Parametrized physics-informed deep operator networks for Design of Experiments applied to Lithium-Ion-Battery cells

Model-based state estimation of lithium-ion batteries relies on a robust, yet efficient parametrization of the underlying model under different conditions, which can be analyzed and improved through the lenses of Design-of-Experiments (DoE) methodologies. This paper presents parametrized physics-informed deep operator networks (PI-DeepONets) trained without any measured or synthetic data to predict solutions of a Single-Particle-Model for varying current profiles and electrode-specific diffusivity values. The prediction accuracy is evaluated based on three use cases representing three sets of current profiles featuring constant, smoothly time-dependent and non-smooth pulse profiles. After training PI-DeepONets, lithium concentration profiles are predicted within milliseconds achieving normalized percentage errors on the particle surfaces below 0.3% for constant or smoothly time-dependent current profiles and below 2% for non-smooth pulse profiles. The fast approximation of Fisher-Information-Matrices (FIMs) based on the trained PI-DeepONets offers additional speed-up potentials for DoE methodologies and yields a speed-up factor of 30 in the considered use case when compared to classical FIM approximation via finite differences on numerical reference solutions.