Manufacturing complexities and uncertainties have impeded the transition from material prototypes to commercial batteries, making prototype verification critical to quality assessment. A fundamental challenge involves deciphering intertwined chemical processes to characterize degradation patterns and their quantitative relationship with battery performance. Here we show that a physics-informed machine learning approach can quantify and visualize temporally resolved losses concerning thermodynamics and kinetics only using electric signals. Our method enables non-destructive degradation pattern characterization, expediting temperature-adaptable predictions of entire lifetime trajectories, rather than end-of-life points. The verification speed is 25 times faster yet maintaining 95.1% accuracy across temperatures. Such advances facilitate more sustainable management of defective prototypes before massive production, establishing a 19.76 billion USD scrap material recycling market by 2060 in China. By incorporating stepwise charge acceptance as a measure of the initial manufacturing variability of normally identical batteries, we can immediately identify long-term degradation variations. We attribute the predictive power to interpreting machine learning insights using material-agnostic featurization taxonomy for degradation pattern decoupling. Our findings offer new possibilities for dynamic system analysis, such as battery prototype degradation, demonstrating that complex pattern evolutions can be accurately predicted in a non-destructive and data-driven fashion by integrating physics-informed machine learning.

Rapidly growing product lines and services require a finer-granularity forecast that considers geographic locales. However the open question remains, how to assess the quality of a spatio-temporal forecast? In this manuscript we introduce a metric to evaluate spatio-temporal forecasts. This metric is based on an Opti- mal Transport (OT) problem. The metric we propose is a constrained OT objec- tive function using the Gini impurity function as a regularizer. We demonstrate through computer experiments both the qualitative and the quantitative charac- teristics of the Gini regularized OT problem. Moreover, we show that the Gini regularized OT problem converges to the classical OT problem, when the Gini regularized problem is considered as a function of {\lambda}, the regularization parame-ter. The convergence to the classical OT solution is faster than the state-of-the-art Entropic-regularized OT[Cuturi, 2013] and results in a numerically more stable algorithm.