arXiv subjects

Rajiv Singh

Publications and source records attributed to Rajiv Singh.

7 recordsLinked to original sources

arXiv2026

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

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.

eess.SY↗

arXiv2025

On-the-fly Surrogation for Complex Nonlinear Dynamics

High-fidelity models are essential for accurately capturing nonlinear system dynamics. However, simulation of these models is often computationally too expensive and, due to their complexity, they are not directly suitable for analysis, control design or real-time applications. Surrogate modelling techniques seek to construct simplified representations of these systems with minimal complexity, but adequate information on the dynamics given a simulation, analysis or synthesis objective at hand. Despite the widespread availability of system linearizations and the growing computational potential of autograd methods, there is no established approach that systematically exploits them to capture the underlying global nonlinear dynamics. This work proposes a novel surrogate modelling approach that can efficiently build a global representation of the dynamics on-the-fly from local system linearizations without ever explicitly computing a model. Using radial basis function interpolation and the second fundamental theorem of calculus, the surrogate model is only computed at its evaluation, enabling rapid computation for simulation and analysis and seamless incorporation of new linearization data. The efficiency and modelling capabilities of the method are demonstrated on simulation examples.

eess.SY↗

arXiv2024

Deep Learning of Dynamic Systems using System Identification Toolbox(TM)

MATLAB(R) releases over the last 3 years have witnessed a continuing growth in the dynamic modeling capabilities offered by the System Identification Toolbox(TM). The emphasis has been on integrating deep learning architectures and training techniques that facilitate the use of deep neural networks as building blocks of nonlinear models. The toolbox offers neural state-space models which can be extended with auto-encoding features that are particularly suited for reduced-order modeling of large systems. The toolbox contains several other enhancements that deepen its integration with the state-of-art machine learning techniques, leverage auto-differentiation features for state estimation, and enable a direct use of raw numeric matrices and timetables for training models.

cs.LG↗

arXiv2020

Improving Linear State-Space Models with Additional Iterations

An estimated state-space model can possibly be improved by further iterations with estimation data. This contribution specifically studies if models obtained by subspace estimation can be improved by subsequent re-estimation of the B, C, and D matrices (which involves linear estimation problems). Several tests are performed, which shows that it is generally advisable to do such further re-estimation steps using the maximum likelihood criterion. Stated more succinctly in terms of MATLAB functions, ssest generally outperforms n4sid.

eess.SY↗

arXiv2018

Model for competing pathways in protein-aggregation: role of membrane bound proteins

Motivated by the biologically important and complex phenomena of Aβ peptide aggregation in Alzheimer's disease, we introduce a model and simulation methodology for studying protein aggregation that includes extra-cellular aggregation, aggregation on the cell-surface assisted by a membrane bound protein, and in addition, supply, clearance, production and sequestration of peptides and proteins. The model is used to produce equilibrium and kinetic-aggregation phase diagrams for aggregation onset and of reduced stable Aβ monomer concentrations due to aggregation. The methodology we implemented permits modeling of a phenomenon involving orders of magnitude differences in time scales and concentrations which can be retained in the simulation. We demonstrate how to identify ranges of parameter values that give monomer concentration depletion upon aggregation similar to that observed in Alzheimer's disease. We show how very different behavior can be obtained as reaction parameters and protein concentrations vary, and discuss the difficulty reconciling results of experiments from two vastly different concentration regimes. The latter is an important general issue in relating in-vitro and mice based experiments to humans.

q-bio.QM↗

arXiv2018

Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid

Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochlores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalisation, numerical linked-cluster and series expansions, we find that the previously-studied U(1) quantum spin liquid, in its pi-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2) point.

cond-mat.str-el↗

arXiv2006

Crossover of spectral features from Dimerized to Haldane behavior in alternating antiferromagnetic-ferromagnetic spin-half chains

We calculate the excitation spectrum and spectral weights of the alternating antiferromagnetic-ferromagnetic spin-half Heisenberg chain with exchange couplings $J$ and $-|λ|J$ as a power series in $λ$. For small $|λ|$, the gapped one-particle spectrum has a maximum at $k=0$ and there is a rich structure of bound (and anti-bound) states below (and above) the 2-particle continuum. As $|λ|$ is increased past unity the spectrum crosses over to the Haldane regime, where the peak shifts away from $k=0$, the one particle states merge with the bottom of the continuum near $k=0$, and the spectral weights associated with the one-particle states become very small. Extrapolation of the spectrum to large $|λ|$ confirms that the ground state energy and excitation gap map onto those of the spin-one chain.

cond-mat.str-el↗