362 research outputs found
A path-integral approach to Bayesian inference for inverse problems using the semiclassical approximation
We demonstrate how path integrals often used in problems of theoretical
physics can be adapted to provide a machinery for performing Bayesian inference
in function spaces. Such inference comes about naturally in the study of
inverse problems of recovering continuous (infinite dimensional) coefficient
functions from ordinary or partial differential equations (ODE, PDE), a problem
which is typically ill-posed. Regularization of these problems using
function spaces (Tikhonov regularization) is equivalent to Bayesian
probabilistic inference, using a Gaussian prior. The Bayesian interpretation of
inverse problem regularization is useful since it allows one to quantify and
characterize error and degree of precision in the solution of inverse problems,
as well as examine assumptions made in solving the problem -- namely whether
the subjective choice of regularization is compatible with prior knowledge.
Using path-integral formalism, Bayesian inference can be explored through
various perturbative techniques, such as the semiclassical approximation, which
we use in this manuscript. Perturbative path-integral approaches, while
offering alternatives to computational approaches like Markov-Chain-Monte-Carlo
(MCMC), also provide natural starting points for MCMC methods that can be used
to refine approximations.
In this manuscript, we illustrate a path-integral formulation for inverse
problems and demonstrate it on an inverse problem in membrane biophysics as
well as inverse problems in potential theories involving the Poisson equation.Comment: Fixed some spelling errors and the author affiliations. This is the
version accepted for publication by J Stat Phy
Expert-guided Bayesian Optimisation for Human-in-the-loop Experimental Design of Known Systems
Domain experts often possess valuable physical insights that are overlooked
in fully automated decision-making processes such as Bayesian optimisation. In
this article we apply high-throughput (batch) Bayesian optimisation alongside
anthropological decision theory to enable domain experts to influence the
selection of optimal experiments. Our methodology exploits the hypothesis that
humans are better at making discrete choices than continuous ones and enables
experts to influence critical early decisions. At each iteration we solve an
augmented multi-objective optimisation problem across a number of alternate
solutions, maximising both the sum of their utility function values and the
determinant of their covariance matrix, equivalent to their total variability.
By taking the solution at the knee point of the Pareto front, we return a set
of alternate solutions at each iteration that have both high utility values and
are reasonably distinct, from which the expert selects one for evaluation. We
demonstrate that even in the case of an uninformed practitioner, our algorithm
recovers the regret of standard Bayesian optimisation.Comment: NeurIPS 2023 Workshop on Adaptive Experimental Design and Active
Learning in the Real World. Main text: 6 page
Understanding the assumptions underlying Mendelian randomization
With the rapidly increasing availability of large genetic data sets in recent years, Mendelian Randomization (MR) has quickly gained popularity as a novel secondary analysis method. Leveraging genetic variants as instrumental variables, MR can be used to estimate the causal effects of one phenotype on another even when experimental research is not feasible, and therefore has the potential to be highly informative. It is dependent on strong assumptions however, often producing biased results if these are not met. It is therefore imperative that these assumptions are well-understood by researchers aiming to use MR, in order to evaluate their validity in the context of their analyses and data. The aim of this perspective is therefore to further elucidate these assumptions and the role they play in MR, as well as how different kinds of data can be used to further support them
Jubilee mugs:the monarchy and the Sex Pistols
With rare exceptions sociologists have traditionally had little to say about the British monarchy. In the exceptional cases of the Durkheimian functionalism of Shills and Young (1953), the left humanism of Birnbaum (1955), or the archaic state/backward nation thesis of Nairn (1988), the British nation has been conceived as a homogenous mass. The brief episode of the Sex Pistols' Jubilee year song 'God Save the Queen' exposed some of the divisions within the national 'mass', forcing a re-ordering of the balance between detachment and belonging to the Royal idea. I argue that the song acted as a kind of 'breaching experiment'. Its wilful provocation of Royalist sentiment revealed the level of sanction available to the media-industrial complex to enforce compliance to British self-images of loyal and devoted national communicants
Multi-Fidelity Data-Driven Design and Analysis of Reactor and Tube Simulations
The development of new manufacturing techniques such as 3D printing have
enabled the creation of previously infeasible chemical reactor designs.
Systematically optimizing the highly parameterized geometries involved in these
new classes of reactor is vital to ensure enhanced mixing characteristics and
feasible manufacturability. Here we present a framework to rapidly solve this
nonlinear, computationally expensive, and derivative-free problem, enabling the
fast prototype of novel reactor parameterizations. We take advantage of
Gaussian processes to adaptively learn a multi-fidelity model of reactor
simulations across a number of different continuous mesh fidelities. The search
space of reactor geometries is explored through an amalgam of different,
potentially lower, fidelity simulations which are chosen for evaluation based
on weighted acquisition function, trading off information gain with cost of
simulation. Within our framework we derive a novel criteria for monitoring the
progress and dictating the termination of multi-fidelity Bayesian optimization,
ensuring a high fidelity solution is returned before experimental budget is
exhausted. The class of reactor we investigate are helical-tube reactors under
pulsed-flow conditions, which have demonstrated outstanding mixing
characteristics, have the potential to be highly parameterized, and are easily
manufactured using 3D printing. To validate our results, we 3D print and
experimentally validate the optimal reactor geometry, confirming its mixing
performance. In doing so we demonstrate our design framework to be extensible
to a broad variety of expensive simulation-based optimization problems,
supporting the design of the next generation of highly parameterized chemical
reactors.Comment: 22 Pages with Appendi
Machine Learning-Assisted Discovery of Novel Reactor Designs via CFD-Coupled Multi-fidelity Bayesian Optimisation
Additive manufacturing has enabled the production of more advanced reactor
geometries, resulting in the potential for significantly larger and more
complex design spaces. Identifying and optimising promising configurations
within broader design spaces presents a significant challenge for existing
human-centric design approaches. As such, existing parameterisations of
coiled-tube reactor geometries are low-dimensional with expensive optimisation
limiting more complex solutions. Given algorithmic improvements and the onset
of additive manufacturing, we propose two novel coiled-tube parameterisations
enabling the variation of cross-section and coil path, resulting in a series of
high dimensional, complex optimisation problems. To ensure tractable, non-local
optimisation where gradients are not available, we apply multi-fidelity
Bayesian optimisation. Our approach characterises multiple continuous
fidelities and is coupled with parameterised meshing and simulation, enabling
lower quality, but faster simulations to be exploited throughout optimisation.
Through maximising the plug-flow performance, we identify key characteristics
of optimal reactor designs, and extrapolate these to produce two novel
geometries that we 3D print and experimentally validate. By demonstrating the
design, optimisation, and manufacture of highly parameterised reactors, we seek
to establish a framework for the next-generation of reactors, demonstrating
that intelligent design coupled with new manufacturing processes can
significantly improve the performance and sustainability of future chemical
processes.Comment: 11 pages, 8 figure
Keepers of the Metaphorical Gate: The Role of Journal Editors
Academic journals are central to a discipline’s professionalism and are the principal means of communication. The purpose of this symposium is explore the nature academic journals, their purposes and what they reveal about the field from the perspective of nine editors whose primary mission is to cover the broad field of adult education
The Metallicity and Dust Content of HVC 287.5+22.5+240: Evidence for a Magellanic Clouds Origin
We estimate the abundances of S and Fe in the high velocity cloud HVC
287.5+22.5+240, which has a velocity of +240 km/s with respect to the local
standard of rest and is in the Galactic direction l~287, b~23. The measurements
are based on UV absorption lines of these elements in the Hubble Space
Telescope spectrum of NGC 3783, a background Seyfert galaxy, as well as new H I
21-cm interferometric data taken with the Australia Telescope. We find
S/H=0.25+/-0.07 and Fe/H=0.033+/-0.006 solar, with S/Fe=7.6+/-2.2 times the
solar ratio. The S/H value provides an accurate measure of the chemical
enrichment level in the HVC, while the super-solar S/Fe ratio clearly indicates
the presence of dust, which depletes the gas-phase abundance of Fe. The
metallicity and depletion information obtained here, coupled with the velocity
and the position of the HVC in the sky, strongly suggest that the HVC
originated from the Magellanic Clouds. It is likely (though not necessary) that
the same process(es) that generated the Magellanic Stream is also responsible
for HVC 287.5+22.5+240.Comment: AASTEX, 3 postscript figures, AJ, 1998, Jan issu
An Operational Model of Iceberg Drift
A new iceberg drift, deterioration and calving model has been under development at the Canadian Ice Service (CIS). The model includes several new features including the utilization of detailed environmental forcing input, and a robust implicit numerical solution method. In particular, the vertical distribution of water current is incorporated in calculations of water drag force on the iceberg keel. The model is also the first to include treatment of calving, prediction of calved ice piece size distribution and deterioration, as well as the drift of calved pieces. This paper gives a description of the drift model formulation, and verification tests that include comparisons of model predictions with field observations. Additionally, the paper presents the outcome of a parametric study aimed at examining the sensitivity of iceberg drift to input parameters and environmental forcing. Tests examined the role of water and air drag coefficients, water current, wind waves and the waterline length of the iceberg. A number of scenarios of input water current, and wind drag force were also considered. The results determine the impact of the input parameters and variables on predicted iceberg tracks.NRC publication: Ye
Flow of Ice through Long Converging Channels
This paper examines some issues of the flow of ice in long and converging channels which may affect navigation. The emphasis is on pressure distributions and the role of ice properties and tidal currents. The present work employs an ice dynamics model that is based on a viscous plastic constitutive model with an elliptical yield envelope, the thickness redistribution model of Savage (2007), and a Particle-In-Cell (PIC) advection approach. Pressure distributions are obtained for an idealized geometry and uniform wind forcing. The results indicate that zones of relatively low pressures develop along the centre of the channel. Increasing the shear strength of the ice cover leads to somewhat lower pressures within such zones along the centre of the channel. That reduction of pressure is caused by the increased transfer of wind forces to land boundaries. Tides are shown to generally decrease pressures. The tidal currents also increase the overall drift, although drift slows and even reverses direction during parts of the tidal cycle.NRC publication: Ye
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