 Award ID(s):
 1932611
 NSFPAR ID:
 10402368
 Date Published:
 Journal Name:
 11th Bulk Power Systems Dynamics and Control Symposium (IREP 2022)
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Embedding properties of network realizations of dissipative reduced order models Jörn Zimmerling, Mikhail Zaslavsky,Rob Remis, Shasri Moskow, Alexander Mamonov, Murthy Guddati, Vladimir Druskin, and Liliana Borcea Mathematical Sciences Department, Worcester Polytechnic Institute https://www.wpi.edu/people/vdruskin Abstract Realizations of reduced order models of passive SISO or MIMO LTI problems can be transformed to tridiagonal and blocktridiagonal forms, respectively, via dierent modications of the Lanczos algorithm. Generally, such realizations can be interpreted as ladder resistorcapacitorinductor (RCL) networks. They gave rise to network syntheses in the rst half of the 20th century that was at the base of modern electronics design and consecutively to MOR that tremendously impacted many areas of engineering (electrical, mechanical, aerospace, etc.) by enabling ecient compression of the underlining dynamical systems. In his seminal 1950s works Krein realized that in addition to their compressing properties, network realizations can be used to embed the data back into the state space of the underlying continuum problems. In more recent works of the authors Krein's ideas gave rise to socalled nitedierence Gaussian quadrature rules (FDGQR), allowing to approximately map the ROM statespace representation to its full order continuum counterpart on a judicially chosen grid. Thus, the state variables can be accessed directly from the transfer function without solving the full problem and even explicit knowledge of the PDE coecients in the interior, i.e., the FDGQR directly learns" the problem from its transfer function. This embedding property found applications in PDE solvers, inverse problems and unsupervised machine learning. Here we show a generalization of this approach to dissipative PDE problems, e.g., electromagnetic and acoustic wave propagation in lossy dispersive media. Potential applications include solution of inverse scattering problems in dispersive media, such as seismic exploration, radars and sonars. To x the idea, we consider a passive irreducible SISO ROM fn(s) = Xn j=1 yi s + σj , (62) assuming that all complex terms in (62) come in conjugate pairs. We will seek ladder realization of (62) as rjuj + vj − vj−1 = −shˆjuj , uj+1 − uj + ˆrj vj = −shj vj , (63) for j = 0, . . . , n with boundary conditions un+1 = 0, v1 = −1, and 4n real parameters hi, hˆi, ri and rˆi, i = 1, . . . , n, that can be considered, respectively, as the equivalent discrete inductances, capacitors and also primary and dual conductors. Alternatively, they can be viewed as respectively masses, spring stiness, primary and dual dampers of a mechanical string. Reordering variables would bring (63) into tridiagonal form, so from the spectral measure given by (62 ) the coecients of (63) can be obtained via a nonsymmetric Lanczos algorithm written in Jsymmetric form and fn(s) can be equivalently computed as fn(s) = u1. The cases considered in the original FDGQR correspond to either (i) real y, θ or (ii) real y and imaginary θ. Both cases are covered by the Stieltjes theorem, that yields in case (i) real positive h, hˆ and trivial r, rˆ, and in case (ii) real positive h,r and trivial hˆ,rˆ. This result allowed us a simple interpretation of (62) as the staggered nitedierence approximation of the underlying PDE problem [2]. For PDEs in more than one variables (including topologically rich datamanifolds), a nitedierence interpretation is obtained via a MIMO extensions in block form, e.g., [4, 3]. The main diculty of extending this approach to general passive problems is that the Stieltjes theory is no longer applicable. Moreover, the tridiagonal realization of a passive ROM transfer function (62) via the ladder network (63) cannot always be obtained in portHamiltonian form, i.e., the equivalent primary and dual conductors may change sign [1]. 100 Embedding of the Stieltjes problems, e.g., the case (i) was done by mapping h and hˆ into values of acoustic (or electromagnetic) impedance at grid cells, that required a special coordinate stretching (known as travel time coordinate transform) for continuous problems. Likewise, to circumvent possible nonpositivity of conductors for the nonStieltjes case, we introduce an additional complex sdependent coordinate stretching, vanishing as s → ∞ [1]. This stretching applied in the discrete setting induces a diagonal factorization, removes oscillating coecients, and leads to an accurate embedding for moderate variations of the coecients of the continuum problems, i.e., it maps discrete coecients onto the values of their continuum counterparts. Not only does this embedding yields an approximate linear algebraic algorithm for the solution of the inverse problems for dissipative PDEs, it also leads to new insight into the properties of their ROM realizations. We will also discuss another approach to embedding, based on KreinNudelman theory [5], that results in special datadriven adaptive grids. References [1] Borcea, Liliana and Druskin, Vladimir and Zimmerling, Jörn, A reduced order model approach to inverse scattering in lossy layered media, Journal of Scientic Computing, V. 89, N1, pp. 136,2021 [2] Druskin, Vladimir and Knizhnerman, Leonid, Gaussian spectral rules for the threepoint second dierences: I. A twopoint positive denite problem in a semiinnite domain, SIAM Journal on Numerical Analysis, V. 37, N 2, pp.403422, 1999 [3] Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Distance preserving model order reduction of graphLaplacians and cluster analysis, Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Journal of Scientic Computing, V. 90, N 1, pp 130, 2022 [4] Druskin, Vladimir and Moskow, Shari and Zaslavsky, Mikhail LippmannSchwingerLanczos algorithm for inverse scattering problems, Inverse Problems, V. 37, N. 7, 2021, [5] Mark Adolfovich Nudelman The Krein String and Characteristic Functions of Maximal Dissipative Operators, Journal of Mathematical Sciences, 2004, V 124, pp 49184934 Go back to Plenary Speakers Go back to Speakers Go backmore » « less

In this work, we investigate gridforming control for power systems containing threephase and singlephase converters connected to unbalanced distribution and transmission networks, investigate selfbalancing between singlephase converters, and propose a novel balancing feedback for gridforming control that explicitly allows to tradeoff unbalances in voltage and power. We develop a quasisteadystate power network model that allows to analyze the interactions between threephase and singlephase power converters across transmission, distribution, and standard transformer interconnections. We first investigate conditions under which this general network admits a wellposed kronreduced quasisteadystate network model. Our main contribution leverages this reducedorder model to develop analytical conditions for stability of the overall network with gridforming threephase and singlephase converters connected through standard transformer interconnections. Specifically, we provide conditions on the network topology under which (i) singlephase converters autonomously selfsynchronize to a phasebalanced operating point and (ii) singlephase converters phasebalance through synchronization with threephase converters. Moreover, we establish that the conditions can be relaxed if a phasebalancing feedback control is used. Finally, case studies combining detailed models of transmission systems (i.e., IEEE 9bus) and distribution systems (i.e., IEEE 13bus) are used to illustrate the results for (i) a power system containing a mix of transmission and distribution connected converters and, (ii) a power system solely using distributionconnected converters at the grid edge.more » « less

Abstract Bayesian networks are powerful statistical models to understand causal relationships in realworld probabilistic problems such as diagnosis, forecasting, computer vision, etc. For systems that involve complex causal dependencies among many variables, the complexity of the associated Bayesian networks become computationally intractable. As a result, direct hardware implementation of these networks is one promising approach to reducing power consumption and execution time. However, the few hardware implementations of Bayesian networks presented in literature rely on deterministic CMOS devices that are not efficient in representing the stochastic variables in a Bayesian network that encode the probability of occurrence of the associated event. This work presents an experimental demonstration of a Bayesian network building block implemented with inherently stochastic spintronic devices based on the natural physics of nanomagnets. These devices are based on nanomagnets with perpendicular magnetic anisotropy, initialized to their hard axes by the spin orbit torque from a heavy metal underlayer utilizing the giant spin Hall effect, enabling stochastic behavior. We construct an electrically interconnected network of two stochastic devices and manipulate the correlations between their states by changing connection weights and biases. By mapping given conditional probability tables to the circuit hardware, we demonstrate that any two node Bayesian networks can be implemented by our stochastic network. We then present the stochastic simulation of an example case of a four node Bayesian network using our proposed device, with parameters taken from the experiment. We view this work as a first step towards the large scale hardware implementation of Bayesian networks.

Aims. We present a variability, color, and morphologybased classifier designed to identify multiple classes of transients and persistently variable and nonvariable sources from the Zwicky Transient Facility (ZTF) Data Release 11 (DR11) light curves of extended and point sources. The main motivation to develop this model was to identify active galactic nuclei (AGN) at different redshift ranges to be observed by the 4MOST Chilean AGN/Galaxy Evolution Survey (ChANGES). That being said, it also serves as a more general timedomain astronomy study. Methods. The model uses nine colors computed from CatWISE and PanSTARRS1 (PS1), a morphology score from PS1, and 61 singleband variability features computed from the ZTF DR11 g and r light curves. We trained two versions of the model, one for each ZTF band, since ZTF DR11 treats the light curves observed in a particular combination of field, filter, and chargecoupled device (CCD) quadrant independently. We used a hierarchical local classifier per parent node approachwhere each node is composed of a balanced random forest model. We adopted a taxonomy with 17 classes: nonvariable stars, nonvariable galaxies, three transients (SNIa, SNother, and CV/Nova), five classes of stochastic variables (lowzAGN, midzAGN, highzAGN, Blazar, and YSO), and seven classes of periodic variables (LPV, EA, EB/EW, DSCT, RRL, CEP, and Periodicother). Results. The macroaveraged precision, recall, and F1score are 0.61, 0.75, and 0.62 for the g band model, and 0.60, 0.74, and 0.61, for the r band model. When grouping the four AGN classes (lowzAGN, midzAGN, highzAGN, and Blazar) into one single class, its precisionrecall, and F1score are 1.00, 0.95, and 0.97, respectively, for both the g and r bands. This demonstrates the good performance of the model in classifying AGN candidates. We applied the model to all the sources in the ZTF/4MOST overlapping sky (−28 ≤ Dec ≤ 8.5), avoiding ZTF fields that cover the Galactic bulge ( gal_b  ≤ 9 and gal_l ≤ 50). This area includes 86 576 577 light curves in the g band and 140 409 824 in the r band with 20 or more observations and with an average magnitude in the corresponding band lower than 20.5. Only 0.73% of the g band light curves and 2.62% of the r band light curves were classified as stochastic, periodic, or transient with high probability ( P init ≥ 0.9). Even though the metrics obtained for the two models are similar, we find that, in general, more reliable results are obtained when using the g band model. With it, we identified 384 242 AGN candidates (including low, mid, and highredshift AGN and Blazars), 287 156 of which have P init ≥ 0.9.more » « less

Abstract Despite the advances in discovering new nuclei, modeling microscopic nuclear structure, nuclear reactors, and stellar nucleosynthesis, we still lack a systemic tool, such as a network approach, to understand the structure and dynamics of over 70 thousands reactions compiled in JINA REACLIB. To this end, we develop an analysis framework, under which it is simple to know which reactions generally are possible and which are not, by counting neutrons and protons incoming to and outgoing from any target nucleus. Specifically, we assemble here a nuclear reaction network in which a node represents a nuclide, and a link represents a direct reaction between nuclides. Interestingly, the degree distribution of nuclear network exhibits a bimodal distribution that significantly deviates from the common powerlaw distribution of scalefree networks and Poisson distribution of random networks. Based on the dynamics from the cross section parameterizations in REACLIB, we surprisingly find that the distribution is universal for reactions with a rate below the threshold, λ < e − T γ , where T is the temperature and γ ≈ 1.05. Moreover, we discover three rules that govern the structure pattern of nuclear reaction network: (i) reactiontype is determined by linking choices, (ii) network distances between the reacting nuclides on 2D grid of Z vs N of nuclides are short, and (iii) each node in and outdegrees are close to each other. By incorporating these three rules, our model universally unveils the underlying nuclear reaction patterns hidden in a large and dense nuclear reaction network regardless of nuclide chart expansions. It enables us to predict missing links that represent possible new nuclear reactions not yet discovered.more » « less