TY - JOUR A1 - Kaiser, Eurika A1 - Noack, Bernd R. A1 - Cordier, Laurent A1 - Spohn, Andreas A1 - Segond, Marc A1 - Abel, Markus A1 - Daviller, Guillaume A1 - Osth, Jan A1 - Krajnovic, Sinisa A1 - Niven, Robert K. T1 - Cluster-based reduced-order modelling of a mixing layer JF - Journal of fluid mechanics KW - low-dimensional models KW - nonlinear dynamical systems KW - shear layers Y1 - 2014 U6 - https://doi.org/10.1017/jfm.2014.355 SN - 0022-1120 SN - 1469-7645 VL - 754 SP - 365 EP - 414 PB - Cambridge Univ. Press CY - New York ER - TY - JOUR A1 - Niven, Robert K. A1 - Abel, Markus A1 - Schlegel, Michael A1 - Waldrip, Steven H. T1 - Maximum Entropy Analysis of Flow Networks: Theoretical Foundation and Applications JF - Entropy N2 - The concept of a "flow network"-a set of nodes and links which carries one or more flows-unites many different disciplines, including pipe flow, fluid flow, electrical, chemical reaction, ecological, epidemiological, neurological, communications, transportation, financial, economic and human social networks. This Feature Paper presents a generalized maximum entropy framework to infer the state of a flow network, including its flow rates and other properties, in probabilistic form. In this method, the network uncertainty is represented by a joint probability function over its unknowns, subject to all that is known. This gives a relative entropy function which is maximized, subject to the constraints, to determine the most probable or most representative state of the network. The constraints can include "observable" constraints on various parameters, "physical" constraints such as conservation laws and frictional properties, and "graphical" constraints arising from uncertainty in the network structure itself. Since the method is probabilistic, it enables the prediction of network properties when there is insufficient information to obtain a deterministic solution. The derived framework can incorporate nonlinear constraints or nonlinear interdependencies between variables, at the cost of requiring numerical solution. The theoretical foundations of the method are first presented, followed by its application to a variety of flow networks. KW - maximum entropy analysis KW - flow network KW - probabilistic inference Y1 - 2019 U6 - https://doi.org/10.3390/e21080776 SN - 1099-4300 VL - 21 IS - 8 SP - 776 PB - MDPI CY - Basel ER - TY - JOUR A1 - Quade, Markus A1 - Abel, Markus A1 - Shafi, Kamran A1 - Niven, Robert K. A1 - Noack, Bernd R. T1 - Prediction of dynamical systems by symbolic regression JF - Physical review : E, Statistical, nonlinear and soft matter physics N2 - We study the modeling and prediction of dynamical systems based on conventional models derived from measurements. Such algorithms are highly desirable in situations where the underlying dynamics are hard to model from physical principles or simplified models need to be found. We focus on symbolic regression methods as a part of machine learning. These algorithms are capable of learning an analytically tractable model from data, a highly valuable property. Symbolic regression methods can be considered as generalized regression methods. We investigate two particular algorithms, the so-called fast function extraction which is a generalized linear regression algorithm, and genetic programming which is a very general method. Both are able to combine functions in a certain way such that a good model for the prediction of the temporal evolution of a dynamical system can be identified. We illustrate the algorithms by finding a prediction for the evolution of a harmonic oscillator based on measurements, by detecting an arriving front in an excitable system, and as a real-world application, the prediction of solar power production based on energy production observations at a given site together with the weather forecast. Y1 - 2016 U6 - https://doi.org/10.1103/PhysRevE.94.012214 SN - 2470-0045 SN - 2470-0053 VL - 94 PB - American Society for Pharmacology and Experimental Therapeutics CY - Bethesda ER - TY - JOUR A1 - Waldrip, S. H. A1 - Niven, Robert K. A1 - Abel, Markus A1 - Schlegel, M. T1 - Reduced-Parameter Method for Maximum Entropy Analysis of Hydraulic Pipe Flow Networks JF - Journal of hydraulic engineering N2 - A maximum entropy (MaxEnt) method is developed to predict flow rates or pressure gradients in hydraulic pipe networks without sufficient information to give a closed-form (deterministic) solution. This methodology substantially extends existing deterministic flow network analysis methods. It builds on the MaxEnt framework previously developed by the authors. This study uses a continuous relative entropy defined on a reduced parameter set, here based on the external flow rates. This formulation ensures consistency between different representations of the same network. The relative entropy is maximized subject to observable constraints on the mean values of a subset of flow rates or potential differences, the frictional properties of each pipe, and physical constraints arising from Kirchhoff’s first and second laws. The new method is demonstrated by application to a simple one-loop network and a 1,123-node, 1,140-pipe water distribution network in the suburb of Torrens, Australian Capital Territory, Australia. KW - Maximum entropy method KW - Water distribution systems KW - Hydraulic networks KW - Pipe networks KW - Hydraulic models KW - Nonlinear analysis KW - Probability Y1 - 2017 U6 - https://doi.org/10.1061/(ASCE)HY.1943-7900.0001379 SN - 0733-9429 SN - 1943-7900 VL - 144 IS - 2 PB - American Society of Civil Engineers CY - Reston ER - TY - JOUR A1 - Gout, Julien A1 - Quade, Markus A1 - Shafi, Kamran A1 - Niven, Robert K. A1 - Abel, Markus T1 - Synchronization control of oscillator networks using symbolic regression JF - Nonlinear Dynamics N2 - Networks of coupled dynamical systems provide a powerful way to model systems with enormously complex dynamics, such as the human brain. Control of synchronization in such networked systems has far-reaching applications in many domains, including engineering and medicine. In this paper, we formulate the synchronization control in dynamical systems as an optimization problem and present a multi-objective genetic programming-based approach to infer optimal control functions that drive the system from a synchronized to a non-synchronized state and vice versa. The genetic programming-based controller allows learning optimal control functions in an interpretable symbolic form. The effectiveness of the proposed approach is demonstrated in controlling synchronization in coupled oscillator systems linked in networks of increasing order complexity, ranging from a simple coupled oscillator system to a hierarchical network of coupled oscillators. The results show that the proposed method can learn highly effective and interpretable control functions for such systems. KW - Dynamical systems KW - Synchronization control KW - Genetic programming Y1 - 2017 U6 - https://doi.org/10.1007/s11071-017-3925-z SN - 0924-090X SN - 1573-269X VL - 91 IS - 2 SP - 1001 EP - 1021 PB - Springer CY - Dordrecht ER -