# NeuralSI: Structural Parameter Identification in Nonlinear Dynamical Systems

arXiv: https://arxiv.org/abs/2208.12771 · HTML: https://mlsanity.com/paper/2208.12771/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 43 references that are in the map.
- First posted on arXiv 26 Aug 2022.

## Builds on (most cited first, 11 of 11)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Decoupled Weight Decay Regularization](https://mlsanity.com/paper/1711.05101/) (2017)
- [Characterizing possible failure modes in physics-informed neural networks](https://mlsanity.com/paper/2109.01050/) (2021)
- [Message Passing Neural PDE Solvers](https://mlsanity.com/paper/2202.03376/) (2022)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Lie Point Symmetry Data Augmentation for Neural PDE Solvers](https://mlsanity.com/paper/2202.07643/) (2022)
- [Beyond Predictions in Neural ODEs: Identification and Interventions](https://mlsanity.com/paper/2106.12430/) (2021)
- [NeuralPDE: Modelling Dynamical Systems from Data](https://mlsanity.com/paper/2111.07671/) (2021)
- [ModelingToolkit: A Composable Graph Transformation System For Equation-Based Modeling](https://mlsanity.com/paper/2103.05244/) (2021)
- [Incorporating prior knowledge about structural constraints in model identification](https://mlsanity.com/paper/2007.04030/) (2020)

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

- [Estimating Parameter Fields in Multi-Physics PDEs from Scarce Measurements](https://mlsanity.com/paper/2509.00203/) (2025)

## Abstract (arXiv)

Structural monitoring for complex built environments often suffers from mismatch between design, laboratory testing, and actual built parameters. Additionally, real-world structural identification problems encounter many challenges. For example, the lack of accurate baseline models, high dimensionality, and complex multivariate partial differential equations (PDEs) pose significant difficulties in training and learning conventional data-driven algorithms. This paper explores a new framework, dubbed NeuralSI, for structural identification by augmenting PDEs that govern structural dynamics with neural networks. Our approach seeks to estimate nonlinear parameters from governing equations. We consider the vibration of nonlinear beams with two unknown parameters, one that represents geometric and material variations, and another that captures energy losses in the system mainly through damping. The data for parameter estimation is obtained from a limited set of measurements, which is conducive to applications in structural health monitoring where the exact state of an existing structure is typically unknown and only a limited amount of data samples can be collected in the field. The trained model can also be extrapolated under both standard and extreme conditions using the identified structural parameters. We compare with pure data-driven Neural Networks and other classical Physics-Informed Neural Networks (PINNs). Our approach reduces both interpolation and extrapolation errors in displacement distribution by two to five orders of magnitude over the baselines. Code is available at https://github.com/human-analysis/neural-structural-identification