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An explainable artificial intelligence framework enabled by a separable neural architecture
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DOI：10.1007/s00466-025-02719-w.png)
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Abstract
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Data-driven science and computation have advanced immensely to construct complex functional relationships using trainable parameters. However, efficiently discovering interpretable and accurate closed-form expressions from complex dataset remains a challenge. This article presents a novel approach that uses an accurate, frugal, fast, separable, and scalable neural architecture with symbolic regression to discover closed-form expressions from limited observation. The article presents a two-step algorithm with a separability checker embedded in it. The model’s accuracy and efficiency are tested on a canonical benchmark suite, as well as dynamical system discovery, and identification from noisy data. The model generally shows outstanding approximation capability in these benchmarks, producing orders of magnitude smaller errors compared to reference data and traditional symbolic regression. Later, the model is applied to three engineering applications: i) discovering a closed-form fatigue equation, ii) identification of hardness from micro-indentation test data, and iii) discovering an expression for the yield surface with data. In every case, the model outperformed the reference methods used in the literature.
Keywords:
Interpretable machine learning
Hierarchical deep learning neural network
Data-driven model discovery
Indentation
Fatigue
Yield-surface
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