💻 computer science

Remaining Useful Life Estimation of Lithium-Ion Batteries: A Controlled Benchmark of Physics-Informed Features and Mamba-Based Architectures on CALCE CS2

This paper presents a controlled benchmark on CALCE CS2 data showing that a standard GRU model outperforms advanced Mamba-based architectures in predicting lithium-ion battery remaining useful life, highlighting the critical importance of physics-informed features like capacity normalization while noting that current results reflect oracle-based evaluation rather than deployment-ready performance.

Original authors: Dikshant Dikshant, Praveen Kumar Agarwal

Published 2026-08-11

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Dikshant Dikshant, Praveen Kumar Agarwal

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine your smartphone or electric car battery as a marathon runner. At the start of their career, they are fresh, fast, and full of energy. But as they run more miles (or charge and discharge more times), their legs get tired, their pace slows, and eventually, they can't finish the race. In the world of science, this is called "battery degradation." The big question researchers are trying to answer is: How many miles does this runner have left before they collapse? This is known as predicting the "Remaining Useful Life" (RUL). Getting this right is a superpower for electric vehicles and grid storage; it helps us know when to swap a battery before it fails, saving money and preventing breakdowns. To solve this, scientists use "machine learning," which is like teaching a computer to spot patterns in the runner's history—like their heart rate, speed, and breathing—to guess how long they can keep going.

Now, picture a team of researchers at Motilal Nehru National Institute of Technology in India. They decided to put some very fancy, new computer brains to the test against some older, simpler ones. They were looking at a specific type of lithium-ion battery (the kind in your phone and car) and wanted to see if a new, trendy architecture called "Mamba" could predict the battery's retirement date better than the classic "GRU" (Gated Recurrent Unit) models. They fed these computers a special set of 13 clues about the battery's health, including a "normalized health score" that tells the computer how much energy the battery has left compared to when it was brand new.

Here is the twist: The new, high-tech Mamba models, which were designed to be super smart and efficient at reading long stories, actually stumbled. The old-school GRU model, which is like a reliable, hardworking veteran, won the race hands down. On the test batteries, the GRU was incredibly accurate, missing the true retirement date by only about 4 to 7 cycles (a cycle is one full charge and discharge). In contrast, the fancy Mamba models were off by 28 to 38 cycles. It turns out that for this specific job, the secret sauce wasn't the complexity of the computer brain, but the quality of the clues (features) they were given. When the researchers removed the most important clue—the normalized health score—the Mamba models got even worse, proving that even the smartest AI needs good data to work its magic.

The Story of the Battery Race

The Setup: A Controlled Track
The researchers used a dataset called CALCE CS2, which is like a perfectly controlled gym for batteries. These batteries were run in a lab at a steady temperature, charged and discharged at a constant speed, just like a runner on a treadmill. They picked two specific batteries, CS2_37 and CS2_38, to be the "test runners" that the computers had never seen before. The goal was to predict exactly how many more cycles these batteries could survive before they hit their "End of Life" (when they are too weak to be useful).

The Tools: Old School vs. New School
The team built a few different "coaches" (computer models) to predict the finish line:

The Veterans (LSTM and GRU): These are established, reliable models that have been used for years. They look at the history of the battery's performance step-by-step.
The Trendy Newcomers (Mamba-based models): These are the shiny new kids on the block. They use something called "Selective State-Space Models." Imagine a Mamba model as a reader who can scan a whole book in a single glance, remembering only the important parts and ignoring the fluff. The researchers created two versions:
- MambaRUL: This model tried to use "Degradation Anchor Cross-Attention." Think of this as having three special bookmarks (anchors) in the battery's life story: one for the early days, one for the middle, and one for the end. The model was supposed to use these bookmarks to focus on the right part of the story.
- PhysicsMambaRUL: This one was even more ambitious. It didn't just guess the retirement date; it also tried to guess the speed of the battery's decline and fit a mathematical curve to its life story, all while trying to make sure its guesses followed the laws of physics.

The Race: Who Won?
When the race started, the results were surprising. The GRU (the veteran) was the clear winner.

On battery CS2_37, the GRU was off by only 4.39 cycles.
On battery CS2_38, it was off by 7.48 cycles.
It was so accurate that 100% of its predictions were within 20 cycles of the true answer.

The Mamba models, however, struggled.

The standard MambaRUL was off by 28.54 cycles and 38.57 cycles.
The PhysicsMambaRUL did a bit better but still lagged behind the GRU, with errors of 13.60 and 20.49 cycles.

The researchers found that the fancy "bookmarks" (anchors) in the Mamba model didn't help as much as expected. In fact, when they tried removing the "bookmarks" and just used a basic Mamba model, it performed slightly better, though still not as well as the GRU.

The Secret Weapon: The 13 Clues
The most important discovery wasn't about the computer brain at all; it was about the clues (features) fed into the brain. The team used 13 different pieces of information, like voltage, temperature, and energy. But the star of the show was a single clue called cap_pct. This is a ratio that tells the computer, "How much of its original power does the battery have left?"

When the researchers took this one clue away from the Mamba model, the model's performance tanked. Its error jumped by 10.83 cycles on one battery and 11.67 cycles on the other. This proved that the Mamba model wasn't failing because it was too simple; it was failing because it was trying to guess the battery's health without its most obvious hint. The GRU, on the other hand, was robust enough to handle the clues perfectly, even without the Mamba's complex attention mechanisms.

The Physics Check
The researchers also tried to force the PhysicsMamba model to be more "physics-consistent" by adding a penalty if its guesses didn't match the laws of battery degradation. They found that when they turned this penalty on (with a setting called $\lambda = 0.3$ ), the model's error dropped from 19.47 to 14.72 cycles on one battery. This suggests that while the model wasn't perfect, adding a little bit of "common sense" about how batteries actually work did help it think more clearly.

The Bottom Line
The paper concludes that for this specific type of battery and this specific dataset, the "fancy new" Mamba architecture did not beat the "reliable old" GRU. The key to success wasn't the complexity of the algorithm, but the quality of the data features, especially the normalized health score. The researchers are careful to note that this is a controlled lab experiment. In the real world, where conditions are messy and unpredictable, the results might be different. But for now, in this controlled race, the simple, well-trained GRU with the right clues was the champion, leaving the high-tech Mamba models in the dust.

Technical Summary: Remaining Useful Life Estimation of Lithium-Ion Batteries

Problem Statement
The paper addresses the challenge of predicting the Remaining Useful Life (RUL) of Lithium-ion batteries, a critical function for Battery Management Systems (BMS) in electric vehicles and stationary storage. While capacity fade follows distinct electrochemical regimes—initial Solid-Electrolyte Interphase (SEI) growth, followed by Loss of Active Material (LAM), and finally accelerated degradation due to lithium plating—standard models often treat degradation sequences uniformly. Furthermore, while recent studies have proposed Selective State-Space Models (Mamba) as efficient alternatives to Transformers for long sequences, it remains unclear how much of the attainable accuracy stems from the sequence architecture versus the quality of the input feature representation. This study aims to disentangle these factors through a controlled benchmark on the CALCE CS2 dataset.

Methodology
The research evaluates two novel Mamba-based architectures against established recurrent and attention-based baselines (LSTM, GRU, Transformer) under a strictly controlled protocol.

Feature Engineering: A 13-feature physics-informed representation is constructed for each charge-discharge cycle. The core of this set is the normalized capacity ratio, $cap\_pct = C(t)/C(0)$ , which expresses cell health independent of absolute initial capacity. Other features include voltage statistics, temperature, energy metrics, and a local fade rate.
Proposed Architectures:
- MambaRUL: Utilizes a Mamba selective state-space model encoder coupled with Degradation Anchor Cross-Attention (DACA). This module employs three learnable query vectors (anchors) intended to attend to early, mid, and late degradation phases without explicit phase labels.
- PhysicsMambaRUL: Extends MambaRUL with three parallel prediction heads: (1) direct RUL regression, (2) a fade-rate-based RUL estimate, and (3) a double-exponential capacity curve fit. These are combined via learned softmax weights, and the model is trained with a physics-consistency loss ( $\lambda$ ) to penalize disagreement between the heads.
Experimental Protocol:
- Dataset: CALCE CS2 (LCO chemistry, 1.1 Ah, 25°C).
- Split: Training on CS2_35, CX2_16, CX2_33, CX2_36, CX2_37, CX2_38; Validation on CS2_34; Held-out Test on CS2_37 and CS2_38.
- Normalization: RUL targets are normalized by the complete observed lifetime of each cell ( $L_{cell}$ ). The authors explicitly note that $L_{cell}$ is an "oracle" quantity unavailable during real-world inference; thus, results represent a controlled benchmark rather than deployment-ready online accuracy.
- Baselines: All models (including baselines) are trained on the same 13 features, same data split, and same random seed (42) to isolate architectural effects.

Key Results
Contrary to the hypothesis that advanced sequence models like Mamba would outperform simpler recurrent networks, the GRU trained on the 13-feature set achieved the lowest error across all metrics.

Performance on Test Cells (CS2_37 and CS2_38):
- GRU: RMSE of 4.39 and 7.48 cycles respectively ( $R^2 > 0.99$ ). All predictions fell within 20 cycles of the true RUL (W20 = 100%).
- LSTM: Slightly higher error (6.57 and 11.71 cycles) but still highly accurate.
- PhysicsMambaRUL: RMSE of 13.60 and 20.49 cycles.
- MambaRUL: Highest error among the proposed models (28.54 and 38.57 cycles).
Ablation Findings:
- Feature Importance: Removing the $cap\_pct$ feature from the MambaRUL input increased RMSE by approximately 11 cycles on both test cells, indicating that the normalized capacity ratio is the dominant factor in prediction accuracy, outweighing the choice of sequence model.
- Anchor Count: An exploratory analysis suggested that using only 2 degradation anchors (early and late) performed better than the default 3, though this was not used for the final reported configuration.
- Physics Consistency: Applying the physics-consistency loss ( $\lambda=0.3$ ) in PhysicsMambaRUL reduced RMSE on CS2_37 from 19.47 to 14.72 cycles, though the effect was less pronounced on CS2_38.

Significance and Claims
The paper's primary contribution is a controlled benchmark demonstrating that, under the specific conditions of the CALCE CS2 dataset and the 13-feature representation used, input representation quality is more critical than sequence model complexity.

Modest Claims: The authors explicitly state that the GRU's superior performance suggests that the "feature-enhanced" approach is more effective than the proposed Mamba variants for this specific task. They caution that these results are specific to the protocol used (oracle lifetime normalization) and do not claim that Mamba is inherently inferior for battery RUL in all contexts.
Limitations: The study acknowledges that the use of the total observed lifetime for normalization limits the applicability of these results to online, real-time prediction scenarios. Additionally, the experiments were run with a single random seed, and the dataset consists of laboratory-controlled cells, excluding field-aged data or other chemistries.
Future Work: The paper identifies the need for online RUL estimation without oracle lifetime data, variance quantification across multiple seeds, and validation on diverse datasets and chemistries, particularly those relevant to Indian EV duty cycles.

In summary, the paper concludes that while Mamba-based architectures offer theoretical advantages in sequence modeling, their application to battery RUL must be carefully weighed against the efficacy of physics-informed feature engineering, which in this study proved to be the decisive factor in prediction accuracy.

The Story of the Battery Race

Technical Summary: Remaining Useful Life Estimation of Lithium-Ion Batteries

More like this