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

arXiv: https://arxiv.org/abs/2404.10296 · HTML: https://mlsanity.com/paper/2404.10296/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 44 references that are in the map.
- First posted on arXiv 16 Apr 2024.

## Builds on (most cited first, 6 of 6)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [RT-1: Robotics Transformer for Real-World Control at Scale](https://mlsanity.com/paper/2212.06817/) (2022)
- [Variational Physics-Informed Neural Networks For Solving Partial Differential Equations](https://mlsanity.com/paper/1912.00873/) (2019)
- [Learning Activation Functions to Improve Deep Neural Networks](https://mlsanity.com/paper/1412.6830/) (2014)
- [Statistical Parameterized Physics-Based Machine Learning Digital Twin Models for Laser Powder Bed Fusion Process](https://mlsanity.com/paper/2311.07821/) (2023)

## Built on by (most cited first, 1 of 1)

- [KHRONOS: a Kernel-Based Neural Architecture for Rapid, Resource-Efficient Scientific Computation](https://mlsanity.com/paper/2505.13315/) (2025)

## Abstract (arXiv)

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.