Data-Driven Nonlinear System Identification Using Time Delayed Maps with Application to Multi-Attractor Systems
This paper introduces a novel data-driven method called Nonlinear Delayed Maps (NLDM) for identifying nonlinear dynamical systems, particularly those with multiple attractors, by leveraging time-delayed states and nonlinear feature mappings to improve prediction accuracy across different regions of the phase space.
Identification of Analytic Nonlinear Dynamical Systems with Non-asymptotic Guarantees Using Least Squares Estimation and Set Membership Estimation
This research paper demonstrates that non-active exploration using i.i.d. random inputs is sufficient for efficient parameter estimation in linearly parameterized nonlinear systems, provided that the feature functions are real-analytic and the noise/disturbance distributions are semi-continuous.
Identifying Equations of Motion in Vibrating Structures from Measurements Using a Data-Driven, Energy-Based Approach
This paper presents a novel data-driven method called Energy-Based Dual-Phase Dynamics Identification (EDDI) for identifying equations of motion in nonlinear vibrating structures directly from measurements, leveraging energy relationships to model damping and stiffness forces.
Weak-form Modified Sparse Identification of Nonlinear Dynamics: A Comparative Study on Improving System Identification and Noise Modeling in Noisy Environments
Integrating the weak SINDy (WSINDy) framework into the modified SINDy (mSINDy) framework, creating the weak mSINDy (WmSINDy) algorithm, enhances the accuracy and robustness of identifying nonlinear dynamical systems and characterizing noise in data compared to existing methods, especially in high noise scenarios.
ADAM-SINDy: Enhancing Sparse Identification of Nonlinear Dynamics with Adaptive Optimization for Parameter Estimation
ADAM-SINDy improves upon the traditional SINDy algorithm by incorporating the ADAM optimization algorithm, enabling simultaneous identification of governing equations and estimation of nonlinear parameters in dynamical systems.
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