Under the supervision of Prof. Bikram Phookun (Ashoka University), Prof. Abhinav Gupta (St. Stephen's College, Delhi University), Dr. Ramakrishna Ramaswamy (IISER Behrampur)
Abstract
Reservoir computing is a machine learning framework where a fixed dynamical system maps input signals into a high-dimensional feature space, and only a single linear readout is trained. The choice of reservoir determines the structure and quality of these features and therefore the predictions, yet is often made empirically without mathematical guarantees on linear independence or numerical stability. In this project, we ask what makes a good reservoir and demonstrate that a more principled choice of dynamical system leads to better predictions. We first implement the logistic map and tent map as reservoirs, reproducing and extending existing results from literature, and use the observations to motivate a more structured alternative based on orthogonal polynomials. We then implement a Chebyshev polynomial reservoir in which inputs are encoded into the rotation dynamics and recurrence relation of Chebyshev polynomials of the first kind, generating features that are orthogonal, bounded and explicitly interpretable. Both reservoirs are tested on two tasks: approximating a seventh-degree polynomial (static task) and reconstructing the dynamics of one variable of the Lorenz system from another (temporal task).