Methodological evolution of SESM: toward an adaptive and scalable version through new learning schemes and dimensionality-reduction strategies

This proposal addresses the methodological evolution of the surrogate model known as SESM (Sparse-Encoded Surrogate Model), with the aim of developing an adaptive and scalable version. The work is framed within the research line of mathematical modeling, optimization, and machine learning, applied to high-computational-cost and high-dimensional problems, and represents a continuation of the previous project entitled “Mejoramiento del modelo sustituto basado en codificación dispersa denominado SESM”, in which high accuracy with limited data was demonstrated.
The central research problem arises from the limitations of classical surrogate modeling approaches, which tend to lose accuracy and efficiency in scenarios characterized by high dimensionality, nonlinear coupling, and limited data availability. Although SESM has shown advantages in overcoming some of these challenges, its current structure faces three main issues: the rigidity of dictionaries based solely on Gaussian functions, the absence of adaptive sampling mechanisms, and the lack of robust dimensionality reduction strategies to ensure scalability in large decision spaces.
The importance and relevance of this research lie in its potential to extend the use of surrogate models to real-world, high-complexity problems, where experimental or numerical evaluations are costly or even infeasible. The proposal seeks to integrate principles of signal processing, machine learning, search space exploration, and dimensionality reduction within a unified framework capable of efficiently representing complex functions, reducing uncertainty in critical regions, and maintaining accuracy in large-scale spaces. This approach represents a novel methodological advancement in the field of functional modeling and contributes to the efficient optimization of computational resources in industrial, scientific, and engineering contexts.
The general objective of the project is to develop enhancement strategies for the SESM model through the incorporation of adaptive dictionaries, dimensionality reduction schemes, and dynamic mechanisms for selecting new training points, in order to strengthen its accuracy, generalization capability, and applicability to real-world problems.
Methodologically, the project is organized into three complementary axes: (i) the development of adaptive dictionaries that combine different families of basis functions; (ii) the implementation of adaptive sampling or active learning techniques to refine the model in high-uncertainty regions; and (iii) the integration of dimensionality reduction strategies to mitigate accuracy loss associated with the curse of dimensionality.
The expected impact encompasses both scientific innovation and practical application. On one hand, the project will generate a modular, reproducible, and open-source surrogate model, useful to the scientific and industrial communities; on the other hand, it will strengthen an interdisciplinary research line at the Instituto Tecnológico de Costa Rica (ITCR), linking applied mathematics, engineering, and computational science. In the long term, the evolved version of the SESM model is projected to become a national and international benchmark in the development of advanced surrogate models, contributing to the positioning of ITCR in the field of simulation and optimization of complex problems.

Develop improvement strategies for SESM through the incorporation of adaptive dictionaries, dimensionality-reduction schemes, and dynamic mechanisms for selecting new training points, with the aim of validating and strengthening its performance, generalization capability, and applicability to real-world problems, thereby enhancing the model’s efficiency and scope.

Applied mathematics, data processing, control, and optimization