SeqBattNet: Adaptive Battery Voltage Forecasting

• SeqBattNet is a discrete-state, physics-informed neural network that predicts lithium-ion battery terminal voltage using an encoder-decoder structure.
• It integrates a cycle-adaptive encoder with an equivalent-circuit-model decoder to infer aging-sensitive parameters from only three basic battery inputs.
• The model employs discrete time state propagation and Coulomb counting to accurately estimate remaining discharge time and energy for battery management.

SeqBattNet is a discrete-state physics-informed neural network for battery modeling that predicts the terminal-voltage trajectory of a lithium-ion battery during discharge from the applied current profile. It is presented as a battery-management-system submodel for forecasting quantities such as remaining discharge time and remaining discharge energy, both of which depend on accurately predicting when the voltage will cross the end-of-discharge cutoff. The model combines a cycle-adaptive encoder with an equivalent-circuit-model decoder, requires only three basic battery parameters—$V_0$, $V_{\mathrm{EOD}}$, and $C$—and is designed to remain computationally efficient while generalizing across cells even when trained on data from a single cell (Tran et al., 22 Sep 2025).

1. Problem setting and design rationale

SeqBattNet addresses the specific task of forecasting terminal voltage during the discharge process. In the formulation used by the paper, this task is not treated as an isolated regression problem: voltage prediction is the mechanism by which downstream battery-management quantities are obtained, especially remaining discharge time (RDT) and remaining discharge energy (RDE). If the predicted voltage trajectory is inaccurate, the predicted cutoff time is also inaccurate, which directly degrades time-to-empty and remaining-energy estimates (Tran et al., 22 Sep 2025).

The model is motivated by limitations in three established method families. Classical model-based approaches, including electrochemical models and equivalent circuit models (ECMs), are physically grounded but require many parameters that are difficult to identify and calibrate. High-fidelity electrochemical models such as P2D/DFN or SPM are especially costly for real-time use. Purely data-driven methods avoid explicit physics but require large labeled datasets spanning many operating conditions and degradation states, and the paper characterizes them as less interpretable. Prior physics-informed neural networks partially bridge these two regimes, but the paper identifies three remaining shortcomings: some depend on continuous-time ODE state generation, some still require additional physical parameters such as $R_p$, $R_s$, $C_{sp}$, and $C_s$, and some do not explicitly adapt to aging (Tran et al., 22 Sep 2025).

Against this background, SeqBattNet is defined by three coupled design choices. It is physics-informed because its decoder is structured as a discrete-time ECM with explicit state transitions and an output equation following battery circuit dynamics. It is discrete-state because internal states are propagated step by step in discrete time rather than regenerated by integrating an ODE over a preset horizon. It is aging-adaptive because the model infers cycle-specific latent physical parameters from an initial observed current-voltage segment at the start of each discharge cycle. The paper claims four main advantages: only three basic battery parameters are required; battery evolution is modeled through discrete physical states; the method is robust even when trained on data from only a single cell; and it remains computationally efficient (Tran et al., 22 Sep 2025).

A recurrent point in the paper is that discrete-state rollout is operationally aligned with battery-management deployment. The decoder can advance one sample at a time and stop as soon as the predicted voltage falls below the cutoff, rather than rolling continuously to an externally chosen terminal time. This is presented as especially relevant for proactive stopping in RDT and RDE estimation (Tran et al., 22 Sep 2025).

2. Encoder-decoder architecture and aging adaptation

SeqBattNet is an encoder-decoder model. For each discharge cycle, the encoder consumes the first $n$ time steps of the current and voltage sequences and outputs cycle-specific adaptation parameters. The decoder then uses those adaptation parameters together with the subsequent current sequence to roll forward the voltage trajectory (Tran et al., 22 Sep 2025).

The encoder input is

$$\mathbf{x} = [I_{\mathrm{init}}, V_{\mathrm{init}}] \in \mathbb{R}^{n \times 2},$$

where $I_{\mathrm{init}}$ and $V_{\mathrm{EOD}}$0 are the first $V_{\mathrm{EOD}}$1 current and voltage samples of the cycle. This sequence is embedded by a linear layer,

$V_{\mathrm{EOD}}$2

The encoder is the paper’s proposed HRM-GRU module, where HRM denotes Hierarchical Reasoning Model. The architecture adapts a hierarchical-reasoning design that originally used Transformers, but replaces them with GRUs to reduce computational complexity and, according to the reported experiments, improve performance. HRM-GRU maintains low-level hidden states $V_{\mathrm{EOD}}$3 and high-level hidden states $V_{\mathrm{EOD}}$4, and introduces gradient-free preparatory micro-updates before each main update. For each sequence index $V_{\mathrm{EOD}}$5, it performs $V_{\mathrm{EOD}}$6 micro-updates,

$V_{\mathrm{EOD}}$7

followed by the main update,

$V_{\mathrm{EOD}}$8

This two-level low-to-high recurrence is intended to capture more structured temporal dependencies than a one-level GRU (Tran et al., 22 Sep 2025).

After dropout and layer normalization of the high-level state, a linear head produces

$V_{\mathrm{EOD}}$9

with

$C$0

Using the final output $C$1, the encoder predicts

$C$2

where $C$3 is the ohmic resistance, $C$4 are RC branch time constants, $C$5 is the initial state of charge, $C$6 is the state of health, and $C$7 are weights used to initialize the RC branch voltages. The number of RC branches is fixed to $C$8 (Tran et al., 22 Sep 2025).

The raw outputs are mapped into physically plausible ranges: $C$9

$R_p$0

$R_p$1

with

$R_p$2

The paper presents these mappings as a key physics-consistency mechanism because they enforce positivity, boundedness, and normalized RC initialization weights by construction (Tran et al., 22 Sep 2025).

The encoder also computes the initial RC branch voltages: $R_p$3

$R_p$4

$R_p$5

Here $R_p$6 and $R_p$7 are the final current and voltage samples in the initial observed segment, and $R_p$8 is the decoder’s feedforward network mapping SOC to OCV. The paper interprets $R_p$9 as the residual between OCV and measured loaded voltage after subtracting the ohmic drop, with $R_s$0 partitioning that residual across the RC branches (Tran et al., 22 Sep 2025).

The aging-adaptation mechanism operates once per discharge cycle rather than at every decoder step. For each cycle, the first $R_s$1 measured current-voltage samples yield one set of adaptation parameters,

$R_s$2

which are then held fixed during decoder rollout, except for decoder-internal quantities such as $R_s$3, $R_s$4, and $R_s$5, which evolve over time. The paper provides qualitative support for this mechanism using PCA of encoder embeddings that form smooth trajectories across cycle index (Tran et al., 22 Sep 2025).

3. Discrete-time ECM decoder and physics-informed formulation

The decoder is a discrete-time, physics-informed ECM that uses the cycle-adaptive parameters

$R_s$6

together with the future current sequence $R_s$7 to generate future terminal voltage (Tran et al., 22 Sep 2025).

The RC decay coefficients are

$R_s$8

with the exponential applied elementwise over the RC branches. At each step $R_s$9, the open-circuit voltage is predicted from the current SOC: $C_{sp}$0 This constrains OCV to the interval between cutoff voltage $C_{sp}$1 and nominal full-charge voltage $C_{sp}$2 (Tran et al., 22 Sep 2025).

The dynamic RC branch resistances are generated by a second neural network: $C_{sp}$3 with $C_{sp}$4 and $C_{sp}$5. In this formulation, polarization resistance depends on both the present charge state and health state (Tran et al., 22 Sep 2025).

The RC branch voltages obey the discrete first-order relaxation equation

$C_{sp}$6

This is the central state transition of the model. Because the decoder explicitly carries forward $C_{sp}$7, the state is not regenerated from scratch; it evolves causally in discrete time (Tran et al., 22 Sep 2025).

SOC is propagated by Coulomb counting: $C_{sp}$8 where $C_{sp}$9 clips to $C_s$0, and $C_s$1 is the degradation-adjusted effective capacity,

$C_s$2

The paper states that $C_s$3 is typically $C_s$4, and uses $C_s$5 “to account for capacity fade.” For the NASA dataset, $C_s$6 is used instead (Tran et al., 22 Sep 2025).

The ECM output equation is

$C_s$7

Thus the predicted terminal voltage is the equilibrium voltage minus an instantaneous ohmic drop minus the polarization drops from the RC branches. The complete predicted sequence is written as

$C_s$8

where the measured early segment is concatenated with the predicted future segment (Tran et al., 22 Sep 2025).

The paper uses this decoder structure to distinguish SeqBattNet from unconstrained sequence models. The model does not directly map $C_s$9-history to future voltage with a black-box neural network. Instead, it predicts physically interpretable latent quantities—$n$0, $n$1, SOC, SOH, RC voltages, OCV, and RC resistances—and evolves them through explicit state equations. Neural subnetworks are inserted only where nonlinear constitutive relations are learned: OCV as a function of SOC via $n$2, and RC resistance as a function of SOC and SOH via $n$3 (Tran et al., 22 Sep 2025).

A related conceptual point is the paper’s distinction between physics-informed and merely physics-inspired modeling. In SeqBattNet, the physical structure is not a post hoc regularizer but part of the forward model itself. The exact effect of removing the ECM decoder is not quantified by a direct decoder-ablation table, but the reported comparisons against plain LSTM, GRU, and Transformer sequence models are used to argue that the combination of learned adaptation and ECM structure yields materially lower error on TRI and RT-Batt (Tran et al., 22 Sep 2025).

4. Training objective, implementation, and battery metadata requirements

SeqBattNet is trained using a weighted Huber loss over the voltage trajectory: $n$4 where $n$5 is a mask for zero-padded sequences and $n$6 is a time-dependent weight. The Huber loss is

$n$7

with $n$8. The adaptive temporal weights are designed to emphasize both the beginning of the trajectory and especially the final prediction step near end of discharge (Tran et al., 22 Sep 2025).

The loss-function study reports that this weighted Huber loss outperforms both plain MSE and the baseline loss from Wang et al. On TRI-b1c4, RMSE drops from $n$9 with MSE and $$\mathbf{x} = [I_{\mathrm{init}}, V_{\mathrm{init}}] \in \mathbb{R}^{n \times 2},$$0 with the baseline loss to $$\mathbf{x} = [I_{\mathrm{init}}, V_{\mathrm{init}}] \in \mathbb{R}^{n \times 2},$$1 with the proposed loss. On RT-Batt-1-2, RMSE improves from $$\mathbf{x} = [I_{\mathrm{init}}, V_{\mathrm{init}}] \in \mathbb{R}^{n \times 2},$$2 and $$\mathbf{x} = [I_{\mathrm{init}}, V_{\mathrm{init}}] \in \mathbb{R}^{n \times 2},$$3 to $$\mathbf{x} = [I_{\mathrm{init}}, V_{\mathrm{init}}] \in \mathbb{R}^{n \times 2},$$4. On NASA-RW5, RMSE improves from $$\mathbf{x} = [I_{\mathrm{init}}, V_{\mathrm{init}}] \in \mathbb{R}^{n \times 2},$$5 and $$\mathbf{x} = [I_{\mathrm{init}}, V_{\mathrm{init}}] \in \mathbb{R}^{n \times 2},$$6 to $$\mathbf{x} = [I_{\mathrm{init}}, V_{\mathrm{init}}] \in \mathbb{R}^{n \times 2},$$7. MAE and MAPE are reported to follow the same trend (Tran et al., 22 Sep 2025).

The model is implemented in PyTorch and optimized with AdamW. Training uses 1000 epochs, batch size 128, and an NVIDIA 4080 GPU. The learning rate starts at $$\mathbf{x} = [I_{\mathrm{init}}, V_{\mathrm{init}}] \in \mathbb{R}^{n \times 2},$$8 and is reduced by ReduceLROnPlateau when validation loss stagnates, with a floor at $$\mathbf{x} = [I_{\mathrm{init}}, V_{\mathrm{init}}] \in \mathbb{R}^{n \times 2},$$9. Each experiment is repeated five times, and final predictions are averaged across runs. The HRM-GRU hyperparameters selected by grid search are $I_{\mathrm{init}}$0, $I_{\mathrm{init}}$1, $I_{\mathrm{init}}$2, $I_{\mathrm{init}}$3, and $I_{\mathrm{init}}$4. The OCV network $I_{\mathrm{init}}$5 is a 3-layer FNN with dimensions $I_{\mathrm{init}}$6, using SiLU, then SiLU, then Sigmoid. The RC-resistance network $I_{\mathrm{init}}$7 is $I_{\mathrm{init}}$8, using SiLU and then Sigmoid (Tran et al., 22 Sep 2025).

A central deployment claim is that SeqBattNet requires only three basic battery parameters: $I_{\mathrm{init}}$9 More concretely, the capacity term is the rated capacity $V_{\mathrm{EOD}}$00, together with an end-of-life capacity setting for each dataset. $V_{\mathrm{EOD}}$01 sets the upper limit of the OCV range, $V_{\mathrm{EOD}}$02 sets the lower limit and the discharge stopping criterion, and capacity provides the scale for SOC propagation by Coulomb counting. The paper explicitly emphasizes that users do not need to pre-identify additional ECM parameters such as $V_{\mathrm{EOD}}$03, $V_{\mathrm{EOD}}$04, $V_{\mathrm{EOD}}$05, or $V_{\mathrm{EOD}}$06; instead, $V_{\mathrm{EOD}}$07, $V_{\mathrm{EOD}}$08, and RC-resistance profiles are inferred from data in a constrained way (Tran et al., 22 Sep 2025).

5. Datasets, evaluation protocol, and empirical results

The evaluation is deliberately organized around cross-cell generalization. On each dataset, training is performed on one cell, validation on a different cell, and testing on different cells again. The paper presents this as stricter than splitting cycles within a single cell, and explicitly criticizes Wang et al.’s BattNN protocol for splitting within a cell because training and test fragments then share the same cell and cycle-trajectory context (Tran et al., 22 Sep 2025).

Dataset	Cell split	Battery settings
TRI	train b1c0; val b2c13; test b1c4, b1c2	$V_{\mathrm{EOD}}$09 Ah, $V_{\mathrm{EOD}}$10 Ah, $V_{\mathrm{EOD}}$11 V, $V_{\mathrm{EOD}}$12 V
RT-Batt	train 1-1; val 1-4; test 1-2, 1-3	$V_{\mathrm{EOD}}$13 Ah, $V_{\mathrm{EOD}}$14 Ah, $V_{\mathrm{EOD}}$15 V, $V_{\mathrm{EOD}}$16 V
NASA	train RW3; val RW6; test RW4, RW5	$V_{\mathrm{EOD}}$17 Ah, $V_{\mathrm{EOD}}$18 Ah, $V_{\mathrm{EOD}}$19 V, $V_{\mathrm{EOD}}$20 V

The three datasets differ in discharge-profile variability. TRI contains 124 LFP/graphite A123 APR18650M1A cells with highly standardized constant 4C discharge down to $V_{\mathrm{EOD}}$21 V, while charge protocols vary. RT-Batt also uses A123 APR18650M1A LFP/graphite cells, but each cell has its own multistage discharge profile that remains fixed across that cell’s cycles. NASA contains four 18650 lithium-ion cells RW3–RW6 from the NASA Ames repository, charged at constant 2 A to $V_{\mathrm{EOD}}$22 V and discharged to $V_{\mathrm{EOD}}$23 V with randomized current profiles between 0.5 A and 4 A; both cells and cycles vary in discharge profile. The initial adaptation window length is chosen empirically: $V_{\mathrm{EOD}}$24 works best on TRI and RT-Batt, while $V_{\mathrm{EOD}}$25 works best on NASA (Tran et al., 22 Sep 2025).

The main baseline set includes BattNN, plain LSTM, plain GRU, plain Transformer, and multiple SeqBattNet variants that keep the same decoder and change only the encoder: LSTM, GRU, Transformer, FNN, HRM-LSTM, HRM-GRU, and HRM-Transformer. This design isolates the contribution of the aging encoder from that of the physics-informed decoder (Tran et al., 22 Sep 2025).

Relative to BattNN, classical sequence models already improve performance substantially. On TRI-b1c4, BattNN has RMSE $V_{\mathrm{EOD}}$26, whereas LSTM and GRU are around $V_{\mathrm{EOD}}$27. On RT-Batt-1-2, BattNN has RMSE $V_{\mathrm{EOD}}$28, while LSTM achieves $V_{\mathrm{EOD}}$29 and Transformer $V_{\mathrm{EOD}}$30. On NASA-RW4, BattNN has RMSE $V_{\mathrm{EOD}}$31, while Transformer reaches $V_{\mathrm{EOD}}$32 (Tran et al., 22 Sep 2025).

Within the SeqBattNet family, the proposed HRM-GRU encoder is strongest on TRI and RT-Batt, and second-best on NASA, where the simple FNN encoder performs slightly better. The paper explicitly identifies this as dataset-specific encoder suitability rather than a universal dominance claim (Tran et al., 22 Sep 2025).

Test case	HRM-GRU RMSE	HRM-GRU MAE / MAPE
TRI-b1c4	0.0280	0.0113 / 0.0042
TRI-b1c2	0.0416	0.0168 / 0.0063
RT-Batt-1-2	0.0346	0.0120 / 0.0044
RT-Batt-1-3	0.0491	0.0171 / 0.0063
NASA-RW4	0.0257	0.0191 / 0.0055
NASA-RW5	0.0253	0.0191 / 0.0055

Two ablation trends are especially clear. First, hierarchical recurrent encoding matters on TRI and RT-Batt: on TRI-b1c4, plain SeqBattNet with a GRU encoder gives RMSE $V_{\mathrm{EOD}}$33, while HRM-GRU gives $V_{\mathrm{EOD}}$34; on RT-Batt-1-2, plain SeqBattNet with GRU gives $V_{\mathrm{EOD}}$35, while HRM-GRU gives $V_{\mathrm{EOD}}$36. Second, the specific hierarchical design matters: HRM-GRU is both more accurate and faster than HRM-Transformer on TRI and RT-Batt. On TRI-b1c4, HRM-Transformer gives RMSE $V_{\mathrm{EOD}}$37 and takes $V_{\mathrm{EOD}}$38 s, whereas HRM-GRU gives $V_{\mathrm{EOD}}$39 and takes $V_{\mathrm{EOD}}$40 s (Tran et al., 22 Sep 2025).

The paper also reports favorable runtime. SeqBattNet-HRM-GRU takes roughly $V_{\mathrm{EOD}}$41–$V_{\mathrm{EOD}}$42 s per experiment on TRI and RT-Batt and under 1 s on NASA in the reported setup, while remaining competitive with or faster than several sequence baselines and much faster than HRM-Transformer. The model does not provide a total neural parameter count, so its “low parameterization” is explicitly framed as low physical-parameter requirements rather than a quantified network-size comparison (Tran et al., 22 Sep 2025).

6. Interpretation, scope, and limitations

The paper’s interpretation of SeqBattNet’s performance is that it balances inductive bias and adaptability. The encoder extracts degradation-sensitive information from a short initial discharge fragment, while the decoder constrains prediction through explicit battery physics: SOC decreases by Coulomb counting, RC voltages relax exponentially, terminal voltage is assembled from OCV minus ohmic and polarization drops, and latent variables are confined to physically valid ranges. This suggests that the model avoids spending representational capacity on rediscovering known structure while retaining flexibility where constitutive mappings are nonlinear (Tran et al., 22 Sep 2025).

Several clarifications follow from the reported evidence. First, aging adaptation is inferred once per sequence or cycle, not continuously at every decoder step. Second, the paper argues for the value of the discrete-state design conceptually—particularly proactive stopping at cutoff and causal state carryover—but does not report a numerical ablation against a continuous-state version. Third, qualitative PCA evidence is provided for aging-aware embeddings, but the physics-informed decoder is not isolated in a direct “decoder removed” ablation table (Tran et al., 22 Sep 2025).

The paper also states its limitations clearly. The model uses only voltage and current as inputs and explicitly ignores temperature. All datasets come from controlled laboratory conditions with minimal temperature variation, so the method has not been validated under realistic environmental variation where temperature influences internal resistance, capacity fade, and voltage response. The work focuses on discharge rather than charge dynamics, and its chemistry and operating-condition coverage is limited to the benchmark datasets used: mainly A123 APR18650M1A LFP/graphite cells in TRI and RT-Batt, and the specific NASA randomized-use cells. Future work is identified as incorporating ambient and cell temperature as additional inputs and validating on real-world datasets with more diverse environmental and operational conditions (Tran et al., 22 Sep 2025).

In the form presented, SeqBattNet occupies a specific position in battery modeling. It is more constrained and physically structured than a black-box sequence model, yet less dependent on hand-calibrated physical parameter sets than traditional ECM or electrochemical modeling. Its principal contribution is a cycle-adaptive, discrete-time voltage predictor that embeds ECM state evolution directly into the prediction loop, infers aging-sensitive parameters from a short initial discharge segment, and demonstrates low RMSE with single-cell training across TRI, RT-Batt, and NASA benchmarks (Tran et al., 22 Sep 2025).