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A Practitioner's Guide to Automatic Kernel Search for Gaussian Processes in Battery Applications

Huang Zhang, Xixi Liu, Faisal Altaf, Torsten Wik

TL;DR

The paper tackles the challenge of kernel selection for Gaussian Process regression in battery-related data by applying an automatic kernel search that builds composite kernels from a base set using greedy, level-wise expansion and evaluates candidates with model-evidence criteria. It compares AIC, BIC, and Laplace-based approximations, finding that composite kernels consistently outperform the baseline Ma5 in two numerical tasks: battery capacity estimation and residual load prediction, with BIC typically providing the best trade-off between accuracy and computational cost. The Laplace approach yields strong performance but at a higher computational burden, whereas AIC tends to be less favorable for overall trade-offs. The work provides practical guidance for practitioners seeking automated, scalable kernel design in real-world battery analytics and highlights directions for improving scalability and cross-device information sharing.

Abstract

Gaussian process (GP) models have been used in a wide range of battery applications, in which different kernels were manually selected with considerable expertise. However, to capture complex relationships in the ever-growing amount of real-world data, selecting a suitable kernel for the GP model in battery applications is increasingly challenging. In this work, we first review existing GP kernels used in battery applications and then extend an automatic kernel search method with a new base kernel and model selection criteria. The GP models with composite kernels outperform the baseline kernel in two numerical examples of battery applications, i.e., battery capacity estimation and residual load prediction. Particularly, the results indicate that the Bayesian Information Criterion may be the best model selection criterion as it achieves a good trade-off between kernel performance and computational complexity. This work should, therefore, be of value to practitioners wishing to automate their kernel search process in battery applications.

A Practitioner's Guide to Automatic Kernel Search for Gaussian Processes in Battery Applications

TL;DR

The paper tackles the challenge of kernel selection for Gaussian Process regression in battery-related data by applying an automatic kernel search that builds composite kernels from a base set using greedy, level-wise expansion and evaluates candidates with model-evidence criteria. It compares AIC, BIC, and Laplace-based approximations, finding that composite kernels consistently outperform the baseline Ma5 in two numerical tasks: battery capacity estimation and residual load prediction, with BIC typically providing the best trade-off between accuracy and computational cost. The Laplace approach yields strong performance but at a higher computational burden, whereas AIC tends to be less favorable for overall trade-offs. The work provides practical guidance for practitioners seeking automated, scalable kernel design in real-world battery analytics and highlights directions for improving scalability and cross-device information sharing.

Abstract

Gaussian process (GP) models have been used in a wide range of battery applications, in which different kernels were manually selected with considerable expertise. However, to capture complex relationships in the ever-growing amount of real-world data, selecting a suitable kernel for the GP model in battery applications is increasingly challenging. In this work, we first review existing GP kernels used in battery applications and then extend an automatic kernel search method with a new base kernel and model selection criteria. The GP models with composite kernels outperform the baseline kernel in two numerical examples of battery applications, i.e., battery capacity estimation and residual load prediction. Particularly, the results indicate that the Bayesian Information Criterion may be the best model selection criterion as it achieves a good trade-off between kernel performance and computational complexity. This work should, therefore, be of value to practitioners wishing to automate their kernel search process in battery applications.
Paper Structure (20 sections, 16 equations, 4 figures, 3 tables, 1 algorithm)

This paper contains 20 sections, 16 equations, 4 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Gaussian Process Regression
  3. Hyperparameter Optimization
  4. Inference
  5. Automatic Kernel Search Method
  6. Base Kernels and Operations
  7. Model Selection Criteria
  8. Kernel Search Algorithms
  9. Numerical Examples
  10. Example 1 - Battery Capacity Estimation
  11. Battery aging dataset
  12. Feature engineering
  13. Train-test split
  14. Kernel search and performance evaluation
  15. Example 2 - Residual Load Demand Prediction
  16. ...and 5 more sections

Figures (4)

  • Figure 1: One full charge-discharge cycle of a sample cell [W4] in the dataset.
  • Figure 2: Capacity change versus Oxford 3 features at one stratified train-test split.
  • Figure 3: Predicted versus observed $\Delta Q$ (left) and predicted capacity versus time (right) of a sample cell [W8] in the test set. Note that the composite kernel (Ma5 $\times$ Ma5 $\times$ Pe) found using Laplace approximation is used here.
  • Figure 4: Predicted versus observed residual load demand (left) and predicted residual load demand versus time (right) over 24 hours in the test set. Note that the RQ kernel found using Laplace approximation is used here.

Theorems & Definitions (2)

  • Definition III.1: Stationary Kernel Functions
  • Definition III.2: Non-Stationary Kernel Functions