Neural posterior estimation for scalable and accurate inverse parameter inference in Li-ion batteries

arXiv cs.LG / 4/6/2026

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Key Points

The paper addresses scalable, accurate inverse parameter inference for Li-ion battery state diagnostics by replacing computationally intensive Bayesian calibration with neural posterior estimation (NPE).
NPE amortizes the cost into offline data generation and model training, reducing per-inference time from minutes to milliseconds and enabling near real-time use.
The authors report that NPE achieves parameter calibration accuracy comparable to or better than Bayesian calibration across 6–27 estimated parameters, while noting a potential downside of higher voltage prediction errors.
The method also provides interpretability benefits, including local parameter sensitivity across specific voltage-curve regions.
The approach is validated on an experimental fast-charge dataset with parameter estimates checked against measurements such as loss of lithium inventory and loss of active material, and the implementation is released via a companion GitHub repository.

Abstract

Diagnosing the internal state of Li-ion batteries is critical for battery research, operation of real-world systems, and prognostic evaluation of remaining lifetime. By using physics-based models to perform probabilistic parameter estimation via Bayesian calibration, diagnostics can account for the uncertainty due to model fitness, data noise, and the observability of any given parameter. However, Bayesian calibration in Li-ion batteries using electrochemical data is computationally intensive even when using a fast surrogate in place of physics-based models, requiring many thousands of model evaluations. A fully amortized alternative is neural posterior estimation (NPE). NPE shifts the computational burden from the parameter estimation step to data generation and model training, reducing the parameter estimation time from minutes to milliseconds, enabling real-time applications. The present work shows that NPE calibrates parameters equally or more accurately than Bayesian calibration, and we demonstrate that the higher computational costs for data generation are tractable even in high-dimensional cases (ranging from 6 to 27 estimated parameters), but the NPE method can lead to higher voltage prediction errors. The NPE method also offers several interpretability advantages over Bayesian calibration, such as local parameter sensitivity to specific regions of the voltage curve. The NPE method is demonstrated using an experimental fast charge dataset, with parameter estimates validated against measurements of loss of lithium inventory and loss of active material. The implementation is made available in a companion repository (https://github.com/NatLabRockies/BatFIT).