# Data-free Non-intrusive Model Reduction for Nonlinear Finite Element Models via Spectral Submanifolds

arXiv: https://arxiv.org/abs/2409.10126 · HTML: https://mlsanity.com/paper/2409.10126/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2024.

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

- [A discrete physics-informed training for projection-based reduced order models with neural networks](https://mlsanity.com/paper/2504.13875/) (2025)

## Abstract (arXiv)

The theory of spectral submanifolds (SSMs) has emerged as a powerful tool for constructing rigorous, low-dimensional reduced-order models (ROMs) of high-dimensional nonlinear mechanical systems. A direct computation of SSMs requires explicit knowledge of nonlinear coefficients in the equations of motion, which limits their applicability to generic finite-element (FE) solvers. Here, we propose a non-intrusive algorithm for the computation of the SSMs and the associated ROMs up to arbitrary polynomial orders. This non-intrusive algorithm only requires system nonlinearity as a black box and hence, enables SSM-based model reduction via generic finite-element software. Our expressions and algorithms are valid for systems with up to cubic-order nonlinearities, including velocity-dependent nonlinear terms, asymmetric damping, and stiffness matrices, and hence work for a large class of mechanics problems. We demonstrate the effectiveness of the proposed non-intrusive approach over a variety of FE examples of increasing complexity, including a micro-resonator FE model containing more than a million degrees of freedom.