Defence Science and Technology Group, Joint and Operations Analysis Division
The End of Equations? A case study of modelling complex warfighting
Abstract: With the developments of complex systems science in the last 20 years and the increase of computational power available to modellers, it has become standard to believe that traditional equation-based modelling of human socio-technical systems is neither required nor feasible. By complex systems we mean here systems of many disparate components or actors interacting with each other leading to bottom-up manifestation of system wide behaviours, and in these terms, it is undisputed that many real world social/economic/military/business environments are, and have long been, truly complex. A case in point of the role of equation modelling is warfighting. In 1916, the same year of the carnage of the Somme, Frederick Lanchester published his Aircraft in Warfare – the Dawn of the Fourth Arm, which articulated a differential equation-based approach to modelling combat. With varying tweaks, the Lanchester model has remained an actively used representation in military Operations Research but its value has been challenged in light of the complexity revolution of recent decades – where bottom up agent based approaches, and associated computational power and data farming approaches have become very popular. The complexity of warfare is seen in not merely being the domain of simply two sides engaged in mutual attrition but multiple warfighting ‘functions’, such as command and control, manoeuvre, and intelligence-surveillance-reconnaissance; it involves multiple parties and agencies beyond two adversaries; and it is fought by multiple means by which one side applies ‘effects’ over the other, aside from the physical destruction of ‘men and materiel’. Can an equation-based approach hope to capture such diversity, and what good can come of it? This talk will present the journey that researchers in DST’s Modelling Complex Warfighting initiative are undertaking to this end, to develop a differential-equation based dynamical systems model for complex warfighting, marrying the Lanchester model with the highly cited Kuramoto model of oscillator synchronisation on complex networks, to fulfil this challenging goal
Short Bio: Alex Kalloniatis is a Specialist Scientist with the Joint and Operations Analysis Division of the Defence Science and Technology (DST) Group. His background is a theoretical physicist (PhD Adelaide 1992) of 18 years’ experience in academic particle physics (research fellowships at Max-Planck Institute Heidelberg, Universities of Erlangen, and Dortmund, and QEII Fellow at University of Adelaide). He joined DST in 2005 and since then has developed deep research into networked dynamical systems, command and control, and military history with published work across physics-based journals, and professional military science conferences and journals. From 2014-2017 he undertook a Chief Defence Scientist Fellowship to advance mathematical modelling of command and control, and presently leads the stream ‘Concepts for Complexity-Enabled warfare’ in DST’s Modelling Complex Warfighting strategic research initiative.
Department of Mathematics and Statistics, School of Engineering and Mathematical Sciences, La Trobe University
Academic integrity and engineering mathematics students – worth the bother?
Abstract: The forms of academic misconduct, such as plagiarism, that may arise in student work in disciplines which use prose text for most of their assessment are well-covered by most universities’ policies and educative materials. But when it comes to calculations, code, diagrams or designs, or when there seems to be collusion rather than plagiarism, it all gets a bit harder. Shouldn’t all correct maths look the same, anyway? Is it worthwhile or even possible to tackle the problem? Is it even a problem? In this talk, we take a hard look at a difficult issue, and the reasons we should care about it.
Short Bio: Katherine Seaton is an Associate Professor and the Teaching and Learning Coordinator in the Department of Mathematics and Statistics at La Trobe University, Australia. She sits on the University Appeals Committee and is a member of the Standing Committee for Mathematics Education of the Australian Mathematical Society. Her research interests include mathematical physics (the field of her PhD), mathematics and the arts, and the scholarship of teaching and learning as it relates particularly to assessment in undergraduate mathematics education. She is the author of over 30 refereed journal articles in these areas, and in applications of mathematics, and has written a number of outreach articles for secondary teachers. Her book Don’t cheat yourself: Scenarios to clarify collusion confusion was released by La Trobe University e-Bureau in 2018.
School of Mathematics and Statistics & School of Earth Sciences, Faculty of Science, University of Melbourne
Cascading failures in complex structures from data
Abstract: In this presentation, I will share highlights of a recent journey in the broad field of Engineering Mathematics, which focused on early prediction of cascading failures in complex natural and engineered structures from data. This journey covers a vast range of scales and discipline areas in both mathematics and engineering. A key highlight is recent work on early prediction of granular failure from bench scale to field scale -- including catastrophic landslides that stretch several kilometres across. This work has raised a pressing need to develop mathematical and statistical tools capable of analysing and modelling complex precursory failure dynamics from big spatio-temporal data in real-time. Certain aspects of this dynamics transcend scale and manifest fascinating similarities with other complex systems, such as swarming and flocking behaviour in animals in the presence of predators.
Short Bio: Antoinette Tordesillas conducts research across the domains of mathematics, engineering, physics and geophysics. She has been chief investigator on projects from a wide range of application domains, including off-road vehicle mobility in terrestrial and
extra-terrestrial environments, sensor networks, infrastructure and geological materials, and biological structures. Her recent work is focused on granular data analytics with a focus on using failure dynamics to understand resilience in networked systems. These efforts involve international collaborations with multidisciplinary teams from the experimental and high-performance computing fronts, with funding from US Department of Defense agencies like the US Army and US Air Force. Recent highlights include a patented code on landslide prediction with Professor Robin Batterham, spotlighted by agencies around the world including the United Nations Office for Disaster Risk Reduction, The Australian Bulk Handling Review, The Smithsonian, US DoD Scientific Advisory Board Conference and UNESCO. Her work was recently recognized through a new grant from the US DoD High Performance Computing Modernization Program which supports transdisciplinary research into networked systems. The research will see Antoinette (lead CI) and her collaborators from Statistics and the School of Computing & Information Systems at the University of Melbourne combine their data analytics expertise and capabilities to develop new methods “Towards Designing Complex Networks Resilient to Stealthy Attack and Cascading Failure”.
Robert K. Niven
School of Engineering and Information Technology, The University of New South Wales, Canberra
Probabilistic Inference by Maximum Entropy and Bayesian Methods
Abstract: In recent years, the research group led by the author has developed probabilistic methods to infer the state of a variety of scientific and engineering systems. We first examine the use of maximum entropy and Bayesian frameworks for the analysis of a flow network, defined as a set of nodes connected by flow paths. This provides a common foundation for many different networks, including water distribution, transportation, electrical, chemical reaction, ecological, epidemiological and human networks. In the MaxEnt approach, an entropy function characterising the uncertainties in the network is chosen and then maximised, subject to the constraints, to infer the state of the network. The constraints can include physical laws, observed parameter values and constraints on the network structure. The method is demonstrated by (i) a 1140-pipe water distribution network in Torrens, ACT, Australia; (ii) a 327-node centralised and distributed electricity network in Campbell, ACT, Australia; and (iii) several transport systems under various cost and routing constraints. An alternative Bayesian framework is also presented. We then consider the problem of the identification of a dynamical system from its time-series data. Currently, this is conducted by sparse regression methods, generally involving a regularisation procedure. We demonstrate that such methods fall within the framework of Bayesian inverse methods. Firstly, the Bayesian maximum a posteriori method is shown to be equivalent to Tikhonov regularisation based on Euclidean norms, providing a Bayesian rationale for the choice of residual and regularisation terms. Secondly, the Bayesian framework enables the estimation of uncertainties in the inferred parameters and model, the ranking of models by posterior Bayes factors, and the estimation or elimination of intermediate variables. Finally, Bayesian algorithms can be used to explore the posterior probability distribution. We demonstrate these features by the analysis of several dynamical systems in fluid mechanics and hydrology. Finally, we present new spatial and parametric generalisations of the Reynolds transport theorem, the foundation of integral conservation laws in fluid mechanics, which in turn give new forms of the Liouville equation, and the Perron-Frobenius and Koopman operators. The parametric formulation implements a multivariate extension of exterior calculus, including the Lie derivative and other operators.
Short Bio: Biography: A/Prof Robert K. Niven is an internationally recognised research leader in (a) the theory and applications of probabilistic inference, including maximum entropy analysis and Bayesian inference; and (b) studies of environmental contaminants, systems and impacts. These include the development of Bayesian methods for the identification of dynamical systems and fluid flow systems from time-series data; the application of maximum entropy methods for the probabilistic analysis of flows on networks (including water distribution, transport and electricity networks); the development of spatial and parametric analogues of the Reynolds transport theorem and Liouville equation; and the development of a new formulation of non-equilibrium thermodynamics based on probabilities defined over fluxes. A/Prof. Niven has been recognised by a career total in research funding of A$3.4 million, including ARC Discovery and SRI grants, and a number of prestigious international research fellowships.