Taming High-Dimensional Dynamics: Learning Optimal Projections onto Spectral Submanifolds
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918135451353088 |
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| author | Buurmeijer, Hugo Pabon, Luis A. Alora, John Irvin Kaundinya, Roshan S. Haller, George Pavone, Marco |
| author_facet | Buurmeijer, Hugo Pabon, Luis A. Alora, John Irvin Kaundinya, Roshan S. Haller, George Pavone, Marco |
| contents | High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on orthogonal projections, a simplification that may lead to large prediction errors. In this work, we derive optimality of fiber-aligned projections onto spectral submanifolds, preserving the nonlinear geometric structure and minimizing long-term prediction error. We propose a data-driven procedure to learn these projections from trajectories and demonstrate its effectiveness through a 180-dimensional robotic system. Our reduced-order models achieve up to fivefold improvement in trajectory tracking accuracy under model predictive control compared to the state of the art. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03157 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Taming High-Dimensional Dynamics: Learning Optimal Projections onto Spectral Submanifolds Buurmeijer, Hugo Pabon, Luis A. Alora, John Irvin Kaundinya, Roshan S. Haller, George Pavone, Marco Systems and Control Robotics High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on orthogonal projections, a simplification that may lead to large prediction errors. In this work, we derive optimality of fiber-aligned projections onto spectral submanifolds, preserving the nonlinear geometric structure and minimizing long-term prediction error. We propose a data-driven procedure to learn these projections from trajectories and demonstrate its effectiveness through a 180-dimensional robotic system. Our reduced-order models achieve up to fivefold improvement in trajectory tracking accuracy under model predictive control compared to the state of the art. |
| title | Taming High-Dimensional Dynamics: Learning Optimal Projections onto Spectral Submanifolds |
| topic | Systems and Control Robotics |
| url | https://arxiv.org/abs/2504.03157 |