Model order reduction for parametrized variational inequalities: application to crowd motion
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911649423687680 |
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| author | Sambataro, Giulia Ehrlacher, Virginie |
| author_facet | Sambataro, Giulia Ehrlacher, Virginie |
| contents | This work investigates model order reduction for time-dependent parametrized variational inequalities, with a focus on discrete contact problems. As a prototypical example, we consider an agent-based crowd model [Maury et al., 2011] in which agent velocities are obtained at each time step from a constrained least-squares problem. Geometric parameter variations induce significant variability in both agent positions and contact forces, leading to a slowly decaying Kolmogorov $n$-width of the solution manifold. We propose a nonlinear approach that combines a linear reduced-order model with a deep-learning-based correction. The method utilizes a greedy index selection (gIS) algorithm for compressing Lagrange multipliers and Proper Orthogonal Decomposition (POD) applied to velocity snapshots. Additionally, we explore hyper-reduction techniques, comparing the Empirical Interpolation Method (EIM) and the Empirical Quadrature (EQ) procedure from both computational complexity and accuracy perspectives. Finally, we demonstrate the applicability of the methodology in a complex scenario involving many agents in a highly congested geometric configuration. This work represents the first attempt to apply model order reduction to a discrete contact problem of the type introduced in [Maury et al., 2011] and paves the way for future advancements in nonlinear MOR specifically for this class of problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04037 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Model order reduction for parametrized variational inequalities: application to crowd motion Sambataro, Giulia Ehrlacher, Virginie Numerical Analysis This work investigates model order reduction for time-dependent parametrized variational inequalities, with a focus on discrete contact problems. As a prototypical example, we consider an agent-based crowd model [Maury et al., 2011] in which agent velocities are obtained at each time step from a constrained least-squares problem. Geometric parameter variations induce significant variability in both agent positions and contact forces, leading to a slowly decaying Kolmogorov $n$-width of the solution manifold. We propose a nonlinear approach that combines a linear reduced-order model with a deep-learning-based correction. The method utilizes a greedy index selection (gIS) algorithm for compressing Lagrange multipliers and Proper Orthogonal Decomposition (POD) applied to velocity snapshots. Additionally, we explore hyper-reduction techniques, comparing the Empirical Interpolation Method (EIM) and the Empirical Quadrature (EQ) procedure from both computational complexity and accuracy perspectives. Finally, we demonstrate the applicability of the methodology in a complex scenario involving many agents in a highly congested geometric configuration. This work represents the first attempt to apply model order reduction to a discrete contact problem of the type introduced in [Maury et al., 2011] and paves the way for future advancements in nonlinear MOR specifically for this class of problems. |
| title | Model order reduction for parametrized variational inequalities: application to crowd motion |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2605.04037 |