Deep Learning for parameter estimation in reaction-diffusion PDEs for battery modeling

One of the key development areas in battery research is finding ways to use metallic anodes, like Zn and Mg, but avoiding lithium, which is pyrophoric and sourced only in potentially critical geopolitical areas. Unfortunately, use of post-Li batteries is impaired by poorly understood shape changes, responsible for various failure modes.

Over the past decade, in the framework of the RD-PDEs, a powerful mathematical approach has been developed in [1], able to capture the essential features of unstable material growth in electrochemical systems in terms of Turing pattern formation. Recharge instability problems in batteries with metal anodes are a special case of this phenomenon. On the other hand, the difficulty of studying materials in real-life battery context leads to a methodological gap between theory and experiments. For this reason, parameter identification in the above PDE modelling is crucial for advancement in this direction.

In this research, based on [2], we propose to apply Deep-Learning as a new approach for parameter estimation, instead of the more traditional PDE constrained optimization, as for example in [3]. In the seminar we will discuss the Convolutional Neural Network devised for our goals, trained with the numerical solutions of the morphochemical PDE model that is able to capture the essential features of unstable material growth in electrochemical systems.

We will show that the CNN carries out three tasks:

1. automatic partitioning of the parameter space associated to the PDE model, according to the types of patterns generated;
2. classification of simulated and experimental patterns;
3. identification of the model parameters for experimental electrode images.

References

1. B. Bozzini, D. Lacitignola, I. Sgura. Spatio-temporal organization in alloy electrodeposition: a morphochemical mathematical model and its experimental validation. J. Solid State Electrochem (2013).
2. I. Sgura, L. Mainetti, F. Negro, M. G. Quarta, B. Bozzini. Deep-Learning based parameter identification enables rationalization of battery material evolution in complex electrochemical systems. J. of Computational Science (2023).
3. I. Sgura, A. Lawless, B. Bozzini. Parameter estimation for a morphochemical reaction-diffusion model of electrochemical pattern formation. Inverse Probl. Sci. Eng. (2019).