Non-destructive degradation pattern decoupling for early battery trajectory prediction via physics-informed learning

Abstract

Manufacturing complexities and uncertainties have impeded the transition from material prototypes to commercial batteries, making their verification a critical quality assessment link. A fundamental challenge is to decouple electrochemical interactions for establishing a quantitative mapping from electrochemical parameters to macro battery performance. Here, we show that the proposed physics-informed learning model can quantify and visualize temporally resolved thermodynamic and kinetic parameters from field accessible electric signals, facilitating a non-destructive degradation pattern decoupling. The lifetime trajectory prediction is 25 times faster than the traditional capacity calibration test while retaining a 95.1% average accuracy across temperatures, underpinned by projected electrochemical data from early cycle observations which have not yet been established. We rationalize this predictability to the interpretation of statistical insights from material-agnostic featurization, excited by a multistep charging scheme with different current intensities and their switching conditions. The waste management of defective prototypes is enabled by statistically and non-destructively interpreting internal electrochemical states, demonstrating a 19.76 billion USD defective material recycling market by 2060. This paper highlights the potential of revisiting electrochemical degradation behaviors using physics-informed learning and dynamic current excitations, facilitating next-generation battery manufacturing, reuse, and recycling sustainability.

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Broader context

Battery research and development (R&D) faces fierce competition in selecting future energy storage technologies but generating endless defective battery prototypes. Performance mismatches between theoretical designs and as-manufactured batteries remain a bottleneck due to time-consuming, costly, and often destructive verification. Although machine learning has been well-documented in battery R&D, it fails to decouple electrochemical degradation patterns that support interpretable decisions. Here, distinct from purely statistical modeling, we compute thermodynamic and kinetic degradation parameters from initial manufacturing differences among normally identical batteries and project them into future states which have not yet been established, saving data acquisition costs otherwise required for model inference. This physics-informed model shows promise in merging electrochemical priors into statistical learning, demonstrating sustainable and economic superiorities by managing defective prototype batteries before massive production.

The transition towards future renewable energy systems emphasizes the advanced role of battery energy storage, with demand expected to exceed 200 terawatts by 2050 for both lithium-based and alternative chemistries.^1–3 The lack of rapid and uniform prototype verification hinders the transition from battery prototypes to commercial products, leading to high scrap rates and extra environmental costs.^4–6 Battery prototype verification is critical to accelerate the discovery and commercialization of next-generation batteries, yet current verification timelines, stretching from months to years, have imposed significant time and financial burdens.^7,8

In battery manufacturing, capacity calibration is a standardized way to verify the prototype quality.⁹ This conventional method needs extensive durability testing time on selected samples to statistically validate quality in batches.^10,11 Although accelerated tests are conducted under harsh conditions, such as higher current densities and temperatures, they still necessitate extensive cycles per sample until end-of-life (EOL), such as 80% of the nominal capacity. However, translating outcomes from accelerated tests to standard conditions poses challenges for novel battery research and development (R&D) due to the uneven quality benchmarking conditions.⁴ The challenges are amplified by initial manufacturing variabilities (IMVs), resulting from material preparation, assembly, and coupled degradation patterns, such as voltage fade and electrochemical dynamics.^12–16 The degradation patterns, including kinetics and thermodynamics, manifest as impedance increase, loss of lithium-ion inventory (LLI), and loss of active material (LAM), and are traditionally analyzed by destructive post-mortem methods, contradicting practical needs of timely quality feedback. Efforts to mitigate these degradations prioritize automated production lines in reducing human error and improving stringent control of micro properties.^17–19 Unfortunately, the destructive characterizations and control of micro parameters are still unaffordable in massive battery production practices.

Emerging technologies such as smart manufacturing and digital twins enable monitoring of battery production, yet integrating recent advances like novel sensors for internal detection faces challenges in production line integration and long-term use.^20–27 Manufacturers find the available signals, such as current, voltage, and capacity, integrated with machine learning, promising for predicting battery lifetime trajectories and internal states under diverse conditions.^28–35 However, these models struggle to predict intermediate degradations, with lifetime trajectory prediction posing a greater challenge due to the need for more sensory data that has not yet been established at the time of prediction.^36–38 Despite the extrapolation abilities, the statistical model still relies on the availability of long-term observational data, where necessary data collecting time conflicts with the goals of reducing verification time and costs.³⁹ Though mitigating data requirements, empirical models extrapolate lifetime trajectories with significant requirements for parameter tunings under changing operation conditions. Stable and interpretable insights into degradation patterns are critical to projecting the current chemical process data into future states by using physical laws, as they can mitigate the need for extra data curation experiments. However, the coupled degradation patterns make the electrochemical modeling of underlying physics even more challenging. The integration of physical knowledge into the statistical models shows great promise in balancing experimental data acquisition and experiment-free electrochemical modeling, particularly relevant to advising rational reuse, recycling, and remanufacturing of defective products to improve their lifecycle sustainability,^40,41 but remains significantly underexplored.

In this study, we introduce a lifetime trajectory prediction method using early cycle data (50 cycles, 4% of total lifetime) from both newly manufactured and accelerated aging batteries to supervise a statistical model, shown in Fig. 1a. The proposed method predicts entire battery lifetime trajectories, rather than EOL points, by computing thermodynamic and kinetic parameters and projecting them to future states that have not yet been established for model inference. Without directly measuring the internal states, we use projected chemical processes to bypass the need for post-failure observational data requirements, otherwise obtained from lengthy and costly capacity calibration tests. Fig. 1b shows IMVs through stepwise charge acceptance, helping to adjust chemical process projections considering cell-to-cell variability. The proposed statistical model forecasts chemical processes across temperatures from early data, further used as an input to the lifetime trajectory prediction model. The proposed method prioritizes studying degradations, including thermodynamic and kinetic losses and polarizations, excited from a multi-step charging profile with different current intensities and switching conditions. Fig. 1c details the method application for battery R&D, enabling timely and accurate quality assessment and waste management of defective prototypes, minimizing economic and environmental losses. This paper highlights the model interpretability, non-destructive lifetime trajectory prediction, and sustainable potential in emerging applications for next-generation prototype quality assessment and waste management before massive battery production.

Fig. 1 Model motivation, model construction, and model deployment. (a) The verification of as-manufactured batteries using early data, and existing guiding samples from accelerated aging tests. (b) The early prediction model uses subtle initial manufacturing variabilities (IMVs) as a condition of battery aging, identified from a multi-step charging before cycling. Multi-dimensional chemical processes influenced by degradation mechanisms, including thermodynamic loss (ΔE) and kinetic loss (η) can be evolved from IMVs by characterizing stepwise charge acceptance. Physics-informed transferability metrics enable temperature adaptation, where E_a is the activation energy, k_B is the Boltzmann constant, T_s is the source domain temperature and T_t is the target domain temperature. The predicted state s_t+1 at time t + 1 is continuously updated by previous state s_t at time t. (c) Routine (pyrometallurgy, hydrometallurgy, and direct recycling) selection, advised by machine learning insights, saves verification time, cost, and greenhouse gas (GHG) emissions.

Results

Data generation

Prototype ternary nickel manganese cobalt lithium-ion batteries (LiNi_0.8Co_0.1Mn_0.1O₂, with 1.1 A h nominal capacity and 13 wt% silicon oxide at graphite anode) were cycled under controlled temperature conditions (25, 35, 45, 55 °C) and multi-step charging (0.33C to 3C, where 1C is 1.1 A) with 1C constant discharge beyond EOL thresholds (specifically, from 73% to 59% of nominal capacities, see Fig. S1, ESI†). IMVs were gauged using switching voltage values to reflect charge acceptance before long-term cycling (see Table S1, ESI†). We generate a unique battery prototype verification dataset spanning lifetimes of 480 to 1025 cycles (average lifetime of 775 with a standard deviation of 175 under EOL80 definition, see Fig. S2, ESI†). The reference performance tests (RPTs) calibrated C rates, with SOH updates feasible in in-vehicle systems (see Fig. S3, ESI†). Data access details are provided in the Data availability section.

Fig. 2a depicts battery capacity declines over cycles, with high temperatures reducing lifespan. Despite identical cycling and manufacturing conditions, variations in degradation trajectories are evident. Fig. 2b demonstrates the key distinction from constant current verification, using a multi-step charge profile relevant to EV fast charging. This protocol charges 75% of the total SOC within 20 minutes, across a range of 0.33C to 3C with 9 consecutive steps. Fig. 2c details SOC allocations per step, with cut-off voltages (U1 to U9) representing charge acceptance at each SOC. Fig. 2d shows these voltages against temperature, indicating a typical voltage decrease as the temperature rises, further battery-averaged in Fig. 2e. Minor voltage variations at a constant temperature signify different charge acceptance in ostensibly identical batteries. IMVs, represented by these voltage variances, are graphed in Fig. 2f as temperature functions, displaying bowl-shaped curves across all steps barring U1. The minor deviations of U1 at 25 °C are noise-sensitive with an mV level signal. IMVs decrease then increase around 45 °C, suggesting temperature-induced reaction accelerations. The bowl-shaped lifetime variations (Fig. S4 and S5, ESI†) establish an immediate correlation between IMVs and macro lifetime, with lifespans (EOL73) of 1218, 1180, 958, and 661 cycles at 25, 35, 45, and 55 °C, respectively, as displayed in Fig. 2g. These trends are consistent across temperatures, affirming that initial IMV probing deterministically affects macro capacity. At 55 °C, unstable correlations (Fig. S5, ESI†) might stem from side reactions surpassing normal reaction rates during extended cycling, a diminishing relationship illustrated in Fig. S6 (ESI†). Thus, challenges persist with long-term degradation characterization due to temporal- and thermal varying conditions. The batch quality is affirmed by the Arrhenius plot depicted in Fig. 2h, where a consistent line across 25 to 55 °C indicates no significant degradation mechanism alteration under fast charging, thus the verification inflicts no damages to battery prototypes.⁴² Leveraging Arrhenius principles allows early verification by comparing AT (Arrhenius transferability) metric between baseline (accelerated aging data) and novel battery early cycle data, as shown in Fig. 2i.

Fig. 2 Data generation and analysis. (a) Aging trajectories under 4 verification scenarios, i.e., 25, 35, 45 and 55 °C. (b) Illustration of the multi-step charging profile. The cut-off voltage values, i.e., from U1 to U9. (c) Stepwise state of charge (SOC) increments and their accumulation. (d) Visualization of cut-off voltage. (e) Temperature-wise trends of cut-off voltage values each charging step averaged over all batteries. (f) The deviation of cut-off voltage values at each temperature, defined as initial manufacturing variabilities (IMVs), for each charging step. IMVs are calculated over batteries at a given temperature. (g) Battery lifetime distribution under EOL73, with lifetime deviations indicated. EOL73 is defined as 73% of the nominal capacity. (h) Arrhenius plot of 4 temperature verification scenarios. (i) Arrhenius transferability (AT) score quantifies dissimilarities between accessible data and early data of batteries to be verified. r_s is the source domain aging rate, r_t is the target domain aging rate, E_a is the activation energy, k_B is the Boltzmann constant, T_s is the source domain temperature and T_t is the target domain temperature.

Physics-informed learning

We design the feature extraction from charging curves, taking two key aspects into account. Firstly, the controllability of charging over discharging in practical use ensures easier signal acquisition. Secondly, our multi-step charging protocol unveils varied internal state dynamics by cycling through different current rates and conditions, as displayed in Fig. 3a, which shows the charging behavior across SOC levels and temperatures (see Fig. S7–S10 for trends, ESI†). Features are derived from material-agnostic electrochemical principles, correlating electrical signals with underlying electrochemical states, traditionally requiring invasive methods to ascertain. Fig. 3b differentiates actual from theoretical battery voltage, partitioning voltage discrepancies into thermodynamic and kinetic losses—the former reflects intrinsic degradation such as LLI and LAM when idle, while the latter becomes pronounced with a high current load. We distinguish kinetics and thermodynamics by varying the current density, specifically, thermodynamics at lower currents, and kinetics at higher. The difference between actual electrode voltage U_actual and the theoretical voltage U_theoretical (when zero current is applied, reflective of intrinsic material properties), can be divided into two components, e.g., thermodynamic loss ΔE (reflective of the shift in intrinsic material properties), and kinetic loss η (current-induced polarization). Fig. 3c shows that the feature taxonomy captures variabilities and chemical processes before and during cycling, demonstrating disparities between actual and theoretical voltages. Extracted features are further categorized into prior- and in-cycling (intra-step and inter-step), where intra-step features are lumped representations of thermodynamic and kinetic loss, while inter-step features are purely linked to kinetic loss by current density switching. Specifically, intra-step features represent differences between U_actual and U_theoretical, with current density deciding thermodynamic or kinetic dominance; inter-step features depict the η, including concentration, activation, and ohmic resistances behaviors. The feature taxonomy aims to decouple total capacity loss into its kinetic and thermodynamic components. For insights on the fundamentals of degradation pattern differentiation and a featurization taxonomy explanation, refer to Supplementary Notes 1–3 (ESI†).

Fig. 3 Featurization taxonomy. (a) Charging dynamics in different verification scenarios, i.e., 25, 35, 45, 55 °C. (b) The fundamental electrochemical principle for featurization taxonomy. (c) Featurization taxonomy, including initial manufacturing variabilities (IMVs) and multi-dimensional chemical processes. (d) Visualization of features and battery-wise variations in the lifetime direction. The color maps normalized feature values, and the size of bubbles maps the deviations across battery instances.

Fig. 3d illustrates extracted features of the chemical process over the first 800 cycles, with the ohmic resistance revealing an increase in ohmic resistance, i.e., a decline in kinetic capacity, across most switching stages, indicative of kinetic deviations in identical batteries and the magnification of IMVs during cycling (Fig. S11–S14, ESI†). Similarly, the lumped resistance, integrating aspects of ohmic, electrochemical, and concentration resistance, shows reduced dynamic capacity and larger deviations over time (Fig. S15–S18, ESI†). Charge acceptance decreases, as evidenced by growing voltage gradient (i.e., polarization rate) for a given stepwise cut-off voltage, suggesting that even slight initial IMVs have a compounding impact on long-term performance, as further indicated by trends in Fig. S19–S22 (ESI†).

Given the impact of IMVs on chemical process variations, battery prototype verification must account for these influences to ensure accuracy. We utilize early-cycle IMVs as benchmarks for tracking chemical process evolution. Our machine learning model, informed by physics, uses these predicted chemical processes as proxies for the actual internal states, operating on the premise that the battery lifetime trajectory can be deduced from these internal insights. Our approach involves a three-stage machine learning pipeline (see Methods and Fig. S23, ESI†). First, we model multi-dimensional chemical processes using early cycle and guiding sample data; second, we adapt these predictions to specific temperatures; and third, we use adapted chemical processes to avoid the need for physical measures in later cycles. The extent of early data used is tailored to meet the desired accuracy, assessed by mean absolute percentage error for consistent cross-stage comparisons.

Performance of battery lifetime trajectory prediction models

To demonstrate the robustness of the proposed method under unseen conditions, we introduce two models for early verification tailored to manufacturer needs under multi- and uni-source domain adaptation, utilizing data at varied temperatures. The full feature set is input into these models, with specifics in Supplementary Notes 2 and 3 (ESI†). The multi-source model utilizes guiding samples from two temperatures (25 and 55 °C), simulating scenarios where mid-range temperature performance should be verified. This model forecasts chemical processes that have not yet been established at the prediction moment, eliminating the need for physical measurements of these states (see Tables S2 and S3, ESI†). Utilizing merely 20% of the lifetime data under EOL75 criteria. Using predicted chemical processes, we attain a mean absolute percentage error under 1% and a standard error deviation under 0.01. Notably, this precision is for predicting the full lifetime trajectory, not EOL points, effective for rigorous verification purposes. Fig. 4a and b present parity plots and error distributions for the target domain at 35 °C and 45 °C, showing mean absolute percentage errors (standard deviation) of 1.4% (0.014) and 0.6% (0.006), respectively. Notably, overestimations occur as batteries near EOL, underscoring the verification challenge across the entire lifetime with early data and emphasizing the verification complexity. We compare the model against state-of-the-art methods across different lifetime phases (early, middle, and late, each representing 10% of the total lifetime) in the test set. Fig. 4c contrasts the model performance with a long-short-term memory (LSTM) network (model 1), a model excluding IMVs (model 2), a model without physics-informed learning (model 3, lacking Arrhenius-based transfer), and a model using empirical formula-based model (model 4), detailed in Supplementary Note 4 (ESI†).

Fig. 4 The prototype verification results. Parity plot of lifetime prediction under (a) 35 and (b) 45 °C verification scenarios (intermediate temperature verification), with battery-wise prediction deviation presented. All numerical results achieved in this plot are under the early verification setting that uses 20% of early data from batteries to be verified, otherwise specified. Experimental settings for (a)–(e) are multi-source domain adaptation, i.e., data at 25 and 55 °C is accessible. (c) Model performance comparison between this work and long-short-term memory (LSTM) neural network, model without considering initial manufacturing variabilities (IMVs), model without physics-informed machine learning, and empirical formula. (d) Model sensitivity under different end-of-life capacities. Model prediction error against (e) early data access and (f) parallel guiding sample requirements of target verification scenarios. Accessible data at 55 °C is assumed, which is used to predict the lifetime of 25, 35, and 45 °C verification scenarios. (g) Feature importance of capacity features (Q) in different charging stages. (h) Feature importance of non-capacity features by charging stages, listed in a stepwise order.

In early cycles (first 10%), our method and model 2 both achieve a MAPE of 0.24%, while model 1 has a slightly higher error at 0.38%. Models 3 and 4, however, struggle with significant errors of 3.48% and 2.82%, respectively, highlighting difficulties with early temperature-induced lifetime deviations (see Fig. S24, ESI†). Notably, model 2 worsens in the last 10% of cycles, with MAPE of 5.82%, underscoring the importance of temperature consideration, which model 2 lacks. Despite initial similarities, IMVs become crucial in later stages, with model 2 showing a late-cycle MAPE of 5.62%. Our model remains robust and precise across all stages, peaking at a MAPE of 1.53% in the last 10% of cycles, demonstrating the efficacy of incorporating IMVs and physics knowledge to address temperature-induced long-term variations. Moreover, the error distribution of the proposed method is significantly lower than the benchmark models, strengthening its practical relevance, especially in quality assurance contexts where prediction performances in extreme cases matter most.

Our analysis extends to sensitivities across varying EOL capacity values for customized verification scenarios, focusing on the degradation path before reaching a specific capacity. Fig. 4d indicates that benchmark models perform worse as the target capacity decreases, underscoring the difficulty of projecting future degradation with initial data alone. Yet, our model consistently surpasses others, with a maximum deviation of 33 cycles, despite predictions being supervised thousands of cycles in advance. To enhance verification speed and computational efficiency, we explore the reduced data availability, showing in Fig. 4e that errors remain below 2% MAPE at both 35 and 45 °C with just 4.2% of lifetime data (50 cycles). The challenge of data scarcity, particularly with a limited number of parallel samples due to constraints in cost or time, was also assessed. A specific test using only high-temperature (55 °C) samples for accelerated verification demonstrates the impact of data paucity: a single sample results in high errors, but increasing to five samples significantly improves verification accuracy across various temperatures (Fig. 4f). In an ultra-early verification setting, prioritizing time over accuracy and utilizing the first 50 cycles, our model achieves average MAPEs of 4.9% across 25, 35, and 45 °C, outperforming benchmarks under similar data limitations (Table S4, ESI†). These findings affirm the viability of the proposed method in real-world verification contexts, offering adaptability in multi- and uni-source domain applications, and providing valuable insights for target domain evaluation with constrained data resources.^28,36

We distinguish between kinetics and thermodynamics based on current stage densities, positing that machine learning-derived insights on thermodynamic loss enhance predictive accuracy at a single temperature while kinetic insights facilitate temperature adaptability. Group-wise analyses in Fig. 4g and h reveal a notable rise in the importance of capacity features in low-current areas versus their reduced significance at high currents, correlating with the observation that thermodynamic losses, not kinetic, predominantly affect degradation with a 79% share. Regarding other features, we note that the temperature impact on verification becomes negligible, indicating that physics-informed machine learning neutralizes temperature influence on predictive performance. Among these features, lumped resistance (RL), ohmic resistance (RO), and polarization speed (Vg) are prioritized for their contribution to verification accuracy. The contribution of Vg, influenced by SOC region sensitivities, is minimized due to its indirect relation to polarization resistance. RL and RO are more significant, incorporating concentration and ohmic polarization components. However, the challenges of prototype verification are dualistic since a satisfactory explanation of dominating loss types does not guarantee a good verification, rather, it also depends on temperature adaptability associated with kinetic behaviors, see Table S5 (ESI†). This is attributable to temperature primarily influencing kinetics, underlined by the Arrhenius law. Our model, predicated on this principle, reveals the expected diminished adaptability of thermodynamic responses to temperature changes. Thus, achieving a balanced verification requires weighing thermodynamic explanation capability against kinetic adaptability, as explored in Supplementary Note 5 and Table S6 (ESI†).

Rationalization of statistical model performance

Fig. 5a delineates the degradation patterns into three principal phases: initial SEI layer formation, the subsequent thickening, and lithium plating, aligning with the finite element analysis (FEA).^43,44 Despite the streamlined degradation model, fully separating the degradation throughout a battery lifetime remains complex due to the dynamic interactions among degradation mechanisms, see Fig. S25 (ESI†). The challenge of distinctly identifying these mechanisms persists, even with advanced diagnostics (Fig. S26–S29, ESI†), which struggle to non-destructively elucidate internal aging states and their interdependencies, limiting practical utility (Supplementary Note 6, ESI†).

Fig. 5 Decoupling battery degradation loss and polarization types. (a) Schematic illustration of battery performance degradation in different lifetime stages. (b) Battery degradation modes and their loss type, i.e., thermodynamics and kinetics. (c) Li-ion concentration visualization inside the battery, i.e., from the anode (Ano.), separator (Sep.) to the cathode (Cat.) under multi-step charging. (d) Overpotential evolution in a lifetime direction from the initial cycle to the 1000th cycle under multi-step charging. (e) Degradation dominance evolution at 25, 35, 45, and 55 °C, respectively, which is calculated by the cycle-wise SAGE importance of features describing relevant microscopic degradation behaviors. (f) Temporally resolved correlation between the thermodynamic loss and concentration polarization. (g) Incremental capacity analysis of discharging curves. (h) Normalized capacity loss types, i.e., thermodynamic and kinetic types, for the unit state of charge (SOC) at 25, 35, 45, and 55 °C, respectively. Proportion comparison of thermodynamic (85%) and kinetic (15%) loss types, averaged over all temperatures. The machine learning insight, i.e., the contribution of thermodynamic loss (79%) is indicated. (i) Normalized polarization types, i.e., concentration and other (ohmic and electrochemical) polarization, at 25, 35, 45, and 55 °C, respectively. The proportion of concentration (82%) and other (18%) polarization averaged over all temperatures. The machine learning insight, i.e., the contribution of concentration polarization (74%) is indicated.

Contrary to bottom-up approaches that trace macro performance back to specific mechanisms, the proposed method employs a data-driven strategy to decouple loss types by correlating observable electrical signals with underlying thermodynamic and kinetic degradation processes, as illustrated in Fig. 5b. We utilize FEA to elucidate complex physical processes that occur internally during degradation by reproducing and visualizing the multi-step charging in Fig. S30–S32 (ESI†). Simulated degradation incorporating modeling of SEI thickening in Fig. 5a can be found in Supplementary Note 7 (ESI†). SEI thickening corresponds to LLI (thermodynamic loss) and contributes to increased impedance (kinetic loss), see Fig. S33 (ESI†). In Fig. S34a (ESI†), the dV/dQ response curve to equilibrium potential is pronounced at the onset of charging, as the battery must surmount energy barriers. While near the end of charging, the vacancies of materials are fully occupied by Li-ions, additional barriers are faced that account for a steeper dV/dQ curve gradient, making the initial and end of SOC represent thermodynamic characteristics.⁴⁵ Moreover, switching between high and low current regions divides the process into thermodynamics and kinetics, see Fig. S34a and b (ESI†).

Fig. 5c illustrates that lithium-ion concentration varies across different charging steps, highlighting disparities between the initial and the 1000th cycles. In kinetic stages, lithium-ion concentrations exhibit a noticeable unevenness, while in thermodynamic stages, negligible concentration variation can be observed. Concentration polarization is increasingly pronounced at the 1000th cycle, and differences between charging stages are more evident, which evidences our featurization taxonomy by deliberately including dynamic information in current switching stages. Fig. 5d delves into total polarization changes across SOC regions, revealing significant increases during kinetic stages due to abrupt high current density shifts that challenge lithium transport and charge transfer capabilities, resulting in uneven lithium-ion distribution and internal particle lithiation (Fig. S30–S32, ESI†). Conversely, low current density stages exhibit less polarization, reflecting that thermodynamics is more significant than kinetics.

In Fig. 5e, we discern the interplay between concentration polarization and thermodynamic loss over a lifetime, observing an initial oscillation due to activation in early cycles that stabilizes into a clear dominance of thermodynamic loss and concentration polarization in the post-activation stage. Fig. 5f explores the correlation between these two degradation patterns across four temperatures, revealing consistent patterns that initial degradation shows a pronounced dip (marked by circle symbols), which becomes more profound and delayed at lower temperatures. This pattern aligns with activation processes including SEI layer formation and electrode structural change, impacting the primary degradation correlation. At lower temperatures, a temporary capacity restoration occurs (Fig. S24, ESI†), leading to a weaker correlation between concentration polarization and thermodynamic loss. At higher temperatures, quicker activation leads to a less dip, transitioning into a phase of predictable aging marked by SEI growth, increased LLI, and thus increased impedance.

As batteries progress to the later stages of their lifetime, another critical point (marked by square symbols) signifies a shift towards irreversible degradation, characterized by significant LAM and the accelerated degradation processes, as shown in Fig. 5a. This phase sees a mixture of degradation mechanisms, leading to a notable decline in the correlation between concentration polarization and thermodynamic loss, with this shift manifesting earlier at higher temperatures. Analyzing quantified SAGE across early, middle, and late phases (Fig. S35–S38, ESI†) reveals distinct aging behaviors at different lifecycle stages. Initially, capacity features fluctuate slightly, but as the battery ages and internal conditions worsen, changes in capacity and resistance features become evident. We note that such degradation patterns, elucidated through machine learning, correlate precisely with statistical predictions. Further, incremental capacity analysis of discharge curves (Fig. 5g and Fig. S39, ESI†) confirms the existence of severe LLI and LAM, evidenced by reduced peak intensity in low SOC areas (indicating LAM at the anode) and peak shifts (signifying LLI).⁴⁶

This analysis underscores the intensification of battery degradation in later lifetime stages, notably with severe LAM under the high-temperature accelerated aging test. Benchmarking degradation patterns (Supplementary Note 8, ESI†) reveal distinct behaviors for thermodynamic and kinetic losses. Thermodynamic loss, averaging 85% of total degradation across temperatures, closely matches our 79% estimation for thermodynamic loss from machine learning interpretation (Fig. 5h). Polarization types, divided into concentration polarization and others, constitute an average of 82% of total polarization, corroborating with our 74% estimation from machine learning interpretation (Fig. 5i). Fig. S40 (ESI†) illustrates thermodynamic and kinetic loss contributions during discharge, where kinetic decay, indicated by impedance rise, can be mitigated by lowering current density. In contrast, thermodynamic loss represents irreversible LAM, persisting at a low current density.

An emerging application for scrap material recycling from defective battery prototypes

The critical points in Fig. 5f, marked by square symbols, have practical implications, highlighting a transition from sublinear aging to accelerated aging. Such distinction aids in the development of nuanced recycling strategies for defective battery prototypes, suggesting pre-critical point lithium replenishment and post-critical point electrode repair as recycling approaches.⁴⁷

Fig. 6 presents an assessment of refined direct recycling and other conventional (direct, hydro-, and pyro-) recycling, concerning the economic viability and environmental impact, see Supplementary Note 9 (ESI†). Refined direct recycling refers to a non-destructive diagnosis of the defective prototypes in the early stages, where lithium supplement is applied before structural defects occur. Fig. 6a shows that the refined direct recycling yields profit across all SOH levels, which can be rationalized by the saved time and cost of materials after the disassembly. Other methods, especially hydrometallurgy recycling, only become profitable with higher SOH. While the advantage of refined direct recycling in Fig. 6b marginally decreases with increasing SOH compared with other recycling methods due to the increased price of recycling products using conventional methods, the superiority of refined direct recycling is stable thanks to the simplified process and affordable lithium supplement price. Here we turn to amplifying the implication of refined direct recycling by incorporating the transport impact model (TIM), considering the interaction between production, the elasticity of vehicle sales, the penetration rate of EVs, and technological advancements, see Supplementary Note 10 (ESI†).

Fig. 6 A technology-economic analysis of the scrap material recycling from defective prototypes using refined direct (ours), direct, hydrometallurgy (hydro-), and pyrometallurgy (pyro-) recycling methods, respectively. See Supplementary Note 9 (ESI†) for the methodology of the technology-economic analysis. (a) The unit profit and (b) incremental unit profit (refined direct recycling compared with baselines) comparison of different recycling methods, for both nickel manganese cobalt (NMC811) and lithium iron phosphate (LFP) batteries, considering SOH. (c) The total production, scrap rate, and scrap scale of new batteries (including NMC and LFP) from 2020 to 2060, derived from the transport impact model (TIM),^48–50 see Supplementary Note 10 (ESI†) for the settings. (d) Annual and accumulated profit from recycling slightly degraded (95% SOH) batteries, calculated based on the production estimation of both NMC and LFP in (c). (e) Unit profit composition against SOH for LFP battery prototypes. (f) Unit environmental and energy impact of recycling slightly degraded NMC (95% SOH) prototype batteries, including volatile organic compounds (VOC), carbon monoxide (CO), nitrogen oxides (NOx), PM₁₀, PM_2.5, sulfur dioxide (SO_x), black carbon (BC), organic carbon (OC), methane (CH₄), nitrous oxide (N₂O), and greenhouse gases (CO₂).

Fig. 6c forecasts battery production scale, scrap rate, and scrap scale over time from 2020 to 2060, showing a surge in scarp battery peaking circa 2035, reaching 230 million kg followed by a decline as advancements in production technology dampen the scrap rate to 0.38% by 2060. In this context, Fig. 6d shows the total projected profit over time by recycling defective prototype LFP and NMC battery at 95% SOH, aligning with the zenith of scrap amount depicted in Fig. 6c. The incremental profit, consequently, anticipates a surge before 2035 and a slowed incremental speed, thereafter, demonstrating an up to 19.76 billion USD scrap recycling market by 2060. We emphasize such a market can be notably larger due to the material diversities in next-generation prototype batteries and the stubbornly higher scrap rate than our estimation in the R&D stage. Fig. 6e depicts the unit profit composition at different SOH for LFP prototype batteries, demonstrating consistently higher revenues (15.64$ per kg) and lower costs (2.37–2.63$ per kg) stemming from its procedural efficiency by inflicting no structure repair requirements, or extra treatment reagents. In Fig. 6f, concerning the environmental and energy impact, the refined direct recycling for NMC prototype batteries exhibits superior performance in all environmental pollutants and energy use.

Discussions

The proposed model predicts entire battery lifetime trajectories across various temperatures with a modest 4.9% error using just 4% of total lifetime data (50 cycles). By deliberately inferring multi-dimensional chemical processes that have not yet been established at prediction moment, the proposed model achieves a 25 times faster verification speed than traditional capacity calibration methods. The model leverages IMVs and machine-learned insights into degradation patterns (thermodynamic and kinetic parameters) for an accurate, physics-based understanding of battery internal chemical processes evolution. This efficiency not only cuts prototype verification costs but also reduces the carbon footprint. It offers a novel, non-destructive solution for proactive production scaling, production scraps recycling, and accessible degradation status diagnostics, by overcoming mechanism-centric and post-mortem methodological challenges.

We prospect that our findings are material-agnostic, thus being widely applicable for promoting battery lifecycle sustainability in prototype manufacturing, electric vehicles, reuse, and recycling with minimized uncertainties, see Supplementary Discussion 1 (ESI†). The proposed physics-informed feature engineering and machine learning method are promising in balancing lifetime trajectory prediction efficiency and confidence by understanding electrochemical level behaviors that are hidden behind electric signals. Future research should expand to include more material compositions and chemistries to generalize findings, even to different battery technologies such as all-solid-state batteries. Addressing open challenges of electrochemical-level decoupling of degradation patterns could further consolidate the statistical evidence. Ultimately, this study shows the promise of non-destructive characterization using a data and electrochemistry fused method, paving the way for enhanced sustainability in future battery manufacturing, reuse, and recycling by investigating complex system evolutions with physics-informed learning.

Methods

Electrochemical fundamentals

Tracking voltage loss offers a straightforward method to analyze capacity degradation. Despite the interconnected mechanisms underlying battery degradation, a battery material-agnostic formula is used to distinguish voltage loss. This formula calculates the difference between the actual electrode voltage and its theoretical counterpart, providing a method to analyze voltage loss (equivalently, capacity decline) amidst battery aging processes:

|U_actual − U_theoretical(*)| = ΔE(SOC,SOH,T) + η(I,SOC,SOH,T) (1)

U _actual is the actual working electrode voltage. U_theoretical is the theoretical open-circuit voltage reflective of the essential characteristics of the battery material as-manufactured prototypes, denoted by the * symbol. The ΔE is the thermodynamic voltage loss, attributed to the intrinsic material change due to aging, as a function of SOC, SOH, and environmental temperature T. η is the current-induced polarization, which can be further subclassified into three parts, e.g., activation polarization (η_act), ohmic polarization (η_ohm), and concentration polarization (η_con) as follows:

η = η_act + η_ohm + η_con (2)

This material agnostic formula quantifies the respective contributions of thermodynamic and kinetic losses to the overall battery degradation, with their relative proportions changing as a function of SOC, SOH, environmental temperature T, and applied current I.

Chemical process prediction model considering initial manufacturing variability

Battery lifetime inconsistencies often stem from manufacturing process instabilities, or initial manufacturing variabilities (IMVs). We probe IMVs during an early cycling phase through a nine-step charging regimen, designating SOC levels at each phase, and measuring corresponding cut-off voltages to approximate IMVs. Essentially, the IMVs are the difference between the U_actual and U_theoretical at the initial cycling stage, reflective of the shift in intrinsic material properties of as-manufactured prototypes.

Considering the cut-off voltage is a scalar vector for each battery, we deliberately broadcast dummy cycling indexes to span the cut-off voltage vector U_m×9 to a cut-off voltage matrix U_(C×m)×10 to predict continuous chemical process, where m is the battery number and C is the total length of cycling index of all batteries, equivalently the length of the entire lifetime. Given a feature matrix F_(C×m)×N (see ESI† for more details on the featurization taxonomy), where N is the number of features, the model learns a composition of L intermediate layers of a neural network:

where, L = 3 in this work. F̂ is the output feature matrix, i.e., F̂_(C×m)×N, Θ = {θ⁽¹⁾,θ⁽²⁾,θ⁽³⁾} is the collection of the network parameters from each layer, U is the broadcasted input voltage matrix U_(C×m)×10, and f_Θ(U) is a neural network predictor. Here all layers are fully connected with f_σ, which is a leaky rectified linear unit (Leaky ReLU) activation function. The number of neurons in hidden layers , , and are 32, 64, and 32 respectively.

The chemical process prediction model is trained on selected temperatures (i.e., temperatures where already measured data are accessible), while the temperature-related chemical process variations are considered using the physics-informed transferability. In each selected temperature, we split the data into 75% and 25% for training and testing, respectively. We train the chemical process prediction model using Adam optimizer, with epochs of 30 and a learning rate of 10⁻⁴. The loss function of the chemical process prediction model is:

where F_i is the ith label of defined chemical processes, F̂_i is the predicted chemical processes feature matrix for the ith cycle, λ₁ is the regularization parameter, which is set to 10⁻⁵.

Physics-informed transferability metric

We propose a physics-informed transferability metric to quantitatively evaluate the effort in the knowledge transfer. The proposed transferability metric integrates prior physics knowledge inspired by the Arrhenius equation:where, A is a constant, r is the aging rate of the battery, E_a is the activation energy, k_B is Boltzmann constant and T is the Kelvin temperature. The Arrhenius equation provides us with important information that the aging rate of batteries is directly related to the temperature. We observe the domain-invariant representation of the aging rate ratio, consequently, the proposed Arrhenius equation-based transferability metric (AT_score) is defined as:where, E^s_a is the activation energy of the source domain, E^t_a is the activation energy of the target domain, T_s and T_t are the Kelvin temperatures of the source domain and the target domain, respectively. The closer the AT_score is to 1, the more similar the source domain and target domain are, so the better the knowledge transfer is expected. Since the dominating aging mechanism is unknown (characterized by E_a) as a posterior, we alternatively determine the aging rate by calculating the first derivative concerning the variations on the predicted chemical process curve:where, F̂ is the predicted chemical process feature matrix. We linearize the calculation in adjacent cycles by sampling the point pairs on the predicted chemical process:where, n is the number of point pairs, start and end are the cycle index where we start and end the sampling, respectively. F_start+i and F_end+i is the feature value for the (start + i)th and the (end + i)th cycle, respectively. This calculation mitigates the noise-induced errors, resulting in a more robust aging rate computation. For domains where the aging mechanism is already known (different domains share the same E_a), the AT_score can be expressed in the following form:where is a constant value. This formula ensures that, in cases where the aging mechanism is known, we can calculate transferability between different domains using only the temperatures of the source and target domains. This allows the model for continuous temperature generalization without any target data.

Multi-domain adaptation using the physics-informed transferability metric

Multi-source domain adaptation is an effective solution to alleviate data scarcity in the target domain. Using the physics-informed transferability metric, we assign a weight vector W_1×K = {W_i} (where K is the number of source domains, W_i is ensemble weight for the ith source domain) to source domains to quantify the contributions when predicting the chemical process of target domain. The W_i is defined as:where, AT^{source i→target}_score is the AT_score from the ith source domain to the target domain. This mechanism ensures the source domain with better transferability has a higher weight, effectively quantifying the contribution of each source domain to the prediction of the target domain. From eqn (6) and (10), we can obtain the aging rate of the target domain:

The multi-source transfer based on AT_score includes the following three steps. Here we give an example for illustration. Detailed settings to reproduce the results in the manuscript are otherwise specified. First, we calculate aging rates r for all target and source domains by using early-stage data, i.e., we set start = 100, end = 200, n = 50 in eqn (8). After calculating aging rates for all features or aging curves, we obtain a target domain aging rate vector r^target_1×N and a source domain aging rate matrix r^source_K×N, where K and N are the number of source domains and the number of features, respectively. Second, we calculate the transferability metric AT_score and weight vector W_1×K = {W_i} by eqn (6) and (10). Third, we predict the late stage (cycles after 200) aging rate of the target domain (r_target) using eqn (11). Note that AT^{source i→target}_score and W_i are obtained by both target and source domain early-stage data, which are used to measure the transferability from source domain to target domain based on their aging rate similarity. rⁱ_source is obtained from all accessible data in the source domain, consistent with our definition of the early-stage estimate problem. Specifically, only early-stage data in target domain is available in practice, while source domains can provide more comprehensive aging information to assist the target prediction using complete data. For multi-source domain adaptation, the source domain temperature is set to 25 °C, and 55 °C, and the target domain temperature is set to 35 °C, and 45 °C, for practical verification purposes that intermediate temperatures should be studied. For uni-source domain adaptation, the source domain temperature is set to 55 °C, and the target domain temperature is set to 25 °C, 35 °C, and 45 °C, for practical verification purposes that use accelerated data (55 °C) to rapidly verify battery performance under other temperatures.

Chain of degradation

Battery chemical process degradation is continuous, which we call the “Chain of degradation”. We have predicted the r_target aging rates of each feature in the target domain, which can be further used to predict the chemical process. Therefore, when using aging rates r_target to calculate each target feature vector F_(C×m)×1 in the feature matrix F_(C×m)×N, the ith cycle target feature vector Fⁱ_target should be based on Fⁱ⁻¹_target and rⁱ⁻¹:where, the Fⁱ_target is the feature value of target domain in the ith cycle, rⁱ⁻¹_source j is the aging rate of source domain j at the (i − 1)th cycle. We concatenate the N feature vectors F_(C×m)×1 to get the feature matrix F_(C×m)×N.

Battery degradation trajectory model

It is assumed that the chemical process of the battery deterministically affects the aging process, we therefore use the predicted chemical process to predict the battery degradation curve. The battery degradation trajectory model learns a composition of L intermediate mappings:where, L = 3 in this work. D̂ is predicted battery degradation trajectories, Θ = {θ⁽¹⁾,θ⁽²⁾,θ⁽³⁾} is the collection of the neural network parameters from each layer, F̂ is the predicted battery chemical process feature matrix, and the f_Θ(F̂) is a neural network predictor. Here all layers are fully connected with f_σ, which is a leaky rectified linear unit (Leaky ReLU) activation function. The number of neurons in hidden layers , , and are 32, 64, and 32 respectively. We train the battery degradation trajectory model using Adam optimizer, with epochs of 100 and a learning rate of 10⁻³. The loss function of the battery degradation trajectory prediction model is defined as:where y_i is the ith label of defined battery capacity trajectory, ŷ_i is the ith predicted battery capacity trajectory, λ₂ is the regularization parameter, which is set to 10⁻⁵.

Feature importance rationalization

We use shapley additive global importance (SAGE) to quantify the feature importance in the battery degradation trajectory model. For the selected feature, we use a window length of 20 cycles to calculate the SAGE within this window and slide the window in the entire battery lifetime. For the ith window Win_i, the feature importance is calculated as:

SAGE_Wini = SAGE(X_Wini,Y_Wini) (15)

where SAGE_{Wini (1×N)} is a vector containing SAGE values for N features in window Win_i. X_{Wini (20×N)} and Y_{Wini (20×1)} are input matrix and output vector of the degradation trajectory prediction model in window Win_i, respectively. The correlation between two chemical processes in window Win_i is defined as their 2nd-order Wasserstein distance. SAGE is a function to calculate the feature importance using the mean squared error loss, which is calculated as:where, Y is the output of the degradation trajectory prediction model, X_S ≡ {X_i|i ∈ S} are subsets of features for different S ⊆ D, where D is the set of all features and D ≡ {1, …, d}. equals to combination numbers of features. SAGE is a weighted average of conditional mutual information, which measures the reduction of uncertainty in output Y given the inclusion of feature X_i in all subsets X_S. The summation is for all possible feature subsets exclusive of feature X_i, thus it exhaustively calculates the importance of feature X_i within each subset.

The average of SAGE in all windows, i.e., across the entire lifetime, is defined as:

where, w = ⌈C/20⌉ is the round-up number of windows.

Evaluation metric

Predictive performance is evaluated by a mean absolute percentage error (MAPE) in percentage:where, y_i and ŷ_i is the ground truth and predicted capacity in ith cycle, respectively.

Author contributions

S. T. conceptualized, designed, and implemented the experiments and prepared the manuscript draft; M. Z. prepared the feature taxonomy method, techno-economic evaluation, machine learning model interpretation, and the manuscript draft. Z. Z. and X. C. implemented and discussed the coding work. H. L., R. M., and X. S. contributed to the techno-economic evaluation. Y. C., L. S., C. B., H. C., S. Z., Z. L., and H. L. reviewed and discussed the manuscript draft. Y. L., W. Y., and Z. X. provided the raw data. H. H., S. M., and Y. L. reviewed and discussed this work. X. Z., X. H., and G. Z. reviewed, discussed, and supervised this work.

Data availability

Data are deposited at https://github.com/terencetaothucb/TBSI-Sunwoda-Battery-Dataset. Code for the modeling work is deposited at https://github.com/terencetaothucb/Early-Battery-Degradation-Prediction-via-Chemical-Process-Inference. The supporting data of this work is provided in the ESI.†

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This research work was supported by Key Scientific Research Support Project of Shanxi Energy Internet Research Institute (No. SXEI2023A002) [X. Z.], Meituan Scholar Program-International Collaboration Project (No. 202209A) [X. Z.], Tsinghua Shenzhen International Graduate School Interdisciplinary Innovative Fund (Grant No. JC2021006) [X. Z. and G. Z.], Tsinghua Shenzhen International Graduate School-Shenzhen Pengrui Young Faculty Program of Shenzhen Pengrui Foundation (No. SZPR2023007) [G. Z.], Guangdong Basic and Applied Basic Research Foundation (No. 2023B1515120099) [G. Z.], National Natural Science Foundation of China (No. U23A20327 and No. 72361137006) [X. H.].

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ee03839h

‡ These authors were of equal contributions.

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