arXiv subjects

Shirin Panahi

Publications and source records attributed to Shirin Panahi.

15 recordsLinked to original sources

arXiv2026

Vestibular reservoir computing

Reservoir computing (RC) is a computational framework known for its training efficiency, making it ideal for physical hardware implementations. However, realizing the complex interconnectivity of traditional reservoirs in physical systems remains a significant challenge. This paper proposes a physical RC scheme inspired by the biological vestibular system. To overcome hardware complexity, we introduce a designed uncoupled topology and demonstrate that it achieves performance comparable to fully coupled networks. We theoretically analyze the difference between these topologies by deriving a memory capacity formula for linear reservoirs, identifying specific conditions where both configurations yield equivalent memory. These analytical results are demonstrated to approximately hold for nonlinear reservoir systems. Furthermore, we systematically examine the impact of reservoir size on predictive statistics and memory capacity. Our findings suggest that uncoupled reservoir architectures offer a mathematically sound and practically feasible pathway for efficient physical reservoir computing.

cs.LG↗

arXiv2025

Unsupervised learning for anticipating critical transitions

For anticipating critical transitions in complex dynamical systems, the recent approach of parameter-driven reservoir computing requires explicit knowledge of the bifurcation parameter. We articulate a framework combining a variational autoencoder (VAE) and reservoir computing to address this challenge. In particular, the driving factor is detected from time series using the VAE in an unsupervised-learning fashion and the extracted information is then used as the parameter input to the reservoir computer for anticipating the critical transition. We demonstrate the power of the unsupervised learning scheme using prototypical dynamical systems including the spatiotemporal Kuramoto-Sivashinsky system. The scheme can also be extended to scenarios where the target system is driven by several independent parameters or with partial state observations.

nlin.CD↗

arXiv2024

High-order exceptional points and stochastic resonance in pseudo-Hermitian systems

Exceptional points, a remarkable phenomenon in physical systems, have been exploited for sensing applications. It has been demonstrated recently that it can also utilize as sensory threshold in which the interplay between exceptional-point dynamics and noise can lead to enhanced performance. Most existing works focused on second-order exceptional points. We investigate the stochastic dynamics associated with high-order exceptional points with a particular eye towards optimizing sensing performance by developing a theoretical framework based on pseudo-Hermiticity. Our analysis reveals three distinct types of frequency responses to external perturbations. A broad type of stochastic resonance is uncovered where, as the noise amplitude increases, the signal-to-noise ratio reaches a global maximum rapidly but with a slow decaying process afterwards, indicating achievable high performance in a wide range of the noise level. These results suggest that stochastic high-order exceptional-point dynamics can be exploited for applications in signal processing and sensor technologies.

physics.app-ph↗

arXiv2024

Kolmogorov-Arnold Network Autoencoders

Deep learning models have revolutionized various domains, with Multi-Layer Perceptrons (MLPs) being a cornerstone for tasks like data regression and image classification. However, a recent study has introduced Kolmogorov-Arnold Networks (KANs) as promising alternatives to MLPs, leveraging activation functions placed on edges rather than nodes. This structural shift aligns KANs closely with the Kolmogorov-Arnold representation theorem, potentially enhancing both model accuracy and interpretability. In this study, we explore the efficacy of KANs in the context of data representation via autoencoders, comparing their performance with traditional Convolutional Neural Networks (CNNs) on the MNIST, SVHN, and CIFAR-10 datasets. Our results demonstrate that KAN-based autoencoders achieve competitive performance in terms of reconstruction accuracy, thereby suggesting their viability as effective tools in data analysis tasks.

cs.LG↗

arXiv2024

Data-driven model discovery with Kolmogorov-Arnold networks

Data-driven model discovery of complex dynamical systems is typically done using sparse optimization, but it has a fundamental limitation: sparsity in that the underlying governing equations of the system contain only a small number of elementary mathematical terms. Examples where sparse optimization fails abound, such as the classic Ikeda or optical-cavity map in nonlinear dynamics and a large variety of ecosystems. Exploiting the recently articulated Kolmogorov-Arnold networks, we develop a general model-discovery framework for any dynamical systems including those that do not satisfy the sparsity condition. In particular, we demonstrate non-uniqueness in that a large number of approximate models of the system can be found which generate the same invariant set with the correct statistics such as the Lyapunov exponents and Kullback-Leibler divergence. An analogy to shadowing of numerical trajectories in chaotic systems is pointed out.

cs.LG↗

arXiv2024

Machine-learning prediction of tipping with applications to the Atlantic Meridional Overturning Circulation

Anticipating a tipping point, a transition from one stable steady state to another, is a problem of broad relevance due to the ubiquity of the phenomenon in diverse fields. The steady-state nature of the dynamics about a tipping point makes its prediction significantly more challenging than predicting other types of critical transitions from oscillatory or chaotic dynamics. Exploiting the benefits of noise, we develop a general data-driven and machine-learning approach to predicting potential future tipping in nonautonomous dynamical systems and validate the framework using examples from different fields. As an application, we address the problem of predicting the potential collapse of the Atlantic Meridional Overturning Circulation (AMOC), possibly driven by climate-induced changes in the freshwater input to the North Atlantic. Our predictions based on synthetic and currently available empirical data place a potential collapse window spanning from 2040 to 2065, in consistency with the results in the current literature.

physics.ao-ph↗

arXiv2023

Rate-induced tipping in complex high-dimensional ecological networks

In an ecosystem, environmental changes as a result of natural and human processes can cause some key parameters of the system to change with time. Depending on how fast such a parameter changes, a tipping point can occur. Existing works on rate-induced tipping, or R-tipping, offered a theoretical way to study this phenomenon but from a local dynamical point of view, revealing, e.g., the existence of a critical rate for some specific initial condition above which a tipping point will occur. As ecosystems are subject to constant disturbances and can drift away from their equilibrium point, it is necessary to study R-tipping from a global perspective in terms of the initial conditions in the entire relevant phase space region. In particular, we introduce the notion of the probability of R-tipping defined for initial conditions taken from the whole relevant phase space. Using a number of real-world, complex mutualistic networks as a paradigm, we discover a scaling law between this probability and the rate of parameter change and provide a geometric theory to explain the law. The real-world implication is that even a slow parameter change can lead to a system collapse with catastrophic consequences. In fact, to mitigate the environmental changes by merely slowing down the parameter drift may not always be effective: only when the rate of parameter change is reduced to practically zero would the tipping be avoided. Our global dynamics approach offers a more complete and physically meaningful way to understand the important phenomenon of R-tipping.

q-bio.PE↗

arXiv2023

Synchronization in networked systems with large parameter heterogeneity

Systems that synchronize in nature are intrinsically different from one another, with possibly large differences from system to system. While a vast part of the literature has investigated the emergence of network synchronization for the case of small parametric mismatches, we consider the general case that parameter mismatches may be large. We present a unified stability analysis that predicts why the range of stability of the synchronous solution either increases or decreases with parameter heterogeneity for a given network. We introduce a parametric approach, based on the definition of a curvature contribution function, which allows us to estimate the effect of mismatches on the stability of the synchronous solution in terms of contributions of pairs of eigenvalues of the Laplacian. For cases in which synchronization occurs in a bounded interval of a parameter, we study the effects of parameter heterogeneity on both transitions (asynchronous to synchronous and synchronous to asynchronous.)

eess.SY↗

arXiv2022

Pinning control of networks: dimensionality reduction through simultaneous block-diagonalization of matrices

In this paper, we study the network pinning control problem in the presence of two different types of coupling: (i) node-to-node coupling among the network nodes and (ii) input-to-node coupling from the source node to the `pinned nodes'. Previous work has mainly focused on the case that (i) and (ii) are of the same type. We decouple the stability analysis of the target synchronous solution into subproblems of the lowest dimension by using the techniques of simultaneous block diagonalization (SBD) of matrices. Interestingly, we obtain two different types of blocks, driven and undriven. The overall dimension of the driven blocks is equal to the dimension of an appropriately defined controllable subspace, while all the remaining undriven blocks are scalar. Our main result is a decomposition of the stability problem into four independent sets of equations, which we call quotient controllable, quotient uncontrollable, redundant controllable, and redundant uncontrollable. Our analysis shows that the number and location of the pinned nodes affect the number and the dimension of each set of equations. We also observe that in a large variety of complex networks, stability of the target synchronous solution is de facto only determined by a single quotient controllable block.

eess.SY↗

arXiv2022

Reply to comment on "Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks"

We respond briefly to a comment [1, arXiv:2110.15493] recently posted online on our paper [2, arXiv:2108.07893]. Complete and cluster synchronization of random networks is undoubtedly a topic of interest in the Physics, Engineering, and Nonlinear Dynamics literature. In [3] we study both complete and cluster synchronization of networks and introduce indices that measure success (or failure) of application of the SBD technique in decoupling the stability problem into problems of lower dimensionality. Our usage of the word `failure' indicates that the technique does not produce a decomposition which results in a system which is easier to analyze, not that the technique fails in correctly decoupling these problems.

eess.SY↗

arXiv2022

Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks

We discuss here the application of the simultaneous block diagonalization (SBD) of matrices to the study of the stability of both complete and cluster synchronization in random (generic) networks. For both problems, we define indices that measure success (or failure) of application of the SBD technique in decoupling the stability problem into problems of lower dimensionality. We then see that in the case of random networks the extent of the dimensionality reduction achievable is the same as that produced by application of a trivial transformation.

cond-mat.dis-nn↗

arXiv2022

Matryoshka and Disjoint Cluster Synchronization of Networks

The main motivation for this paper is to present a definition of network synchronizability for the case of cluster synchronization (CS), in an analogous fashion to Barahona and Pecora for the case of complete synchronization. We find this problem to be substantially more complex than the original one. We distinguish between the two cases of networks with intertwined clusters and no intertwined clusters and between {the two cases that the master stability function is negative either in a bounded range or in an unbounded range of its argument. We first obtain a definition of synchronizability that applies to each individual cluster within a network and then attempt to generalize this definition to the entire network. For CS, the synchronous solution of each cluster may be stable independent of the stability of the other clusters, which results in possibly different ranges in which each cluster synchronizes (isolated CS.) For each pair of clusters, we distinguish between three different cases: Matryoshka Cluster Synchronization (when the range of the stability of the synchronous solution for one cluster is included in that of the other cluster), Partially Disjoint Cluster Synchronization (when the ranges of stability of the synchronous solutions partially overlap), and Complete Disjoint Cluster Synchronization (when the ranges of stability of the synchronous solutions do not overlap.)

eess.SY↗

arXiv2021

Group synchrony, parameter mismatches, and intragroup connections

Group synchronization arises when two or more synchronization patterns coexist in a network formed of oscillators of different types, with the systems in each group synchronizing on the same time-evolution, but systems in different groups synchronizing on distinct time-evolutions. Group synchronization has been observed and characterized when the systems in each group are identical and the couplings between the systems satisfy specific conditions. By relaxing these constraints and allowing them to be satisfied in an approximate rather than exact way, we observe that stable group synchronization may still occur in the presence of small deviations of the parameters of the individual systems and of the couplings from their nominal values. We analyze this case and provide necessary and sufficient conditions for stability through a master stability function approach, {which also allows us to quantify the synchronization error}. We also investigate the stability of group synchronization in the presence of intra group connections and for this case, extend some of the existing results in the literature. Our analysis points out a broader class of matrices describing intra group connections for which the stability problem can be reduced in a low-dimensional form.

nlin.CD↗

arXiv2021

Cluster Synchronization of Networks via a Canonical Transformation for Simultaneous Block Diagonalization of Matrices

We study cluster synchronization of networks and propose a canonical transformation for simultaneous block diagonalization of matrices that we use to analyze stability of the cluster synchronous solution. Our approach has several advantages as it allows us to: (1) decouple the stability problem into subproblems of minimal dimensionality while preserving physically meaningful information; (2) study stability of both orbital and equitable partitions of the network nodes and (3) obtain a parametrization of the problem in a small number of parameters. For the last point, we show how the canonical transformation decouples the problem into blocks that preserve key physical properties of the original system. We also apply our proposed algorithm to analyze several real networks of interest, and we find that it runs faster than alternative algorithms from the literature.

eess.SY↗

arXiv2019

Transitions from chimeras to coherence: An analytical approach by means of the coherent stability function

Chimera states have been a vibrant subject of research in the recent past, but the analytical treatment of transitions from chimeras to coherent states remains a challenge. Here we analytically derive the necessary conditions for this transition by means of the coherent stability function approach, which is akin to the master stability function approach that is traditionally used to study the stability of synchronization in coupled oscillators. In chimera states, there is typically at least one group of oscillators that evolves in a drifting, random manner, while other groups of oscillators follow a smoother, more coherent profile. In the coherent state, there thus exists a smooth functional relationship between the oscillators. This lays the foundation for the coherent stability function approach, where we determine the stability of the coherent state. We subsequently test the analytical prediction numerically by calculating the strength of incoherence during the transition point. We use leech neurons, which exhibit a coexistence of chaotic and periodic tonic spiking depending on initial conditions, coupled via non-local electrical synapses, to demonstrate our approach. We systematically explore various dynamical states with the focus on the transitions between chimeras and coherence, fully confirming the validity of the coherent stability function. We also observe complete synchronization for higher values of the coupling strength, which we verify by the master stability function approach.

nlin.AO↗