Unifying machine learning and interpolation theory via interpolating neural networks

Chanwook Park, Sourav Saha, Jiachen Guo, Hantao Zhang, Xiaoyu Xie, Miguel A. Bessa, Dong Qian, Wei Chen, Gregory J. Wanger, Jian Cao, Thomas J. R. Hughes and Wing Kam Liu ()
Additional contact information
Chanwook Park: Northwestern University
Sourav Saha: Virginia Polytechnic Institute and State University
Jiachen Guo: LLC
Hantao Zhang: Northwestern University
Xiaoyu Xie: Northwestern University
Miguel A. Bessa: Brown University
Dong Qian: LLC
Wei Chen: Northwestern University
Gregory J. Wanger: Northwestern University
Jian Cao: Northwestern University
Thomas J. R. Hughes: University of Texas at Austin
Wing Kam Liu: Northwestern University

Nature Communications, 2025, vol. 16, issue 1, 1-12

Abstract: Abstract Computational science and engineering are shifting toward data-centric, optimization-based, and self-correcting solvers with artificial intelligence. This transition faces challenges such as low accuracy with sparse data, poor scalability, and high computational cost in complex system design. This work introduces Interpolating Neural Network (INN)-a network architecture blending interpolation theory and tensor decomposition. INN significantly reduces computational effort and memory requirements while maintaining high accuracy. Thus, it outperforms traditional partial differential equation (PDE) solvers, machine learning (ML) models, and physics-informed neural networks (PINNs). It also efficiently handles sparse data and enables dynamic updates of nonlinear activation. Demonstrated in metal additive manufacturing, INN rapidly constructs an accurate surrogate model of Laser Powder Bed Fusion (L-PBF) heat transfer simulation. It achieves sub-10-micrometer resolution for a 10 mm path in under 15 minutes on a single GPU, which is 5-8 orders of magnitude faster than competing ML models. This offers a new perspective for addressing challenges in computational science and engineering.

Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.nature.com/articles/s41467-025-63790-8 Abstract (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nat:natcom:v:16:y:2025:i:1:d:10.1038_s41467-025-63790-8

Ordering information: This journal article can be ordered from
https://www.nature.com/ncomms/

DOI: 10.1038/s41467-025-63790-8

Access Statistics for this article

Nature Communications is currently edited by Nathalie Le Bot, Enda Bergin and Fiona Gillespie

More articles in Nature Communications from Nature
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().