Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session L08: Chaos and Nonlinear Dynamics ILive
|
Hide Abstracts |
Sponsoring Units: GSNP Chair: Daniel Lathrop, University of Maryland, College Park |
Wednesday, March 17, 2021 8:00AM - 8:12AM Live |
L08.00001: Teaching Recurrent Neural Networks to Infer Global Temporal Structure from Local Examples Jason Kim, Zhixin Lu, Erfan Nozari, George Pappas, Danielle Bassett The ability to store and manipulate information is a hallmark of computational systems. Whereas computers are carefully engineered to represent and perform mathematical operations on structured data, neurobiological systems adapt to perform analogous functions without needing to be explicitly engineered. However, precisely how neural systems learn to modify these representations remains far from understood. Here we demonstrate that a recurrent neural network (RNN) can learn to modify and infer its representation of complex information using only examples, and we explain the associated learning mechanism with new theory. Specifically, we train an RNN with examples of translated, linearly transformed, or pre-bifurcated time series from a chaotic Lorenz system, and find that it learns to continuously interpolate and extrapolate the translation, transformation, and bifurcation of this representation far beyond the training data by changing the control signal. Further, we demonstrate that RNNs can infer the global bifurcation structure of normal forms and period doubling routes to chaos, and extrapolate non-dynamical, kinematic trajectories. |
Wednesday, March 17, 2021 8:12AM - 8:24AM Live |
L08.00002: Gated recurrent neural networks 2: a novel first-order chaotic transition Tankut Can, Kamesh Krishnamurthy, David J Schwab We study the transition to chaos in gated recurrent neural networks (RNNs). Gating refers to a multiplicative interaction that can modulate the coupling strength between neurons. Such interactions are found in real biological neurons as well as the best performing architectures in machine learning, but their dynamical consequences are not well understood and poorly characterized. We show a striking consequence of gating is the emergence of a first-order transition to chaos, in which the maximal Lyapunov exponent exhibits a discontinuous jump from negative (stable) to positive (chaotic). Furthermore, we observe the decoupling of the topological trivialization transition from the transition to chaos, finding that saddle-points in the dynamics can emerge and proliferate well before chaos emerges. This is in contrast to chaotic transitions in RNNs with additive interactions. Finally, we discuss the consequences such a discontinuous transition might have for machine learning practice. |
Wednesday, March 17, 2021 8:24AM - 8:36AM Not Participating |
L08.00003: Random Boolean Networks – Statistics of Attractors and their Basins of Attraction Fabian Farina, Claudius Gros
|
Wednesday, March 17, 2021 8:36AM - 8:48AM Live |
L08.00004: Maximally predictive ensemble dynamics from data Antonio Carlos Costa, Tosif Ahamed, David Jordan, Greg Stephens We leverage the interplay between microscopic variability and macroscopic order, fundamental to statistical physics, to extract predictive coarse-grained dynamics from data. We define a dynamical state as a sequence of measurements, partition the resulting space, and choose the sequence length to maximize predictive information. We approximate the dynamics of densities in the partitioned space through transfer operators, providing simple, yet accurate, models on multiple scales. The operator spectrum provides a principled means of timescale separation and coarse-graining. Applicable to both deterministic and stochastic systems, we illustrate our approach in the Langevin dynamics of a particle in a double-well potential and the Lorenz system. As an example where the fundamental dynamics are unknown, we consider high-resolution posture measurements of the nematode C. elegans. We show that a long-time (10's of s) ``run’' and ``pirouette’' description of navigation naturally emerges from short-time (10's of ms) posture samples. |
Wednesday, March 17, 2021 8:48AM - 9:00AM Live |
L08.00005: Does scrambling equal chaos? Tianrui Xu, Thomas Scaffidi, Xiangyu Cao Focusing on semiclassical systems, we show that the parametrically long exponential growth of out-of-time order correlators (OTOCs), also known as scrambling, does not necessitate chaos. Indeed, scrambling can simply result from the presence of unstable fixed points in phase space, even in a classically integrable model. We derive a lower bound on the OTOC Lyapunov exponent, which depends only on local properties of such fixed points. We present several models for which this bound is tight, i.e., for which scrambling is dominated by the local dynamics around the fixed points. We propose that the notion of scrambling be distinguished from that of chaos. |
Wednesday, March 17, 2021 9:00AM - 9:12AM Live |
L08.00006: Induced simplicity by multiple delays in delayed differential equations Seyedkamyar Tavakoli, Andre Longtin A highly studied topic in dynamical systems theory has been delay-differential equations (DDEs). It has been shown in many studies that a single delay can induce different dynamical properties such as oscillatory and chaotic behavior, which makes DDEs appropriate to be exploited in a vast range of algorithms and devices. These demand different degrees of complexity, so one of the key challenges in the study of these infinite-dimensional dynamical systems is enhancing or decreasing the degree of chaos. It has been shown that multiple delays can affect the complexity of these systems. For example, time-series obtained experimentally and numerically for the semiconductor laser with multiple delayed feedback show much higher complexity than the single delayed feedback. However, we have found out that when the number of delays becomes large, a simple periodic attractor or stable fixed point can be expected. The transition from chaotic behavior to simplified dynamics upon adding delays is found to be similar to that seen in distributed delay systems (infinite number of delays) as the memory kernel broadens. We explain complexity reduction with increasing number of delays through the calculation of Permutation entropy and Kolmogorov-Sinai entropy estimation in multi-delay dynamics. |
Wednesday, March 17, 2021 9:12AM - 9:24AM Live |
L08.00007: Creating novel patterns with spatially localized perturbations in non-linear reaction-diffusion systems Jason Czak, Michel Pleimling In past attempts to control spatio-temporal transient chaos, spatially extended systems were subjected to protocols that perturbed them as a whole and stabilized globally a new dynamic regime, as for example a uniform steady state. We have shown that selectively applying a time-delayed feedback scheme to only part of a system can generate novel space-time patterns that are not observed when controlling the whole system. Depending on the protocol used, these new patterns can emerge either in the perturbed or the unperturbed region. Specifically, we use spatially localized time-delayed feedback on the one-dimensional Gray-Scott reaction-diffusion system and demonstrate, through the numerical integration of the resulting kinetic equations, the stabilization of novel spatially localized periodic and quasi-periodic space-time patterns. The mechanism underlying the observed pattern generation is related to diffusion across the interfaces separating the different regions. |
Wednesday, March 17, 2021 9:24AM - 9:36AM Live |
L08.00008: The Fermi-Pasta-Ulam-Tsingou Metastability Issue Kevin Reiss, Salvatore Pace, David Campbell The issue of the long metastable state in the Fermi-Pasta-Ulam-Tsingou (FPUT) lattice has been a core concern in Statistical Mechanics since its discovery. The ergodic hypothesis mandates that even arbitrarily small perturbations to a harmonic lattice should allow enough mixing for the time averaged energies to equal the ensemble average. However, the metastable state for specific initial conditions has been observed to have a lifetime longer than computationally achievable, for low enough energy. We use a comparison to the Toda lattice in order to define the end of the metastable state for the α-FPUT model, and then employ a numerical investigation to find the lifetime of this state. In this way, the end of the metastable state demonstrates a transition from nearly integrable dynamics over to non-integrable dynamics. Using many varying initial conditions, we find a scaling of the lifetime of the metastable state for different energies and system sizes. A similar technique is then applied to the β-FPUT model to determine the lifetime of the metastable state in that system. |
Wednesday, March 17, 2021 9:36AM - 9:48AM Live |
L08.00009: Quasicriticality: On the brink of phase transitions and chaos in the cortex Rashid Williams-Garcia The mean-field approximation of the cortical branching model produces a rich phase diagram featuring a number of dynamical transitions indicative of different situations depending on parameter values. One such transition features a shift from convergence to a stable fixed point (an ordered phase), to limiting quasiperiodic oscillations. This quasiperiodic phase may correspond to neurological disorders such as epilepsy and features evidence of unusual routes to chaos, soliton excitations, and a reentrant regime at extreme parameter values. An analytic expression of the mean-field approximation may be possible in this regime via correspondence with a dispersive PDE (e.g., the Kordeweg-de-Vries equation), potentially opening doors to a field theory of complex neural networks. |
Wednesday, March 17, 2021 9:48AM - 10:00AM Live |
L08.00010: Transition between chaotic and stochastic universality classes of kinetic roughening Rodriguez-Fernandez Enrique, Rodolfo Cuerno The dynamics of non-equilibrium spatially extended systems are often dominated by fluctuations, due to e.g. deterministic chaos or to intrinsic stochasticity. This reflects into kinetic roughening behavior classified into universality classes defined by critical exponent values and by the probability distribution function (PDF) of field fluctuations. Geometrical constraints are known to change secondary features of the PDF while keeping the exponent values unchanged, inducing universality subclasses. Working on the Kuramoto-Sivashinsky equation as a paradigm of spatiotemporal chaos (related with the paramount Burgers and Kardar-Parisi-Zhang equations via large-scale asymptotics [1]), we show [2] that the chaotic or stochastic nature of the prevailing fluctuations can also change the universality class while respecting the exponent values, as the PDF is substantially altered. This transition takes place at a non-zero value of the stochastic noise amplitude and may be suitable for experimental verification. |
Wednesday, March 17, 2021 10:00AM - 10:12AM On Demand |
L08.00011: Avalanches and the edge-of-chaos in neuromorphic nanowire networks Joel Hochstetter, Ruomin Zhu, Alon Loeffler, Adrian Diaz-Alvarez, Tomonobu Nakayama, Zdenka Kuncic The brain's efficient information processing is enabled by the interplay between it's neuro-synaptic elements and complex network structure. This work reports on the dynamics of nanowire networks (NWNs), a unique neuromorphic system with synapse-like memristive junctions embedded within a neural network-like structure. Simulation and experiment elucidate how collective memristive switching gives rise to long-range transport pathways, drastically altering the network's global state via a discontinuous phase transition. The spatio-temporal properties of switching dynamics are found to be consistent with avalanches displaying power-law size and life-time distributions, with exponents obeying the crackling noise relationship, suggesting that dynamics are consistent with a critical-like state. Furthermore, NWNs adaptively respond to time varying stimuli, exhibiting diverse dynamics tunable from order to chaos, as measured by the maximal Lyapunov exponent. When networks are tested on increasingly complex learning tasks, dynamical states near the edge-of-chaos are found to optimise information processing. Overall, these results reveal a rich repertoire of emergent, collective neural-like dynamics in NWNs, with potential to be applied as a physical, brain-inspired information processor. |
Follow Us |
Engage
Become an APS Member |
My APS
Renew Membership |
Information for |
About APSThe American Physical Society (APS) is a non-profit membership organization working to advance the knowledge of physics. |
© 2024 American Physical Society
| All rights reserved | Terms of Use
| Contact Us
Headquarters
1 Physics Ellipse, College Park, MD 20740-3844
(301) 209-3200
Editorial Office
100 Motor Pkwy, Suite 110, Hauppauge, NY 11788
(631) 591-4000
Office of Public Affairs
529 14th St NW, Suite 1050, Washington, D.C. 20045-2001
(202) 662-8700