HMSPC: A Hybrid Mechanistic-Stochastic Physical-Continuous Model for Battery Dynamics

Battery voltage dynamics are irregularly sampled, noise-corrupted, and strongly regime-dependent, properties that challenge standard sequential models. I propose HMSPC (Hybrid Mechanistic-Stochastic Physical-Continuous Model), a continuous-time latent variable model that addresses these challenges through two key components: a gated input-conditioned latent ODE that explicitly incorporates exogenous observations (current and temperature) into continuous-time state evolution, and a heteroscedastic observation model with uncertainty regularization that produces calibrated predictive variance. Built on the Latent ODE (Rubanova et al., 2019) framework, HMSPC replaces purely autonomous latent dynamics with a learned gating mechanism that adaptively controls how strongly operating conditions influence trajectory evolution at each integration step. Evaluated on the MIT-Stanford dataset (Severson et al., 2019) against Latent ODE and Vanilla Neural ODE (Chen et al., 2018) baselines across 5 seeds, HMSPC achieves a mean RMSE of 32.37 ± 1.34 mV compared to 58.33 ± 4.19 mV for Latent ODE, yielding a 45% reduction, alongside well-calibrated uncertainty estimates (ECE 0.078). Ablation studies confirm that input-conditioned drift and heteroscedastic noise each contribute meaningfully to both accuracy and calibration.