arXiv subjects

Vanesa Guerrero

Publications and source records attributed to Vanesa Guerrero.

4 recordsLinked to original sources

arXiv2026

On leveraging constrained smooth additive regression models for global optimization

Many real-world decision-making processes rely on solving mixed-integer nonlinear programs (MINLPs). However, finding high-quality solutions to MINLPs is often computationally demanding, motivating the development of specialized algorithms to improve their tractability. In this work, we propose Mixed-Integer Smoothing Surrogate Optimization with Constraints (MISSOC), a novel optimization algorithm that builds and solves approximations of challenging MINLPs. MISSOC approximates complicating functions in an MINLP using smooth additive regression models with \unboldmath{$B-$}splines. Expert knowledge can be incorporated into the approximating functions through shape constraints related to bounds, monotonicity and curvature over the observed domain. A surrogate of the original problem is then obtained by replacing the original complicating functions with their approximations, making it more tractable in practice. MISSOC presents an innovative integration of statistical modeling into mathematical optimization and fills a gap in the literature by building surrogates that are both data-driven and knowledge-driven. The proposed algorithm is illustrated on the real-world Water Distribution Network problem and evaluated through a set of experiments that include benchmark instances and the real-world Hydro Unit Commitment problem. Together, they demonstrate that MISSOC handles MINLPs with integer variables and complicating functions appearing in the objective or in the constraints. MISSOC is evaluated with different state-of-the-art solvers and with the Sequential Convex MINLP (SC-MINLP) algorithm. The latter exploits the separable structure of the approximating functions, which are sums of piecewise univariate polynomials. The experiments show that MISSOC can obtain high-quality solutions for challenging MINLPs, particularly when used in combination with the SC-MINLP algorithm.

math.OC↗

arXiv2026

Automatic knot selection in smooth additive models

B-spline regression constitutes a widely used framework for nonparametric modeling. The performance of this methodology depends on specifying the number and placement of changepoints, known as knots, prior to the estimation process. Such knot sequence determines the dimension of the B-spline basis used to represent the regression function and the number of coefficients to be estimated. Therefore, the knots' choice affects the model's flexibility, influencing its smoothness and goodness-of-fit. Traditionally, this problem has been addressed either by explicitly selecting knots, via knot-selection algorithms, or by regularization methods, such as P-splines, which automatically tune the regressor's smoothness. The latter have become the standard in generalized additive models (GAMs). In contrast, knot-selection techniques, frequently neglected because of computational or modeling limitations, provide certain advantages which can be valuable in some contexts. In this work, we introduce a novel explicit knot-selection technique for GAMs based on an extension of the adaptive splines (A-splines) knot selection methodology, combined with a customized Fellner-Schall scheme for tuning the associated parameters. Our approach is evaluated on various synthetic and real datasets and compared with P-splines and state-of-the-art knot-selection techniques. The results indicate comparable performance, while producing models built on a substantially smaller number of basis elements.

stat.ML↗

arXiv2025

Actuation manifold from snapshot data

We propose a data-driven methodology to learn a low-dimensional manifold of controlled flows. The starting point is resolving snapshot flow data for a representative ensemble of actuations. Key enablers for the actuation manifold are isometric mapping as encoder and a combination of a neural network and a k-nearest-neighbour interpolation as decoder. This methodology is tested for the fluidic pinball, a cluster of three parallel cylinders perpendicular to the oncoming uniform flow. The centres of these cylinders are the vertices of an equilateral triangle pointing upstream. The flow is manipulated by constant rotation of the cylinders, i.e. described by three actuation parameters. The Reynolds number based on a cylinder diameter is chosen to be 30. The unforced flow yields statistically symmetric periodic shedding represented by a one-dimensional limit cycle. The proposed methodology yields a five-dimensional manifold describing a wide range of dynamics with small representation error. Interestingly, the manifold coordinates automatically unveil physically meaningful parameters. Two of them describe the downstream periodic vortex shedding. The other three describe the near-field actuation, i.e. the strength of boat-tailing, the Magnus effect and forward stagnation point. The manifold is shown to be a key enabler for control-oriented flow estimation.

physics.flu-dyn↗

arXiv2022

From snapshots to manifolds - A tale of shear flows

We propose a novel non-linear manifold learning from snapshot data and demonstrate its superiority over Proper Orthogonal Decomposition (POD) for shedding-dominated shear flows. Key enablers are isometric feature mapping, Isomap (Tenenbaum et al., 2000), as encoder and K-nearest neighbours (KNN) algorithm as decoder. The proposed technique is applied to numerical and experimental datasets including the fluidic pinball, a swirling jet, and the wake behind a couple of tandem cylinders. Analyzing the fluidic pinball, the manifold is able to describe the pitchfork bifurcation and the chaotic regime with only three feature coordinates. These coordinates are linked to vortex-shedding phases and the force coefficients. The manifold coordinates of the swirling jet are comparable to the POD mode amplitudes, yet allow for a more distinct manifold identification which is less sensitive to measurement noise. As similar observation is made for the wake of two tandem cylinders (Raiola et al., 2016). The tandem cylinders are aligned in streamwise distance which corresponds to the transition between the single bluff body and the reattachment regimes of vortex shedding. Isomap unveils these two shedding regimes while the Lissajous plots of first two POD mode amplitudes feature a single circle. The reconstruction error of the manifold model is small compared to the fluctuation level, indicating that the low embedding dimensions contains the coherent structure dynamics. The proposed Isomap-KNN manifold learner is expected to be of large importance in estimation, dynamic modeling and control for large range of configurations with dominant coherent structures.

physics.flu-dyn↗