arXiv subjects

Florian de Vuyst

Publications and source records attributed to Florian de Vuyst.

5 recordsLinked to original sources

arXiv2026

Online adaptive non-intrusive model reduction via manifold interpolation and subspace updates: application to FSI convergence acceleration

We introduce a novel online adaptive non-intrusive reduced-order modeling strategy for parameterized dynamical systems involving parameter and time-dependent reduced bases. The proposed framework is based on a unified Grassmann manifold formulation combining three key components: interpolation of local reduced subspaces for unseen parameters, geodesic online subspace updates driven by incoming high-fidelity snapshots, and a latent-space regression strategy relying on Grassmann-distance weighting and Procrustes alignment to consistently aggregate predictions from multiple local models. The adaptive reduced-order model is embedded in a partitioned fluid-structure interaction framework, where it predicts fluid interface forces to provide accurate initial guesses for the nonlinear coupling iterations, thus achieving computational speedups with no loss of accuracy. The reduced basis and the regression operators are adapted independently during the simulation and without requiring the storage of high-dimensional streaming data, preserving computational efficiency while substantially improving predictive capabilities. Numerical results on reference FSI test cases demonstrate superior accuracy with respect to static and global reduced-order models, leading to a significant reduction in the number of fixed-point iterations required for convergence. The proposed framework offers a flexible and fully non-intrusive approach for the efficient simulation of nonlinear parameter-dependent multiphysics problems.

cs.CE↗

arXiv2026

Learning features from Newton's algorithm: a way to accelerate nonlinear parametrized PDE solvers

It is well known that Newton's method converges faster when the initial guess is closer to a root of a system of nonlinear equations. In this paper, a two-stage Newton initial guess strategy is proposed by learning features from a parameter-space sampling and a database of precomputed solutions. The method uses discrete Newton trajectories to construct two complementary reduced spaces: a solution feature space, built from converged states, and a corrective search direction feature space, built from intermediate Newton increments. For an unseen parameter, a regression model is used to predict a surrogate solution approximation. Then, in a second step, a residual-minimizing correction is computed using a dedicated GMRES-based approach. The resulting state is then used as an initial guess for the high-fidelity Newton method, which completes convergence. The corrective step is computationally inexpensive since it only requires residual evaluations and the solution of a small least-squares problem. The methodology is weakly intrusive once the high-fidelity residual fields and a script-based programming interface are available. This strategy reduces the number of Newton iterations and decreases the overall CPU time. Numerical experiments on representative PDE problems show quantifiable speedups compared with standalone surrogate initialization. Significant speedups are observed. This generic approach can be applied to a broad class of large-scale nonlinear problems.

cs.LG↗

arXiv2024

Machine-Learning Enhanced Predictors for Accelerated Convergence of Partitioned Fluid-Structure Interaction Simulations

Stable partitioned techniques for simulating unsteady fluid-structure interaction (FSI) are known to be computationally expensive when high added-mass is involved. Multiple coupling strategies have been developed to accelerate these simulations, but often use predictors in the form of simple finite-difference extrapolations. In this work, we propose a non-intrusive data-driven predictor that couples reduced-order models of both the solid and fluid subproblems, providing an initial guess for the nonlinear problem of the next time step calculation. Each reduced order model is composed of a nonlinear encoder-regressor-decoder architecture and is equipped with an adaptive update strategy that adds robustness for extrapolation. In doing so, the proposed methodology leverages physics-based insights from high-fidelity solvers, thus establishing a physics-aware machine learning predictor. Using three strongly coupled FSI examples, this study demonstrates the improved convergence obtained with the new predictor and the overall computational speedup realized compared to classical approaches.

cs.CE↗

arXiv2023

Non-intrusive reduced order models for partitioned fluid-structure interactions

The main goal of this work is to develop a data-driven Reduced Order Model (ROM) strategy from high-fidelity simulation result data of a Full Order Model (FOM). The goal is to predict at lower computational cost the time evolution of solutions of Fluid-Structure Interaction (FSI) problems. For some FSI applications, the elastic solid FOM (often chosen as quasi-static) can take far more computational time than the fluid one. In this context, for the sake of performance one could only derive a ROM for the structure and try to achieve a partitioned FOM fluid solver coupled with a ROM solid one. In this paper, we present a data-driven partitioned ROM on two study cases: (i) a simplified 1D-1D FSI problem representing an axisymmetric elastic model of an arterial vessel, coupled with an incompressible fluid flow; (ii) an incompressible 2D wake flow over a cylinder facing an elastic solid with two flaps. We evaluate the accuracy and performance of the proposed ROM-FOM strategy on these cases while investigating the effects of the model's hyperparameters. We demonstrate a high prediction accuracy and significant speedup achievements using this strategy.

cs.CE↗

arXiv2013

The Logit lane assignment model: first results

The Logit lane assignment model has been introduced recently in order to describe multi-lane traffic flow from a macroscopic point of view. The model is based on the idea that each available lane has a specific utility for each driver, who chooses the lane with the highest utility. The model is expressed by a system of conservation laws with a smooth but implicitly defined flux function. The first aim of the paper is to explore on two data-sets how traffic data supports the fact that traffic speed constitutes an explanatory variable of lane assignment. Second the paper addresses the problem of discretization of the model. Several numerical schemes are proposed: Lax-Friedrichs, Euler-lagrange remap, Lagrange, and their convergence properties are illustrated on the treatment of the Riemann problem. Directions for future research are outlined.

math.OC↗