Randomized Atomic Feature Models for Physics-Informed Identification of Dynamic Systems

2026-05-14

AI Summary

This work addresses the challenge of identifying dynamic systems under insufficient excitation, where achieving physical consistency, stability, and interpretability simultaneously remains difficult. To this end, we propose a physics-informed framework based on stochastic stable atomic features. The impulse response is modeled as a random superposition of damped complex exponential atoms, and physically interpretable modal parameters are efficiently recovered through convex regularized least squares subject to explicit stability constraints. By integrating perspectives from Disk–Bochner operators, reproducing kernel Hilbert space (RKHS) theory, and the Kalman–Yakubovich–Popov (KYP) lemma, the method embeds engineering priors—such as stability and DC gain—into a finite-dimensional optimization framework. Experimental results demonstrate that the proposed approach significantly improves identification accuracy under poorly excited conditions while rigorously preserving system stability and structural interpretability.

Abstract

We present a physics-informed framework for system identification based on randomized stable atomic features. Impulse responses are represented as random superpositions of stable atoms, namely damped complex exponentials associated with poles sampled inside a prescribed disk. Identification is then cast as a convex regularized least-squares problem with optional linear, second-order-cone, and KYP constraints. The approach generalizes random Fourier and random Laplace features to the damped, nonstationary regime relevant to engineering systems while retaining modal interpretability and scalable finite-dimensional computation. The main analytic point is an operator-theoretic Disk-Bochner viewpoint: positive measures over stable poles generate positive-definite kernels with a radius-dependent shift defect, while a converse scalar disk moment representation for an arbitrary kernel is characterized by subnormality of the canonical shift. We prove this statement, establish an RKHS-to-l1 embedding, show that sampled poles induce a valid finite atomic gauge, discuss random-feature convergence, and state sparse-recovery guarantees conditionally on the restricted-eigenvalue properties of the realized disk-Vandermonde or input-output design matrix. We also connect the normalized transfer function problem to Nevanlinna-Pick interpolation and LFT set-membership. The framework directly encodes stability margins, modal localization, DC-gain bounds, monotonicity, passivity, relative degree, settling-time targets, and time/frequency-domain error bounds. Numerical comparisons illustrate how physically meaningful priors can compensate for poor excitation and improve constrained impulse-response recovery in an under-informative data setting.

Problem

• system identification
• physics-informed
• dynamic systems
• stability constraints
• impulse response

Innovation

• randomized atomic features
• physics-informed system identification
• stable pole sampling
• Disk-Bochner theory
• convex regularized least-squares