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# Applied Dynamics Seminar Series

# Applied Dynamics Seminar Series

## Thursdays, 12:30 p.m.

## IREAP Large Conference Room (ERF 1207)

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### September 13, 2018

#### No seminar

### September 20, 2018

#### Statistical Description of Hamiltonian Mixed Phase Space Systems

Technion University | Department of Physics

*Abstract: Typical physical systems follow deterministic behavior. This behavior can be sensitive to initial conditions, such that it is very difficult to predict their behavior in the longtime limit. The resulting motion is chaotic and looks stochastic or random. In many cases the motion is described by a Hamiltonian and the energy is conserved. The motion can be also regular, that is predictable. In the work reported here we studied systems where depending on initial conditions the motion is either regular or chaotic. The simplest systems of this type are of two degrees--of--freedom, or periodically kicked systems with one degree--of--freedom. For this type of systems transport in the chaotic regions of phase space is dominated by sticking to complicated structures in the vicinity of the regular region. The probability to stay in the vicinity of the initial point is a power law in time characterized by some exponent. The question of the value of this exponent and its universality is the subject of a long controversy. We have developed a statistical description for this type of systems, where statistics are with respect to parameter or family of systems rather than to initial conditions. Following previous studies, it is based on a scaling of periodic and quasi-periodic orbits in a way which relies heavily on number theory. We have found an indication that the statistics of scaling is parameter independent and might be relevant for a wider universality class including the systems we explored. This statistical description is implemented in a stochastic Markov model proposed by Meiss and Ott in 1986. Even though many approximations are used, it predicts important results quantitatively, showing the power law decay exponent to be approximately 51.57 in agreement with direct simulations done in this work and also other works. Its universality is inferred from the universality of the scaling statistics. The model systems used in this work are paradigms for chaotic dynamics (the H'enon map and the standard map) therefore it might indicate a wider universality class. Quantum manifestation of this phenomenon and its relevance for time correlations, is showing different behavior for increasing effective Planck's constant, namely, the Planck's constant divided by the typical action. By using recent results regarding the universality of wave function transmission across barriers in phase space, we generalize the use of the Markov model to describe the results after some modification. The work reported was done in collaboration with Or Alus, James Meiss and Mark Srednicki*

### September 27, 2018

#### Prediction of complex spatiotemporal evolution through machine learning methods improved with the addition of observers

Department of Physics | University of Crete

*Abstract: Can we use machine learning (ML) to predict the evolution of complex, chaotic systems? The recent Maryland-based work showed that the answer is conditionally affirmative once we use some additional “help” provided by a random bath and observers, as defined through reservoir computing (RC) [1]. What about using other “standard” ML methods in forecasting the future of complex systems? The ETH-MIT group showed that the long-short-term-memory (LSTM) method may work in general spatiotemporal evolution of the Kuramoto type [2]. Our work (Crete-Harvard) focused on the following question: Under what circumstances ML can predict spatiotemporal structures that emerge in complex evolution that involves nonlinearity as well as some form of stochasticity? To address this question we used two extreme phenomena, one being turbulent chimeras while the second involves stochastic branching. The former phenomenon generates partially coherent structures in highly nonlinear oscillators interacting through short or long range coupling while the latter appears in wave propagation in weakly disordered media. Examples of the former include biological networks, SQUIDs (superconducting quantum interference devices), coupled lasers, etc while the latter geophysical waves, electronic motion in a graphene surface and other similar wave propagation configurations. In our work we applied and compared three ML methods, viz. LSTM, RC as well as the standard Feed-Forward neural networks (FNNs) in the two extreme spatiotemporal phenomena dominated by coherence, i.e. chimeras, and stochasticity, i.e. branching, respectively [3]. In order to increase the predictability of the methods we augmented LSTM (and FNNs) with observers; specifically we assigned one LSTM network to each system node except for "observer" nodes which provide continual "ground truth" measurements as input; we refer to this method as "Observer LSTM" (OLSTM). We found that even a small number of observers greatly improves the data-driven (model-free) long-term forecasting capability of the LSTM networks and provide the framework for a consistent comparison between the RC and LSTM methods. We find that RC requires smaller training datasets than OLSTMs, but the latter requires fewer observers. Both methods are benchmarked against Feed-Forward neural networks (FNNs), also trained to make predictions with observers (OFNNs). [1] Z. Lu Z, J. Pathak, B. Hunt, M. Girvan, R. Brockett and E. Ott, Reservoir observers: Model free inference of unmeasured variables in chaotic systems. Chaos 27, 041102 (2017); J. Pathak, B. Hunt,M. Girvan, Z. Lu and E. Ott, Model-free prediction of large spatiotemporally chaotic systems from data: A reservoir computing approach, Phys. Rev. Let. 120, 024102 (2018) [2] P. R. Vlachas, W. Byeon, Z. Y. Wan, T. P. Sapsis and P. Koumoutsakos, Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks. Proc.R.Soc.A 474, 20170844 (2018). [3] G. Neofotistos, M. Mattheakis, G. D. Barmparis, J. Hizanidis, G. P. Tsironis and E. Kaxiras, Machine learning with observers predicts complex spatiotemporal evolution, arXiv 1807.10758 (2018) *

### October 4, 2018

#### 'We Have No Good Fundamental Theory (of Turbulence) at All’: Was Feynman Right?

Johns Hopkins University | Department of Applied Mathematics and Statistics

*Abstract: In his famous undergraduate physics lectures, Richard Feynman remarked about the problem of fluid turbulence: "Nobody in physics has really been able to analyze it mathematically satisfactorily in spite of its importance to the sister sciences.” This statement was already false when Feynman made it. Unbeknownst to him, Lars Onsager decades earlier had made an exact mathematical analysis of the high Reynolds-number limit of incompressible fluid turbulence, using a method that would now be described as a non-perturbative renormalization group analysis and discovering the first “conservation-law anomaly” in theoretical physics. Onsager’s results were only cryptically announced in 1949 and he never published any of his detailed calculations. Onsager’s analysis was finally rescued from oblivion and reproduced by the speaker in 1994. The ideas have subsequently been intensively developed in the mathematical PDE community, where deep connections emerged with John Nash’s work on isometric embeddings. Furthermore, the method has more recently been successfully applied to new physics problems, compressible fluid turbulence and relativistic fluid turbulence, yielding many new testable predictions. This talk will briefly review Onsager’s exact analysis of the original incompressible turbulence problem and subsequent developments. Then a new application to kinetic plasma turbulence will be described, with novel predictions for turbulence in nearly colllisionless plasmas such as the solar wind and the terrestrial magnetosheath.*

### October 11, 2018

#### Constructing Chaotic Coordinates for non-integrable dynamical systems

Princeton Plasma Physics Laboratory

*Abstract: TBA*

### October 18, 2018

#### Bifurcations in dynamical control systems for aerospace applications

University of Maryland | Department of Aerospace Engineering

*Abstract: TBA*

### October 25, 2018

#### A computer-assisted study of red coral population dynamics

George Mason University | Department of Mathematics

*Abstract: TBA*

### November 1, 2018

#### Neuronal coding in the insect olfactory system

University of Maryland | Department of Biology

*Abstract: TBA*

### November 8, 2018

#### Modeling methodologies for incorporating personal protection control strategies into vector-born disease systems: relationships and predictions for the influence of diversity amplification on outbreak severity

Dr. Jeff Demers

University of Maryland | Department of Biology

*Abstract: TBA*

### November 15, 2018

#### TBA

TBA

TBA

*Abstract: TBA*

### November 22, 2018

#### Thanksgiving Break - No seminar

### November 29, 2018

#### Confining charged particle orbits using hidden symmetry

University of Maryland | IREAP

*Abstract: TBD*

### December 6, 2018

#### TBA

University of Maryland | Department of Mathematics and IPST

*Abstract: TBA*