arXiv subjects

Claire Sarrat

Publications and source records attributed to Claire Sarrat.

2 recordsLinked to original sources

arXiv2026

Non-intrusive nonlinear reduced-order modeling with variable projection

This work presents a method for constructing nonlinear reduced-order models from input-output time-domain data. The proposed approach, termed Mixed Interpolatory Inference with Variable Projection (MIIvp), exploits the fact that the considered class of nonlinear state-space models is linear in the output equation parameters. By applying the Variable Projection (VarPro) algorithm, the optimization is restricted to the state equation parameters alone, while the output equation parameters are recovered via linear least squares. As a consequence, the output dimension does not enter the nonlinear optimization parameter vector, making the method well suited for systems with very high-dimensional outputs, a setting where many other approaches become computationally prohibitive. Under mild assumptions, it is shown that MIIvp can recover the true model parameters up to similarity. The method is first validated on a synthetic bilinear system, where it achieves machine-precision accuracy and recovers the true eigenvalues. MIIvp is then compared with existing methods on two experimental benchmarks from the nonlinear system identification literature. These numerical experiments showcase both the validity and the limitations of the proposed approach. Finally, directions for improvements and future work are outlined.

eess.SY↗

arXiv2020

Mixed interpolatory and inference non-intrusive reduced order modeling with application to pollutants dispersion

On the basis of input-output time-domain data collected from a complex simulator, this paper proposes a constructive methodology to infer a reduced-order linear, bilinear or quadratic time invariant dynamical model reproducing the underlying phenomena. The approach is essentially based on linear dynamical systems and approximation theory. More specifically, it sequentially involves the interpolatory Pencil and Loewner framework, known to be both very versatile and scalable to large-scale data sets, and a linear least square problem involving the raw data and reduced internal variables. With respect to intrusive methods, no prior knowledge on the operator is needed. In addition, compared to the traditional non-intrusive operator inference ones, the proposed approach alleviates the need of measuring the original full-order model internal variables. It is thus applicable to a wider application range than standard intrusive and non-intrusive methods. The rationale is successfully applied on a large eddy simulation of a pollutants dispersion case over an airport area involving multi-scale and multi-physics dynamical phenomena. Despite the simplicity of the resulting low complexity model, the proposed approach shows satisfactory results to predict the pollutants plume pattern while being significantly faster to simulate.

math.DS↗