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

TL;DR

The paper introduces an interpolating neural network (INN) that unifies machine learning and interpolation theory, significantly reducing model complexity and enhancing efficiency in engineering simulations.

Contribution

It presents a novel INN framework based on interpolation theory and tensor decomposition, enabling faster and more accurate surrogate modeling in engineering applications.

Findings

INN achieves comparable accuracy with fewer parameters than traditional neural networks.

In metal additive manufacturing, INN constructs high-resolution surrogate models rapidly.

Demonstrates sub-10-micrometer resolution in heat transfer simulation within 15 minutes on a single GPU.

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.