HorizON: A Multi-Horizon Deep Operator Network for Property Prediction of Organic Battery Stacks

Subhash V. S. Ganti; Lukas Woelfel; Arla Diengdoh; Tzvetan Mihaylov; Thomas Nevolianis; Jan Meyer; Christopher Kuenneth

cond-mat.mtrl-sciOct 27, 2026

HorizON: A Multi-Horizon Deep Operator Network for Property Prediction of Organic Battery Stacks

Authors: Subhash V. S. Ganti, Lukas Woelfel, Arla Diengdoh, Tzvetan Mihaylov, Thomas Nevolianis, Jan Meyer, Christopher Kuenneth

Organizations: University of Bayreuth, Faculty of Engineering Science, Universitätsstraße 30, 95447 Bayreuth, Germany · University of Bayreuth, Bavarian Center for Battery Technology (BayBatt), Universitätsstraße 30, 95447 Bayreuth, Germany · Digital R&D, Covestro Deutschland AG, Kaiser-Wilhelm-Allee 60, 51373 Leverkusen, Germany

Abstract

Transition-metal-based batteries rely on critical elements such as lithium, cobalt, and nickel. Their extraction creates environmental and supply-chain challenges. Organic electrode materials (OEMs) reduce this reliance and provide broad molecular tunability. However, OEM-based batteries still show limited long-term cycling stability. Their design also requires the joint optimization of coupled metrics such as voltage, specific capacity, capacity retention, and energy density. These metrics depend on the full battery stack and on the interactions among its components rather than on the active material alone. In our previous work, we developed a data-fusion multi-task framework for average discharge voltage and first-cycle specific capacity. Both targets are single-valued. Here, we extend that framework to multi-horizon prediction by predicting a property at every cycle of a discharge trajectory rather than at a single cycle. Our multi-fidelity and Multi-horizon Deep Operator Network learns DFT redox potentials and cycle-dependent specific-capacity trajectories within one model. We train it on complete battery-stack representations and usage conditions, so it learns battery-stack interactions rather than cathode-only effects. This framework supports long-term property prediction, inverse design, and process optimization for organic battery systems.

Figures & tables

Figure 1: Multi-Horizon Deep Operator Network workflow. a The four stages are multi-fidelity dataset construction, battery-stack fingerprinting, Multi-Horizon Deep Operator Network modeling, and inverse design. We encode the cell components as polyBERT fingerprints and combine them with fidelity and usage condition descriptors for multi-property prediction. b The Multi-Horizon Deep Operator Network architecture provides the cycle number to the trunk network and the usage conditions and battery-stack fingerprints to the branch network. A dot product combines the two latent representations to predict the target property. c The inverse-design workflow iteratively modifies the chemical structure of training polymers, screens the generated candidates with the trained model, and uses SHapley Additive exPlanations (SHAP) to derive interpretable polymer design rules.

Property	Subset	Cycle	Method	Data pts.	# Cathodes	# Electrolytes	Range	Fidelity
Capacity	Full-stack a	many	Exp.	457 a	18	6	[ $11.0$ , $223.0$ ]	High
	Active material b	1st	Semi-Exp. c	217	217	—	[ $8.0$ , $691.0$ ]	Medium
	Theoretical b	—	Faraday	130	130	—	[ $93.0$ , $570.0$ ]	Low
Voltage	Active material b,d	1st	Semi-Exp. c	197	197	—	[ $0.6$ , $4.07$ ]	Medium
Voltage	Redox potential d	—	DFT	67 e	45 e	—	[ $-3.2$ , $5.45$ ]	Medium
Total				1068	607	6

Table 1: Overview of the multi-fidelity dataset used to train the model. We combine high-fidelity cycling data with medium-fidelity active-material experimental measurements, medium-fidelity DFT redox potentials, and low-fidelity theoretical capacities. Capacities are reported in

\mathrm{mAh}\text{\,}{\mathrm{g}}^{-1}

and voltages/potentials in

\mathrm{V}

. An em-dash (—) marks quantities not collected for that subset.

Figure 2: Parity plots for HorizON and the meta-learner. Panels a and b show the five-fold averaged HorizON predictions for specific capacity and redox potential (V vs. SHE). Panels c and d show the corresponding meta-learner predictions. Points are colored by fidelity level. Low-fidelity points represent theoretical capacities. Medium-fidelity points represent DFT-computed redox potentials and experimental measurements without usage conditions or electrolyte information. High-fidelity points represent full battery-stack measurements. Each panel reports MAE, RMSE, $R^{2}$ , and the number of test points $N$ .

Figure 3: Specific capacity versus average voltage (panels a to c ) and gravimetric versus volumetric energy density (panels d to f ) for three polymer libraries, predicted at high fidelity for the LiTFSI/TEGDME electrolyte at a 1C rate for the 1st and 200th cycles. Voltage values are average working potentials versus lithium (V vs. $\text{Li}{\vphantom{\text{X}}}^{\vphantom{\smash[t]{\text{2}}}\hphantom{\text{}}\text{+}}$ /Li). Panels a and d : The public polyOne library ( $100\text{\,}\mathrm{M}$ ). Kuenneth and Ramprasad (2022) Panels b and e : The inverse-design library generated in this work ( $4\text{\,}\mathrm{M}$ ). Panels c and f : A single-cycle library from our previous work ( $1.7\text{\,}\mathrm{M}$ ). Ganti et al. (2025) Gravimetric energy density is the product of capacity and voltage; volumetric energy density additionally uses a computationally estimated polymer density. The color scale gives the number of polymers per bin and is shared across all six panels. Dashed lines in panels a to c are energy-density contours ( $\mathrm{W}\text{\,}\mathrm{h}\text{\,}{\mathrm{kg}}^{-1}$ ). Blue points denote the experimental cathodes used to train the property predictors: capacities are measured values, voltages are model predictions, and volumetric energy densities use the same estimated density as the library predictions.

Figure 4: UMAP projections and cycling predictions at high-fidelity for our inverse-design library of $4\text{\,}\mathrm{M}$ polymers. Panels a and b show the predicted specific capacity for the LiTFSI and LiPF 6 electrolytes. Dashed outlines mark the dominant region of each polymer class in the UMAP plot, and solid circles mark the top candidate of each class. Panel c is a ridgeline plot of the library-wide specific-capacity distribution at cycles $1100200300400$ for LiTFSI/TEGDME; the distributions shift toward lower capacity as cycling proceeds. Panel d shows the predicted energy-density retention ( $\mathrm{\%}$ ) of each polymer class over $400$ cycles.

Figure 5: SHapley Additive exPlanations (SHAP) analysis of the specific-capacity predictions. Panel a shows the mean impact of each input component group across all fidelity levels. Panel b shows the mean change in high-fidelity predicted capacity when a given bond type is removed from the cathode active material, with the bond counts given in parentheses. The error bars denote the spread across the sampled polymers. Panel c maps the high-fidelity per-bond capacity attribution to six monomers, which are used as active materials of cathode copolymers. The colors range from capacity-reducing (blue) to capacity-enhancing (red).

Figure 6: Schematic of the automated DFT redox potential workflow. Starting from PSMILES strings, the pipeline proceeds through methyl capping and 3D structure generation (RDKit), conformer search (CREST/GFN2-xTB), geometry optimization (PCM-M06-2X/6-31+G**), and final single-point energy evaluation (SMD-M06-2X/6-31+G**) to yield redox potentials referenced to SHE.

Materials Property Prediction

Materials property prediction uses data and physical models to estimate how composition, structure, and processing determine a material’s behavior.

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BatteryMFormer: Multi-level Learning for Battery Degradation Trajectory Forecasting

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School of Computer Science and Engineering, Central South University · Material Genome Institute, Shanghai University

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Early battery degradation trajectory forecasting (BDTF), which predicts the full-life state-of-health trajectory from early operational data, is critical for battery optimization, manufacturing, and deployment. Battery degradation data exhibit two key characteristics. First, degradation data present a multi-level structure, including regularities shared within aging conditions and trajectory patterns shared across batteries. Second, degradation-related variations in voltage-current profiles are often localized to specific state of charge (SOC) intervals. Existing approaches often fail to explicitly model these characteristics. To bridge this gap, we propose BatteryMFormer, a multi-level Transformer for early BDTF. BatteryMFormer integrates (1) an aging-condition-aware decoder that injects aging-condition priors via aging-condition-informed queries and aging-condition-aware attention, (2) a meta degradation pattern memory that learns and retrieves trajectory prototypes to guide long-horizon forecasting, and (3) a dual-view encoder that jointly captures temporal dynamics and SOC-localized variations from voltage and current time series. Extensive experiments on four battery domains show that BatteryMFormer consistently outperforms state-of-the-art baselines, marking a significant step toward reliable BDTF. Our code is available at https://github.com/Ruifeng-Tan/BatteryMFormer.

Abstract

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