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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
TL;DR
Organic battery design needs long-term predictions that account for full-stack interactions, while existing temporal models are limited to single chemistries or cell designs. HorizON combines multi-fidelity data and stack representations to predict cycle-dependent properties; its meta-learner reports R2 values of 0.96 for specific capacity and 0.97 for redox potential. The framework can support exploration of battery-stack designs and prioritization of cycling experiments, within the scope of its training data.
Problem
Long-term prediction models have focused on single chemistries or cell designs, while practical OEM design requires cycling-stability predictions that capture chemistry and full-stack information.
Source: Introduction · p. 4Method
HorizON jointly trains on high-fidelity full-stack capacity trajectories, medium-fidelity DFT redox potentials, and lower-fidelity proxy targets using battery-stack fingerprints and usage conditions.
Source: Discussion · p. 18Results
The meta-learner has R2 values of 0.96 for specific capacity and 0.97 for redox potential, with reduced variability among fold-specific models.
Source: Results and Discussion · p. 10Takeaways & Limitations
Rapid stack-level predictions of high-fidelity capacity trajectories can support broader exploration of organic battery stacks and help prioritize cycling experiments.
Source: Discussion · p. 18High-fidelity training stacks use lithium-metal anodes; extending the model to other anodes, full-cell configurations, ion systems, or broader electrolyte families requires additional data and experimental validation.
Source: Discussion · p. 18
Abstract
from arXiv · showhide
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.
Introduction
Organic electrode materials offer tunable alternatives to critical-element-based electrodes, but their cycling stability remains limited. HorizON extends prior single-cycle prediction toward long-term, multi-property prediction across organic battery stacks.
Introduction
- Many organic electrode materials lose capacity after hundreds of cycles, mainly through active-species dissolution, side reactions, and low intrinsic electronic conductivity.The introduction frames new OEM design across a large chemical space as a way to address these limitations.Source: Introduction · p. 4
- Earlier machine-learning work commonly represented OEM chemistry with molecular fingerprints, and the authors’ prior multi-task model predicted first-cycle capacity and voltage across cathode–anode pairs [24].The present work extends this single-valued prediction setting to cycle-resolved trajectories.Source: Introduction · p. 4
- Existing temporal models target long-term battery behavior but focus on a single chemistry or cell design, limiting transferability across OEMs.The authors argue that transferability requires capturing both OEM chemistry and information from the full battery stack.Source: Introduction · pp. 4–5
- The authors introduce a multi-horizon, multi-fidelity, multi-property model to predict long-term performance across diverse OEM chemistries using chemistry and full-stack information.The pipeline combines high-fidelity capacity-versus-cycle trajectories with medium-fidelity DFT redox potentials and other battery data; SHAP is used to identify preferred redox-active moieties and design rules.Source: Introduction · p. 5, Figure 1 · p. 6
Results and Discussion
HorizON predicts cycle-dependent capacity trajectories and scalar properties from complete battery-stack representations, combining data across property types and fidelity levels. The results apply this framework to model evaluation, polymer-library screening, cycling predictions, and capacity attribution.
Dataset
- The dataset contains 1068 points across three fidelity levels, including 457 high-fidelity capacity-versus-cycle measurements from complete battery stacks.The medium-fidelity subset includes experimental single-cycle measurements and DFT redox potentials; the low-fidelity subset contains theoretical capacities.Source: Results and Discussion · pp. 7–8
Battery materials stack fingerprinting and HorizON
- The 1807-dimensional input combines cathode, electrolyte, and anode fingerprints with usage-condition and redox-state descriptors.HorizON evaluates the trunk network at multiple cycle numbers to predict a capacity trajectory, while scalar targets use cycle 1.Source: Results and Discussion · pp. 8–9
Model performance
- R2 was 0.87 for specific capacity and 0.89 for voltage in the five-fold HorizON predictions.Error bars in the parity plots represent two standard deviations across the five models.Source: Results and Discussion · p. 9, Figure 2 · p. 11
- R2 reached 0.96 for specific capacity and 0.97 for redox potential with the meta-learner, whose predictions showed reduced scatter across fidelity levels.The meta-learner ensembles predictions from five HorizON models.Source: Results and Discussion · p. 10, Figure 2 · p. 11
Inverse Design
- The four-million-candidate inverse-design library was generated by substituting redox-active moieties and fragments, then ranking candidates by predicted energy density within polymer classes.The complex class includes candidates with several redox-active moieties on one backbone.Source: Results and Discussion · pp. 12, 14
Property-space comparison
- At 200 cycles, predicted capacities shift lower across the three libraries, while the current inverse-design library extends further toward high capacity at intermediate voltages than the previous library [24].The libraries are compared at high fidelity under the same stack and usage conditions; predicted energy densities extend to roughly 550 W h kg−1.Source: Figure 3 · p. 12, Results and Discussion · p. 14
Cycling response
- For LiTFSI/TEGDME candidates, predicted capacity falls by 30–40 mAh g−1 on average over 400 cycles, while each polymer class retains about 89–91% of initial energy density.The capacity distributions shift lower with cycling, while class retention curves overlap within their confidence bands.Source: Figure 4 · p. 13, Results and Discussion · p. 15
SHAP Analysis
- Component-level attribution identifies cathode and electrolyte as dominant capacity inputs, while carbonyl and conjugated-bond features are among the capacity-enhancing fragments.Capacity-fidelity inputs contribute slightly, voltage-fidelity inputs negligibly, and the anode minimally; non-conjugated structures with multiple heteroatoms tend toward lower capacity.Source: Results and Discussion · pp. 16–17, Figure 5 · p. 17
Discussion
HorizON predicts organic-battery stack properties across fidelities and time horizons, including high-fidelity cycle-resolved capacity trajectories. Its predictions can support exploration and cycling experiments, but accuracy and inverse-design candidates remain bounded by training coverage and unassessed feasibility constraints.
Discussion
- HorizON predicts high-fidelity cycle-resolved capacity trajectories for full battery stacks using cathode, electrolyte, and lithium-metal-anode fingerprints.It jointly trains across properties, fidelity levels, and time horizons, connecting high-fidelity trajectories with DFT redox potentials and lower-fidelity proxy targets.Source: Discussion · p. 18
- Joint training combines datasets with missing property or fidelity labels and takes under 1 ms per stack at prediction time.The model uses correlations across tasks and fidelities to let information from one task improve another.Source: Discussion · p. 18
- Rapid stack-level predictions can help explore the large design space and prioritize cycling experiments, but model accuracy is bounded by represented chemistries and cell designs.High-fidelity training stacks use lithium-metal anodes; extending to other anodes, full-cell configurations, ion systems, or broader electrolyte families requires additional data and experimental validation.Source: Discussion · p. 18
- Inverse-design candidates still require synthesis and electrochemical testing because the workflow does not assess key fabrication and material-feasibility factors.It does not evaluate synthetic accessibility, polymerizability, repeat-unit stability, or electrode-fabrication compatibility.Source: Discussion · p. 18
- The authors identify knowledge transfer across related battery domains and targeted data collection for rapid model adaptation as future uses of multi-task, multi-fidelity models.These are proposed directions, not reported evaluation results.Source: Discussion · p. 18
Methods
The methods assemble multi-fidelity battery data and encode complete material stacks and usage conditions for prediction. HorizON combines cross-validated models with a meta-learner, alongside workflows for DFT redox potentials, inverse design, and energy-density estimation.
Data collection and curation
- The dataset combines 1,068 points from experimental cycling, first-cycle properties, theoretical capacities, and DFT redox potentials, with some cycling trajectories extending to approximately 400 cycles.Targets are independently min–max scaled before the training and validation split.Source: Methods · p. 19
DFT Redox Potential Calculations
- DFT redox potentials are calculated from oxidized–reduced free-energy differences after conformer search and geometry optimization, then referenced to SHE.The workflow uses PCM-M06-2X/6-31+G** optimization and SMD-M06-2X/6-31+G** final free energies; stationary points are checked by frequency analysis.Source: Methods · pp. 19–20, Figure 6 · p. 20
Fingerprinting
- Each constituent is encoded as a 600-dimensional polyBERT fingerprint, and stack-component vectors plus seven usage selectors form a 1,807-dimensional model input.Selectors include C-rate, active-material loading, electrolyte molarity, voltage limits, and oxidation and reduction states.Source: Methods · p. 20
Multi-Horizon Deep Operator Network (HorizON) Architecture
- HorizON trains five cross-validated models and a meta-learner that combines their five predictions into the final property prediction.The dataset is split into 80% for cross-validation and 20% for the meta-learner; Optuna tunes each fold's model configuration.Source: Methods · p. 21
Inverse Design
- Inverse design modifies 65 training-set homopolymers to generate approximately 4,000,000 chemically valid candidates, whose predicted redox potentials and capacities are ranked.RDKit and PSMILES checks assess validity after substitutions; the highest-ranked candidates are reported in the Supporting Information.Source: Methods · p. 21
Volumetric & Gravimetric Energy Density Calculations
- Volumetric energy density uses polymer density estimated from repeat-unit SMILES with RDKit's Wildman–Crippen model, and is reported as a model estimate.Gravimetric energy density is calculated from capacity and voltage; volumetric energy density additionally uses the estimated density.Source: Methods · pp. 21–22
SHAP Analysis
- The SHAP analysis estimates bond-level contributions to predicted stack capacity by removing cathode bonds and measuring prediction changes across five cross-validated models.Larger positive attribution values indicate a stronger contribution to predicted capacity.Source: Methods · pp. 22–23
CO2 Emission and Timing
The authors estimate emissions for model training and per-candidate inference.
CO2 Emission and Timing
- A 40 h run on four A100-40 GB GPUs is estimated at approximately 3.44 kg CO2eq, while a 2 s candidate prediction is estimated at 6.5 g CO2eq.The estimates use a Bayreuth cluster carbon intensity of 0.344 kg CO2eq kWh−1.Source: CO2 Emission and Timing · p. 23