# Adaptive Digital Twin of Sheet Metal Forming via Proper Orthogonal Decomposition-Based Koopman Operator with Model Predictive Control

arXiv: https://arxiv.org/abs/2511.10852 · HTML: https://mlsanity.com/paper/2511.10852/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 34 references that are in the map.
- First posted on arXiv 13 Nov 2025.

## Builds on (most cited first, 10 of 10)

- [Inception-v4, Inception-ResNet and the Impact of Residual Connections on Learning](https://mlsanity.com/paper/1602.07261/) (2016)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scale](https://mlsanity.com/paper/2012.05841/) (2020)
- [Active Learning of Dynamics for Data-Driven Control Using Koopman Operators](https://mlsanity.com/paper/1906.05194/) (2019)
- [Extended Dynamic Mode Decomposition with Learned Koopman Eigenfunctions for Prediction and Control](https://mlsanity.com/paper/1911.08751/) (2019)
- [Towards a Digital Twin Framework in Additive Manufacturing: Machine Learning and Bayesian Optimization for Time Series Process Optimization](https://mlsanity.com/paper/2402.17718/) (2024)
- [Real-Time Decision-Making for Digital Twin in Additive Manufacturing with Model Predictive Control using Time-Series Deep Neural Networks](https://mlsanity.com/paper/2501.07601/) (2025)
- [Uncertainty-Aware Digital Twins: Robust Model Predictive Control using Time-Series Deep Quantile Learning](https://mlsanity.com/paper/2501.10337/) (2025)
- [An Attention-based Spatio-Temporal Neural Operator for Evolving Physics](https://mlsanity.com/paper/2506.11328/) (2025)

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

- [A Continual Validation, Updating, and Decision-Making Framework for Self-Adaptive Digital Twins via Robust Model Predictive Control: A Case Study in Additive Manufacturing](https://mlsanity.com/paper/2607.18164/) (2026)

## Abstract (arXiv)

Digital Twin (DT) technologies are transforming manufacturing by enabling real-time prediction, monitoring, and control of complex processes. Yet, applying DT to deformation-based metal forming remains challenging because of the strongly coupled spatial-temporal behavior and the nonlinear relationship between toolpath and material response. For instance, sheet-metal forming by the English wheel, a highly flexible but artisan-dependent process, still lacks digital counterparts that can autonomously plan and adapt forming strategies. This study presents an adaptive DT framework that integrates Proper Orthogonal Decomposition (POD) for physics-aware dimensionality reduction with a Koopman operator for representing nonlinear system in a linear lifted space for the real-time decision-making via model predictive control (MPC). To accommodate evolving process conditions or material states, an online Recursive Least Squares (RLS) algorithm is introduced to update the operator coefficients in real time, enabling continuous adaptation of the DT model as new deformation data become available. The proposed framework is experimentally demonstrated on a robotic English Wheel sheet metal forming system, where deformation fields are measured and modeled under varying toolpaths. Results show that the adaptive DT is capable of controlling the forming process to achieve the given target shape by effectively capturing non-stationary process behaviors. Beyond this case study, the proposed framework establishes a generalizable approach for interpretable, adaptive, and computationally-efficient DT of nonlinear manufacturing systems, bridging reduced-order physics representations with data-driven adaptability to support autonomous process control and optimization.