Robert K Niven

UNSW Canberra · School of Engineering and Information Technology

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 generalize...

Over the past century, hydrologists have developed sophisticated methods for the correlation and prediction of streamflow from rainfall data, including protocols for hyetograph and hydrograph separation, and deconvolu-tion to determine the unit hydrograph. Very recently, some researchers have advocated an alternative approach in which the hydrologi...

In this study, we consider the mathematical framework for inductive or plausible reasoning, or in other words, mathematically rigorous reasoning with uncertainty [1-3], which extends the well-known framework for logical or deductive reasoning (often simply called logic), based on certainty. This framework makes use of the Bayesian interpretation of...

Many inference problems relate to a dynamical system, as represented by dx/dt = f (x), where x ∈ R n is the state vector and f is the (in general nonlinear) system function or model. Since the time of Newton, researchers have pondered the problem of system identification: how should the user accurately and efficiently identify the model f-including...

The Reynolds transport theorem provides a generalized conservation law for the transport of a conserved quantity by fluid flow through a continuous connected control volume. It is close connected to the Liouville equation for the conservation of a local probability density function, which in turn leads to the Perron-Frobenius and Koopman evolution...

We propose an additional category of dimensionless groups based on the principle of {\it entropic similarity}, defined by ratios of (i) entropy production terms; (ii) entropy flow rates or fluxes; or (iii) information flow rates or fluxes. Since all processes involving work against friction, dissipation, diffusion, dispersion, mixing, separation, c...

Adsorptive bubble separation techniques such as foam fractionation have recently been applied for the extraction of per- and polyfluoroalkyl substances (PFAS) from waters at both laboratory and operational scales. However, few authors have developed mathematical models of their removal of PFAS. This study presents a theoretical framework for the ki...

In the Burdekin Basin, Queensland, Australia, groundwater contamination due to agricultural activities has led to concerns over its impacts on globally significant ecosystems such as the Great Barrier Reef. An appropriate method for groundwater vulnerability assessment is essential for the sustainable use of this groundwater resource and its longer...

The Reynolds transport theorem occupies a central place in continuum mechanics, providing a generalized integral conservation equation for the transport of any conserved quantity within a fluid or material volume, which can be connected to its corresponding differential equation. Recently, a more generalized framework was presented for this theorem...

The concept of groundwater vulnerability was first introduced in the 1970s in France to recognize sensitive areas in which surface pollution could affect groundwater, and to enable others to develop management methods for groundwater protection against surface pollutants. Since this time, numerous methods have been developed for groundwater vulnera...

For over a century, models of combat between opposing military forces have been used to assess attrition rates and different military strategies. For two opposing forces, Lanchester (1916) gave the simple coupled first-order decay model dx1 dt = −ax 2 and dx2 dt = −bx 1 , where x 1 (t) and x 2 (t) are normalised populations of the two forces, and a...

Groundwater is a vital resource of water supply throughout the world, and subject to an increasing risk of pollution from many sources (Ouedraogo et al., 2019). This has driven the need to examine the sensitivity of groundwater to surface pollutants, referred to as the groundwater vulnerability (National_Research_Council, 1993). Existing methods of...

This study examines the invariance properties of the thermodynamic entropy production in its global (integral), local (differential), bilinear, and macroscopic formulations, including dimensional scaling, invariance to fixed displacements, rotations or reflections of the coordinates, time antisymmetry, Galilean invariance, and Lie point symmetry. T...

The surface tension isotherms of soluble salts of per- and polyfluoroalkyl substances (PFAS) in electrolyte solutions are typically reported as functions of the PFAS concentration. However, for univalent salts and electrolytes, the Langmuir-Szyszkowski equation is a function of the mean ionic activity a*. Using previously reported data, we show tha...

The Reynolds transport theorem occupies a central place in fluid dynamics, providing a generalized integral conservation equation for the transport of any conserved quantity within a fluid, and connected to its corresponding differential equation. Recently, a new generalized framework was presented for this theorem, enabling parametric transformati...

The Reynolds transport theorem provides a generalized conservation law for a conserved quantity carried by fluid flow through a continuous connected control volume. It is also intimately linked to the Liouville equation for the conservation of a local probability density function (pdf), and to the Perron-Frobenius and Koopman evolution operators. A...

Tribute to former Victorian Premier John Cain

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...

Recently, many researchers have developed sparse regression methods for the identification of a dynamical system from its time-series data. We demonstrate that these methods fall within the framework of Bayesian inverse methods. Indeed, the Bayesian maximum a posteriori method, using Gaussian likelihood and prior functions, is equivalent to Tikhono...

Recently, many researchers have developed sparse regression methods for the identification of a dynamical system from its time-series data. We demonstrate that these methods fall within the framework of Bayesian inverse methods. Indeed, the Bayesian maximum a posteriori method, using Gaussian likelihood and prior functions, is equivalent to Tikhono...

This document is a proposal for the alteration of Field of Research (FoR) Codes in environmental science and engineering, under the Australian and New Zealand Standard Research Classification (ANZSRC). The submission was made to the 10-year review being carried out jointly by the Australian Bureau of Statistics (ABS), Stats NZ, the Australian Resea...

We discuss deficiencies with current arrangements for the regulation of environmental contaminants on land under Commonwealth of Australia jurisdiction, and argue for the creation of a Commonwealth Environmental Protection Agency (CEPA), or similar body, to discharge these legal responsibilities and to exercise national leadership.

We exploit a lesser-known connection between the Reynolds transport theorem, Reynolds averaging and the Liouville equation for a conserved quantity, to derive new spatial and parametric forms of these theorems and associated evolution operators, which provide mappings between different domains (in various spaces) associated with a continuous vector...

Worldwide, mineral exploration is suffering from rising capital costs, due to the depletion of readily recoverable reserves and the need to discover and assess more inaccessible or geologically complex deposits. For gold exploration, this problem is particular acute. We propose an innovative approach to mineral exploration and orebody characterisat...

Worldwide, mineral exploration is suffering from rising capital costs, due to the depletion of readily recoverable reserves and the need to discover and assess more inaccessible or geologically complex deposits. For gold exploration, this problem is particularly acute.We propose an innovative approach to mineral exploration and orebody characterisa...

We have recently developed new maximum entropy (MaxEnt) and Bayesian methods for the analysis of flow networks, including pipe flow, electrical and transportation networks. Both methods of inference update a prior probability density function (pdf) with new information, in the form of data or constraints, to obtain a posterior pdf for the system. W...

This study examines MaxEnt methods for probabilistic inference of the state of flow networks, including pipe flow, electrical and transport networks, subject to physical laws and observed moments. While these typically assume networks of invariant graph structure, we here consider higher-level MaxEnt schemes, in which the network structure constitu...

Submission to the Parliamentary Inquiry into the management of per- and polyfluoroalkyl substances (PFAS) contamination in and around Defence bases

The NSW Government have released proposed Contaminated Land Planning Guidelines and other documents, concerning proposed changes to the management of remediation of contaminated sites. This submission was lodged in response to these proposed changes.

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 th...

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...

I will be presenting a workshop on probabilistic inference on 6 Dec 2017 to MODSIM 2017, for which the details are given below. All those interested are invited to attend! \ http://mssanz.org.au/modsim2017/workshops.html \ Title: Probabilistic Inference using Maximum Entropy Analysis and Bayesian Inference (Theory and Applications) \ What: \ This w...

This study presents a multiphase (water, supercritical fluid and solid species) thermodynamic model applicable to the sequestration of supercritical CO2 in a saline aquifer at high pressures, which accounts for the effects of water activity, solid activity, supercritical fluid fugacity and aqueous species activities. The model is formulated using m...

According to the Minerals Council Australia 44% of today’s exploration projects try to discover gold deposits–a consequence of the risen gold price. However, exploration of an optimal mineral deposit is expensive with respect with time and the equipment required. Expenditure costs are increasing and decrease the profitability of mining companies: r...

The maximum entropy method is used to predict flows on water distribution networks. This analysis extends the water distribution network formulation of Waldrip et al. (2016) Journal of Hydraulic Engineering (ASCE), by the use of a continuous relative entropy defined on a reduced parameter set. This reduction in the parameters that the entropy is de...

The maximum entropy method is used to derive an alternative gravity model for a transport network. The proposed method builds on previous methods which assign the discrete value of a maximum entropy distribution to equal the traffic flow rate. The proposed method however, uses a distribution to represent each flow rate. The proposed method is shown...

A recurring question in mineral exploration is to predict the spatial distribution of ore-bearing minerals, to determine both (i) the economic value of a prospective deposit, and (ii) the optimal locations for mineral discovery (Jébrak M, 1997). In hydrothermal gold deposits such as the Imperial deposit, in the Yilgarn of Western Australia, the gol...

How to build an ore body. Gold'17 Rotorua 2 How does one build an ore body? or How does one design and build a chemical reactor that is an orogenic gold system? 1. Location? Access to raw materials, feed stock and c energy? 2. What kind of reactor are we going to build? 3. What are the operating conditions for maximum yield? 4. How do I ensure stab...

We compare the application of Bayesian inference and the maximum entropy (MaxEnt) method for the analysis of flow networks, such as water, electrical and transport networks. The two methods have the advantage of allowing a probabilistic prediction of flow rates and other variables, when there is insufficient information to obtain a deterministic so...

Both the maximum entropy (MaxEnt) and Bayesian methods update a prior to a posterior probability density function (pdf) by the inclusion of new information in the form of constraints or data respectively. To find the posterior, the MaxEnt method maximizes an entropy function subject to constraints, using the method of Lagrange multipliers, whereas...

We review a number of extremum principles of non-equilibrium thermodynamics based on dissipation, power consumption or entropy production, and their significance to hydrology. The connections between these and various allied methods are reviewed and mapped using the rigorous framework supplied by maximum entropy analysis. Two conjugate maximum and...

In this work we re-derive and improve upon quasi-Newton methods commonly used to find the zeros or extrema of functions, using the maximum entropy method. Unlike Newton’s method, in which the Jacobian or Hessian matrix is calculated at each iteration, quasi-Newton methods find an approximation to the matrix by updating it from the previous iteratio...

We examine Bayesian cyclic networks , here defined as complete directed graphs in which the nodes, representing the domains of discrete or continuous variables, are connected by directed edges representing conditional probabilities between all pairs of variables. The prior probabilities associated with each domain are also included as probabilistic...

A maximum entropy (MaxEnt) method is developed to predict mean external and internal flow rates and mean pressure gradients (potential differences) in hydraulic pipe networks, without or with sufficient constraints to enable a closed-form solution. This substantially extends existing methods for the analysis of flow networks (e.g., Hardy Cross), ap...

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. Th...

This paper presents a maximum-entropy (MaxEnt) derivation of many commonly used quasi-Newton rules. (i) This derivation interprets the elements of the Jacobian or Hessian as means of a multivariate probability distribution; (ii) the variance is chosen to represent the uncertainty about the mean. This interpretation is more intuitive than previous m...

The concept of a flow network - a set of nodes connected by flow paths - encompasses many different disciplines, including electrical, pipe flow, transportation, chemical reaction, ecological, epidemiological, economic and human social networks. Over the past two years, we have developed a maximum entropy (MaxEnt) method to infer the stationary sta...

A Maximum Entropy (MaxEnt) method is developed to infer mean external and internal flow rates and mean pressure gradients (potential differences) in hydraulic pipe networks, without or with sufficient constraints to render the system deterministic. The proposed method substantially extends existing methods for the analysis of flow networks (e.g. Ha...

We present a generalised MaxEnt method to infer the stationary state of a flow network, subject to “observable” constraints on expectations of various parameters, as well as “physical” constraints arising from frictional properties (resistance functions) and conservation laws (Kirchhoff laws). The method invokes an entropy defined over all uncertai...

A maximum entropy (MaxEnt) method is developed to infer the state of a pipe flow network, for situations in which there is insufficient information to form a closed equation set. This approach substantially extends existing deterministic methods for the analysis of engineered flow networks (e.g. Newton's method or the Hardy Cross scheme). The...

Cluster-based reduced-order modelling (CROM) builds on the pioneering works of Gunzburger's group in cluster analysis [1] and Eckhardt's group in transition matrix models [2] and constitutes a potential alternative to reduced-order models based on a proper-orthogonal decomposition (POD). This strategy frames a time-resolved sequence of fl...

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This study examines a generalised maximum entropy (MaxEnt) analysis of a flow network, involving flow rates and potential differences on the network, connected by resistance functions. The analysis gives a generic derivation based on an explicit form of the resistance functions. Accounting for the constraints also leads to an extended form of Gibb...

The Second Law of Thermodynamics governs the average direction of all non-equilibrium dissipative processes. However it tells us nothing about their actual rates, or the probability of fluctuations about the average behaviour. The last few decades have seen significant advances, both theoretical and applied, in understanding and predicting the beha...

We propose a novel cluster-based reduced-order modelling (CROM) strategy of unsteady flows. CROM builds on the pioneering works of Gunzburger's group in cluster analysis (Burkardt et al. 2006) and Eckhardt's group in transition matrix models (Schneider et al. 2007) and constitutes a potential alternative to POD models. This strategy processes a tim...

This chapter concerns "control volume analysis", the standard engineering tool for the analysis of flow systems, and its application to entropy balance calculations. Firstly, the principles of control volume analysis are enunciated and applied to flows of conserved quantities (e.g. mass, momentum, energy) through a control volume, giving integral (...

We respond to two sets of criticisms of our analysis in Noack & Niven, Journal of Fluid Mechanics 700, 187--213 (2012), made by Di Vita, Journal of Thermodynamics & Catalysis, 3: e108 (2012). We show that the criticisms are incorrect and without foundation.

Tutorial session on probability and plausible reasoning, from the Bayesian perspective.

Tutorial presentation on the meaning of the entropy concept and purpose of maximum entropy analysis.

A reduced-order modelling (ROM) strategy is crucial to achieve model-based control in a wide class of flow configurations. In turbulence, ROMs are mostly derived by Galerkin projection of first-principles equations onto the proper orthogonal decomposition (POD) modes. These POD ROMs are known to be relatively fragile when used for control design. T...

We propose a maximum-entropy closure strategy for dissipative dynamical systems building on and generalizing earlier examples (Noack & Niven (2012) [11]). Focus is placed on Galerkin systems arising from a projection of the incompressible Navier–Stokes equation onto orthonormal expansion modes. The maximum-entropy closure is motivated by a simple a...

A maximum entropy-based framework is presented for the synthesis of projections from multiple Earth climate models. This identifies the most representative (most probable) model from a set of climate models—as defined by specified constraints—eliminating the need to calculate the entire set. Two approaches are developed, based on individual climate...

A statistical closure is proposed for a Galerkin model of an incompressible periodic cylinder wake. This closure employs Jaynes' maximum entropy principle to infer the probability distribution for mode amplitudes using exact statistical balance equations as side constraints. The analysis predicts mean amplitude values and modal energy levels in goo...

Recently, the author gave a MaxEnt-based analysis of steady-state flow systems, using an entropy defined on the set of instantaneous fluxes through an infinitesimal fluid element (R.K. Niven, Phys. Rev. E, 80(2) (2009) 021113). The formulation is analogous to Gibbs' formulation of equilibrium thermodynamics, which expresses the effect of changes in...

The frequent use of non-aqueous phase liquids (NAPLs) in cold regions creates serious risks of soil and groundwater contamination. NAPL contaminants can stay in soil for long times due to their entrapment by strong interfacial forces, resulting in a source of pollution caused by their slow dissolution in groundwater over decades. The presence of th...

A statistical physics closure is proposed for Galerkin models of incompressible shear flows. This closure employs a maximum entropy (MaxEnt) principle to infer the probability distribution in Galerkin state space using exact statistical balance equations as side constraints. Application to an empirical Galerkin model of the periodic cylinder wake p...

A maximum entropy-based framework is presented for the synthesis of projections from multiple Earth climate models. This identifies the most representative (most probable) model from a set of climate models -- as defined by specified constraints -- eliminating the need to calculate the entire set. Two approaches are developed, based on individual c...

The pore-scale behavior of a nonaqueous phase liquid (NAPL) trapped as residual contamination in a porous medium, subject to freeze-thaw cycles, was investigated by X-ray microcomputed tomography. It is shown that freeze-thaw cycles cause significant NAPL remobilization in the direction of the freezing front, due to the rupture and transport of a s...