate its states and parameters.