Despite decades of advances in computational science, predictive models of complex systems—from turbulence and climate to battery ageing—remain fundamentally incomplete. Physics‑based equations typically omit unresolved processes and external perturbations, while purely data‑driven models often lack interpretability and fail to generalize. Here we present a physics‑guided stochastic modelling framework that bridges these paradigms. Using Alternating Neural Integrators (ANI), we decompose the system dynamics into a deterministic component derived from domain knowledge and a stochastic residual inferred from observational data. The residual is represented by a conditional normalizing flow enhanced with sinh–arcsinh transformations, which captures non‑Gaussian features including skewness and heavy tails. We validate the framework across multiple domains, demonstrating that it recovers missing stochastic forcing and reproduces empirical trajectory statistics even when the deterministic model is deliberately simplified. As a practical application, we deploy the approach for lithium‑ion battery health prognostics using NASA's ageing dataset. Conditioned on an equivalent‑circuit model, the learned stochastic compensator captures cycle‑to‑cycle variability and model mismatch during charge–discharge operation, yielding probabilistic forecasts that align with observed voltage evolution and capacity fade. Our results establish that imperfect physics models, when systematically augmented with data‑driven stochastic structure, yield predictions that are not only more accurate but also retain physical interpretability—offering a principled route toward reliable forecasting in complex systems where first‑principle knowledge is partial but indispensable.