Scalable Multitask Latent Force Models with Applications to Predicting Lithium-ion Concentration

Engineering applications typically require a mathematical reduction of complex physical model to a more simplistic representation, unfortunately this simplification typically leads to a missing physics problem. In this work we introduce a state space solution to recovering the hidden physics by sharing information between different operating scenarios, referred to as ``tasks''. We introduce an approximation that ensures the resulting model scales linearly in the number of tasks, and provide theoretical guarantees that this solution will exist for sufficiently small time-steps. Finally we demonstrate how this framework may be used to improve the prediction of Lithium-ion concentration in electric batteries.