Mathematical Modeling and Identification of Delay-Driven Systems 

This project investigates delay-driven dynamical systems using mathematical modeling and data-driven discovery techniques. The work combines delay differential equations, reaction–diffusion systems, and sparse identification methods to uncover hidden memory effects in complex systems. The objective is to bridge rigorous mathematical theory with modern computational approaches to produce interpretable models supported by data. 

The figures illustrate the comparison between models identified using classical SINDy with a discrete delay assumption and the proposed LCT-SINDy framework for distributed-delay systems. In the top-left panels, the true system (generated from a distributed-delay model) is compared with a model identified using SINDy under a discrete-delay assumption. As observed, the identified discrete-delay model exhibits noticeable mismatch with the true dynamics. This discrepancy arises because the underlying data are generated from a distributed-delay system, while the identification procedure assumes a single discrete delay, leading to structural model error. In contrast, the right panels demonstrate the performance of the proposed LCT-SINDy method, which incorporates the Linear Chain Trick to represent distributed delays. The identified model closely matches the true distributed-delay dynamics, significantly improving the agreement between simulation and data. The bottom-left figure presents the relative error of the reconstructed distributed-delay state under varying noise levels. The results show that the LCT-based approach maintains robust accuracy across increasing noise intensities, highlighting its stability and reliability in noisy data settings.

Alanazi, M., & Bani-Yaghoub, M. (2026).

Sparse Identification of Nonlinear Distributed-Delay Dynamics via the Linear Chain Trick. arXiv:2601.13536 

View on arXiv: https://arxiv.org/abs/2601.13536