Kolmogorov-Arnold Networks Applied to Materials Property Prediction

Technical Summary: Kolmogorov-Arnold Networks Applied to Materials Property Prediction

Problem Statement
Kolmogorov-Arnold Networks (KANs) have recently emerged as an alternative to traditional Multilayer Perceptron Neural Networks (MLP-NNs), offering potential advantages in parameter efficiency and interpretability by learning activation functions (via splines) rather than linear weights. While KANs have shown promise in synthetic datasets and specific physics problems, their efficacy in the domain of materials science—specifically for predicting diverse materials properties on small-to-medium datasets—remains under-explored. In materials property prediction, Random Forest (RF) models often outperform MLPs on small datasets with minimal tuning. The authors investigate whether KANs can compete with these established "workhorse" models and whether they can provide interpretable, closed-form expressions for complex materials phenomena without extensive domain expertise.

Methodology
The study evaluated KAN performance across 33 distinct materials property datasets, comprising both experimental and calculated data (e.g., bandgaps, yield strengths, thermal expansion, and reactor pressure vessel embrittlement). The datasets ranged from ~100 to ~9,000 data points and utilized elemental or material-specific features.

The authors employed a three-tiered evaluation strategy:

1. Standard KANs: Unoptimized 2-layer architectures (N-2N+1-1) derived directly from the Kolmogorov-Arnold theorem were compared against Random Forest models.
2. Manual Tuning: A subset of seven properties was analyzed by manually adjusting the number of hidden layers (up to 3) and node counts to assess the impact of modest architectural changes.
3. Automated Optimization: Using the Optuna framework, hyperparameters (grid intervals, regularization, spline degrees, layer counts, and node counts) were optimized for 24 datasets to determine the upper bound of KAN performance.
4. Case Study (RPV Embrittlement): A specific focus was placed on predicting Reactor Pressure Vessel (RPV) steel transition temperature shifts (TTS). Here, the authors compared KANs against deep MLP ensembles (>1M parameters) and hand-tuned analytical models (E900). They explored "Tiny KANs" (<50 parameters) and attempted to fit closed-form analytical expressions to the learned spline activation functions.

Key Results

• Standard vs. Random Forest: On average, standard 2-layer KANs performed worse than Random Forest models. Across 31 comparable datasets, Random Forest yielded better fits for 19 properties, while KANs were superior for only 12. When KANs underperformed, the error reduction by Random Forest was substantial (average 36.3% improvement in normalized RMSE), whereas KAN improvements over Random Forest were modest (average 8.5%).
• Impact of Tuning: Modest manual tuning of the network architecture (adding layers or adjusting node counts) reduced prediction errors by an average of 10–20% compared to standard KANs. After such tuning, optimized KANs achieved performance comparable to Random Forest on average.
• Stability: KANs were found to be more difficult to fit than Random Forests, exhibiting greater sensitivity to architecture and hyperparameters, as well as occasional numerical instability leading to high error outliers.
• RPV Embrittlement Case Study:
  • Parameter Efficiency: An optimized KAN achieved accuracy comparable to a deep MLP ensemble (RMSE ~12.4 °C vs. 12.2 °C) while using ~93 times fewer parameters.
  • Tiny Models: "Tiny KANs" with fewer than 50 parameters achieved RMSEs (17.2–17.8 °C) essentially identical to the industry-standard, hand-tuned E900 model (17.5 °C), which required decades of domain expertise to develop.
  • Interpretability: By pruning a Tiny KAN and fitting closed-form functions to its activation nodes, the authors derived an analytical expression with 22 parameters. This closed-form model achieved an RMSE of 14.4 °C, comparable to the hand-tuned E900 model (13.4 °C), but was generated purely through data-centric methods in a matter of hours.

Significance and Claims
The paper concludes that while standard, unoptimized KANs do not currently outperform Random Forests in general materials property prediction, they are competitive regression models that warrant inclusion in the standard toolkit for materials scientists. The authors assert that KANs should be explored as a standard model, particularly when interpretability is desired.

The primary significance of the work lies in the demonstration of KANs' ability to bridge the gap between "black-box" deep learning and traditional hand-tuned physics models. Specifically, the RPV study suggests that KANs can:

1. Replicate the accuracy of deep neural networks with orders of magnitude fewer parameters.
2. Generate simple, interpretable, closed-form expressions that rival models developed by experts with deep domain knowledge, but with significantly less development time and no requirement for manual functional form selection.

The authors maintain a modest tone, noting that while KANs show promise, they currently require more tuning effort than Random Forests and are not yet a universal replacement for established methods. They recommend starting with Random Forests for small datasets but exploring KANs when simplified, interpretable models are a priority.