Technical Summary: KAN-Therm

Problem Statement

Reliable operation of Lithium-ion batteries is critical for safety and longevity, particularly in safety-critical applications like electric vehicles and smart grids. A key challenge is the accurate real-time estimation of the battery core temperature, which is inaccessible to direct measurement. While high-fidelity physics-based models (e.g., H∞ observers, Kalman filters) exist, they suffer from high computational demands, parameterization difficulties, and poor observability, making them unsuitable for resource-constrained physical Battery Management Systems (BMS). Conversely, existing data-driven approaches (e.g., MLPs, LSTMs, XGBoost) offer faster estimation but often require significant memory overhead and computational resources to store complex network structures, creating a trade-off between accuracy and deployability on embedded hardware.

Methodology

The authors propose KAN-Therm, a lightweight, data-driven thermal model based on Kolmogorov-Arnold Networks (KANs) to estimate the core temperature of a cylindrical battery cell.

1. Theoretical Foundation

Unlike traditional Multi-Layer Perceptrons (MLPs) that use fixed nonlinear activation functions with learnable linear weights, KANs replace scalar weights with learnable univariate functions (parameterized by B-splines) on the edges. This architecture is grounded in the Kolmogorov-Arnold representation theorem, allowing the network to capture complex nonlinear relationships with fewer parameters and enhanced interpretability.

2. Data Generation

Training and validation data were generated using a lumped parameter thermal model of a 2.3Ah cylindrical LiFePO4–LiC6 battery cell. The model simulates core temperature ($T_1$), surface temperature ($T_2$), and coolant temperature ($T_\infty$) dynamics under various conditions:

• Inputs: Applied current ($I$), cooling power ($\dot{Q}_c$), coolant temperature ($T_\infty$), and surface temperature ($T_2$).
• Scenarios: Data was collected from Urban Dynamometer Driving Schedule (UDDS), US06, and VEIL2NREL drive cycles, as well as constant current (CC) charging profiles ranging from 0.9C to 10C.
• Noise: Realistic sensor noise (Gaussian noise with $\sigma=0.015K$ for temperature and $\sigma=0.006A$ for current) was added to simulate physical measurements.

3. Model Architecture and Training

• Structure: The KAN-Therm model utilizes a compact architecture with an input layer of 4 nodes, a hidden layer of 1 node, and an output layer of 1 node (configuration [[4, 1, 1]]).
• Hyperparameter Optimization: An exhaustive grid search was conducted to determine optimal settings, including spline order ($k=3$), grid intervals ($G=2$), sparsification penalties ($\lambda, \nu_1, \nu_2$), and training epochs (70).
• Loss Function: The training objective minimizes a combination of mean squared prediction error and regularization terms (L1-norm and self-entropy) to enforce model sparsity and compactness.
• Baselines: The model was compared against four state-of-the-art benchmarks: MLP, RNN, LSTM, and XGBoost, all tuned via grid search.

Key Contributions

1. Development of KAN-Therm: The paper introduces a specific KAN-based architecture tailored for battery core temperature estimation, demonstrating that learnable activation functions can effectively model thermal dynamics with extreme parameter efficiency.
2. Optimization for Physical BMS: Through rigorous hyperparameter tuning, the authors identified a configuration that balances accuracy with the strict memory and computational constraints of physical BMS hardware (e.g., systems with limited FRAM).
3. Comprehensive Benchmarking: The study provides a detailed comparison of KAN against traditional neural networks and tree-based models across five metrics: parameter count, estimation time, and RMSE (training, validation, and testing).

Results

The performance comparison on a test dataset (including constant current and dynamic VEIL2NREL profiles) yielded the following findings:

• Parameter Efficiency: KAN-Therm is the most compact model, requiring only 25 learnable parameters. This is significantly fewer than the RNN (121), MLP (369), LSTM (877), and XGBoost (6,000).
• Computational Speed: KAN-Therm achieved the fastest estimation time at 0.0395 µs per sample. It was approximately 21.7 times faster than the RNN, 12.5 times faster than the LSTM, and 20.4 times faster than XGBoost. It also outperformed the physics-based numerical integration model (1.3 µs).
• Accuracy:
  • Testing RMSE: The RNN achieved the lowest testing RMSE (0.0334 K), followed by LSTM (0.0359 K). KAN-Therm achieved a testing RMSE of 0.0477 K.
  • Error Analysis: The difference in RMSE between the best-performing RNN and KAN-Therm is 0.0143 K, which the authors note is comparable to the sensor noise level (0.015 K).
  • Trade-off: While KAN-Therm has a slightly higher RMSE than the RNN and LSTM, it offers a superior balance of accuracy and efficiency. The relative error of KAN-Therm is approximately 0.0125%, deemed sufficient for downstream safety applications.

Significance and Claims

The paper claims that KAN-Therm successfully addresses the dichotomy between desired estimation accuracy and real-world practicality in battery management. By leveraging the parameter efficiency and interpretability of KANs, the model provides a lightweight alternative suitable for deployment on resource-constrained physical BMS hardware where high-fidelity models are too computationally expensive and standard neural networks are too memory-intensive.

The authors emphasize that while KAN-Therm does not strictly outperform RNNs in raw accuracy, its massive reduction in parameter count (79.3% fewer than RNN) and inference time (21.7x faster) makes it a viable and scalable solution for real-time, safety-critical thermal monitoring in embedded systems. The work suggests that KANs can effectively replace more complex architectures in scenarios where computational resources are limited.