Unifying machine learning and interpolation theory via interpolating neural networks.

Area of Science:

• Computational Science and Engineering
• Artificial Intelligence in Scientific Computing
• Machine Learning for Simulation

Background:

• Current AI-driven solvers face challenges with sparse data, scalability, and high computational costs in complex system design.
• Traditional solvers and existing machine learning (ML) models struggle with efficiency and accuracy in demanding computational tasks.

Purpose of the Study:

• To introduce a novel network architecture, Interpolating Neural Network (INN), that addresses the limitations of current AI solvers.
• To develop a computationally efficient and accurate surrogate modeling technique for complex simulations.

Main Methods:

• Developed Interpolating Neural Network (INN), a hybrid architecture combining interpolation theory and tensor decomposition.
• Applied INN to construct a surrogate model for Laser Powder Bed Fusion (L-PBF) heat transfer simulation in metal additive manufacturing.
• Evaluated INN's performance against traditional partial differential equation (PDE) solvers, ML models, and physics-informed neural networks (PINNs).

Main Results:

• INN significantly reduces computational effort and memory requirements while maintaining high accuracy.
• INN demonstrates superior performance compared to traditional PDE solvers, ML models, and PINNs, especially with sparse data.
• The INN model achieved sub-10-micrometer resolution for a 10 mm path in under 15 minutes on a single GPU, outperforming ML models by 5-8 orders of magnitude.

Conclusions:

• INN provides a computationally efficient and accurate alternative for complex system design and simulation.
• The architecture enables dynamic updates of nonlinear activation and effectively handles sparse data.
• INN offers a promising new perspective for overcoming key challenges in computational science and engineering, particularly in areas like additive manufacturing.