Interpolating neural network: A novel unification of machine learning and interpolation theory

• URL: http://arxiv.org/abs/2404.10296v5
• Date: Mon, 25 Nov 2024 15:00:32 GMT
• Title: Interpolating neural network: A novel unification of machine learning and interpolation theory
• Authors: Chanwook Park, Sourav Saha, Jiachen Guo, Hantao Zhang, Xiaoyu Xie, Miguel A. Bessa, Dong Qian, Wei Chen, Gregory J. Wagner, Jian Cao, Wing Kam Liu,
• Abstract summary: We introduce an interpolating neural network (INN) to realize Engineering Software 2.0. INN offers fewer trainable/solvable parameters for comparable model accuracy than traditional multi-layer perceptron (MLP) or physics-informed neural networks (PINN)
• Score: 6.778453409974683
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Artificial intelligence (AI) has revolutionized software development, shifting from task-specific codes (Software 1.0) to neural network-based approaches (Software 2.0). However, applying this transition in engineering software presents challenges, including low surrogate model accuracy, the curse of dimensionality in inverse design, and rising complexity in physical simulations. We introduce an interpolating neural network (INN), grounded in interpolation theory and tensor decomposition, to realize Engineering Software 2.0 by advancing data training, partial differential equation solving, and parameter calibration. INN offers orders of magnitude fewer trainable/solvable parameters for comparable model accuracy than traditional multi-layer perceptron (MLP) or physics-informed neural networks (PINN). Demonstrated in metal additive manufacturing, INN rapidly constructs an accurate surrogate model of Laser Powder Bed Fusion (L-PBF) heat transfer simulation, achieving sub-10-micrometer resolution for a 10 mm path in under 15 minutes on a single GPU. This makes a transformative step forward across all domains essential to engineering software.

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