arXiv subjects

Reetish Padhi

Publications and source records attributed to Reetish Padhi.

3 recordsLinked to original sources

arXiv2026

Beyond linear subspaces: Nonlinear moment matching meets quadratic manifolds

Quadratic manifold-based model order reduction offers a viable pathway to circumvent the limitations of linear subspaces for linear control systems characterized by slow Kolmogorov $n$-width decay. However, a system-theoretic framework for constructing such quadratic approximations remains absent from the literature. This paper presents a system-agnostic, optimization-free framework for the direct construction of quadratic projection matrices. We prove that the synthesized reduced-order model matches the nonlinear moments of the full-order system and preserves its exact center manifold mapping, thereby ensuring asymptotic tracking of steady-state outputs under specific input classes. Numerical results on transport-dominated benchmark problems, namely, the one-dimensional damped wave and advection equations, show that the proposed framework achieves high-fidelity trajectory reconstruction within a significantly reduced-dimensional state space, yielding substantial online computational savings.

math.OC↗

arXiv2025

Data-driven balanced truncation for linear systems with quadratic outputs

We develop the framework for a non-intrusive, quadrature-based method for approximate balanced truncation (QuadBT) of linear systems with quadratic outputs, thus extending the applicability of QuadBT, which was originally designed for data-driven balanced truncation of standard linear systems with linear outputs only. The new approach makes use of the time-domain and frequency-domain quadrature-based representation of the system's infinite Gramians, only implicitly. We show that by sampling solely the extended impulse responses of the original system and their derivatives (or the corresponding transfer functions), we construct a reduced-order model that mimics the approximation quality of the intrusive (projection-based) balanced truncation. We validate the proposed framework on a numerical example.

math.NA↗

arXiv2023

Variability of echo state network prediction horizon for partially observed dynamical systems

Study of dynamical systems using partial state observation is an important problem due to its applicability to many real-world systems. We address the problem by studying an echo state network (ESN) framework with partial state input with partial or full state output. Application to the Lorenz system and Chua's oscillator (both numerically simulated and experimental systems) demonstrate the effectiveness of our method. We show that the ESN, as an autonomous dynamical system, is capable of making short-term predictions up to a few Lyapunov times. However, the prediction horizon has high variability depending on the initial condition-an aspect that we explore in detail using the distribution of the prediction horizon. Further, using a variety of statistical metrics to compare the long-term dynamics of the ESN predictions with numerically simulated or experimental dynamics and observed similar results, we show that the ESN can effectively learn the system's dynamics even when trained with noisy numerical or experimental datasets. Thus, we demonstrate the potential of ESNs to serve as cheap surrogate models for simulating the dynamics of systems where complete observations are unavailable.

eess.SY↗