Estimating lithium-ion battery state of health (SOH) across operating conditions is challenging because operating profiles, measurement characteristics, and degradation trajectories differ among domains. This study proposes a physics-informed transfer learning (PITL) framework that combines a common health descriptor space, parameter function decomposition, and PINN–DeepHPM regularization. Open-circuit voltage reconstruction is used before feature extraction for dynamic profiles, whereas constant-current data are processed directly in the same descriptor space. During target-domain adaptation, selected shared-representation layers are frozen and the predictor and dynamic constraint parameters remain trainable. In the predefined Cell_1# tests, the resulting feature transfer configuration reduced RMSE relative to full fine-tuning by 23.53% for 21700_Dynamics and 61.78% for CEPREI. In leave-one-cell-out validation, PITL and full fine-tuning had comparable mean RMSEs on 21700_Dynamics, whereas full fine-tuning was more accurate on CEPREI. Freezing approximately 48% of the parameters reduced adaptation time and peak GPU memory. Thus, partial freezing can lower adaptation cost, but its accuracy benefit is target dependent.

The distribution of relaxation times (DRT) resolves electrochemical impedance spectroscopy (EIS) into mechanistically interpretable battery health features, but the deconvolution is severely ill-posed: at the sparse frequencies of rapid or onboard diagnostics, single-spectrum solutions—and the health descriptors built on them—become unstable. Here we present P³-DRT, which constrains this inverse problem with the battery population itself: a score-based prior, learned from 215,250 quality-screened DRT candidates spanning six public datasets, encodes the DRT morphologies real batteries actually exhibit, while the target spectrum's impedance likelihood anchors every posterior solution to the measurement. With only 12 and 8 frequency points, P³-DRT cuts full-spectrum reconstruction RMSE from 1.92% to 0.64% and from 3.37% to 0.70%, and band-integral descriptor errors by up to 86.6%. Posterior descriptors achieve a leave-one-battery-out state-of-health (SOH) RMSE of 4.43%—one third below single-spectrum Bayesian DRT—and transfer to unseen NCA cells without target-domain adaptation, reducing SOH RMSE by 21.5% and 20.6% at 0% and 100% SOC while delineating an SOC-dependent transfer boundary. Population-level empirical priors thus turn sparse impedance measurements into stable, mechanistically interpretable battery diagnostics.