# Interpolating Neural Network-Tensor Decomposition (INN-TD): a scalable and interpretable approach for large-scale physics-based problems

arXiv: https://arxiv.org/abs/2503.02041 · HTML: https://mlsanity.com/paper/2503.02041/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Mar 2025.

## Built on by (most cited first, 4 of 4)

- [Bayesian Interpolating Neural Network (B-INN): a scalable and reliable Bayesian model for large-scale physical systems](https://mlsanity.com/paper/2601.22860/) (2026)
- [PiGRAND: Physics-informed Graph Neural Diffusion for Intelligent Additive Manufacturing](https://mlsanity.com/paper/2603.15194/) (2026)
- [Neural Operators as Efficient Function Interpolators](https://mlsanity.com/paper/2605.07792/) (2026)
- [S2-PINN: Stochastic Separable Physics-Informed Neural Networks](https://mlsanity.com/paper/2610.03303/) (2026)

## Abstract (arXiv)

Deep learning has been extensively employed as a powerful function approximator for modeling physics-based problems described by partial differential equations (PDEs). Despite their popularity, standard deep learning models often demand prohibitively large computational resources and yield limited accuracy when scaling to large-scale, high-dimensional physical problems. Their black-box nature further hinders the application in industrial problems where interpretability and high precision are critical. To overcome these challenges, this paper introduces Interpolating Neural Network-Tensor Decomposition (INN-TD), a scalable and interpretable framework that has the merits of both machine learning and finite element methods for modeling large-scale physical systems. By integrating locally supported interpolation functions from finite element into the network architecture, INN-TD achieves a sparse learning structure with enhanced accuracy, faster training/solving speed, and reduced memory footprint. This makes it particularly effective for tackling large-scale high-dimensional parametric PDEs in training, solving, and inverse optimization tasks in physical problems where high precision is required.