[1] Huang, Y., Zou, C. Li, Y., & Wik, T. (2024). MINN: Learning the dynamics of differential-algebraic equations and application to battery modeling. IEEE Transactions on Pattern Analysis and Machine Intelligence, 46(12), 11331-11344 [PDF].

Received the Best Presentation Award of the 2022 International Conference on Energy and AI. A Python tutorial about PINN and MINN is given at [Link].

MINN stands out through its remarkable accuracy and acceleration, surpassing state-of-the-art benchmarks across the full spectrum of system modeling. In comparison with physics-based simulations, MINN achieved two orders of magnitude speedup while maintaining comparable accuracy. Unlike purely data-driven models, MINN is data-efficient to train and generalizable to unseen operational conditions. Its incorporation of physical parameters and interpretable hidden states, by design, facilitates the learning of system dynamics rather than being limited to input-output relationships. In contrast to the existing practices of physics-based machine learning, MINN offers distinct advantages. Specifically, it can be trained without the need for internal state data, addressing the limitations of current sensing technologies in real-world battery applications. Furthermore, MINN’s unique capability to model general non-autonomous PDAE systems under any control input empowers the implementation of advanced and real-time control strategies for internal states.

[2] Huang, Y., Zhu, Q., Wik, T., Finegan, D., Li, Y., & Zou, C. (2026). BMINN: Learning chemical potentials andparameters from voltage data for multi-phase battery modeling. chemrxiv preprint, DOI: 10.26434/chemrxiv-2025-qrkpq.

Learning hidden physics and unknown parameters in non-autonomous PDE- and PDAE-based systems remains a fundamental challenge, particularly in the presence of parameter uncertainty and measurement noise. In this study, we introduced a physics-based learning framework, BMINN, to systematically bridge this gap. By embedding physics-based formulations within Bayesian neural networks, BMINN learns unmodeled components together with their associated uncertainties, providing robust interpretability and predictive accuracy. Unlike purely data-driven approaches that map inputs to outputs, BMINN incorporates physically meaningful states and parameters by design, enabling the recovery of latent thermodynamics and dynamical rules. 

Applied to lithium–graphite electrodes, BMINN reconstructs electrode-specific Gibbs free energies and chemical potentials directly from routine cycling data. The learned thermodynamics capture staging structures, transient liquid-like phases, and free-energy barriers, reproducing population dynamics and yielding \textit{operando} XRD–comparable signatures of phase transitions. This capability provides a thermodynamically consistent description of metastable states and hysteresis, offering new insights into the microscopic origins of fast-charging limits and plating onset. Compared to OCP-fitted and PET-based models, the BMINN framework recovers a more accurate representation of internal states, with direct relevance to lifetime prognostics, aging-aware impedance modeling, and health-conscious control. 

Beyond batteries, the framework exemplifies a general strategy for embedding physical models into Bayesian inference to recover hidden physics from input–output data. In this sense, BMINN establishes a pathway to uncover free-energy landscapes and governing functions in diverse systems where direct experimental access is limited, from catalytic surfaces and ferroic materials to other multiphase condensed-matter systems.