Importance Sampling Variance Reduction for the Fokker-Planck Rarefied Gas Particle Method

Models and methods that are able to accurately and efficiently predict the flows of low-speed rarefied gases are in high demand, due to the increasing ability to manufacture devices at micro and nano scales. One such model and method is a Fokker-Planck approximation to the Boltzmann equation, which can be solved numerically by a stochastic particle method. The stochastic nature of this method leads to noisy estimates of the thermodynamic quantities one wishes to sample when the signal is small in comparison to the thermal velocity of the gas. Recently, Gorji et al have proposed a method which is able to greatly reduce the variance of the estimators, by creating a correlated stochastic process which acts as a control variate for the noisy estimates. However, there are potential difficulties involved when the geometry of the problem is complex, as the method requires the density to be solved for independently. Importance sampling is a variance reduction technique that has already been shown to successfully reduce the noise in direct simulation Monte Carlo calculations. In this paper we propose an importance sampling method for the Fokker-Planck stochastic particle scheme. The method requires minimal change to the original algorithm, and dramatically reduces the variance of the estimates. We test the importance sampling scheme on a homogeneous relaxation, planar Couette flow and a lid-driven-cavity flow, and find that our method is able to greatly reduce the noise of estimated quantities. Significantly, we find that as the characteristic speed of the flow decreases, the variance of the noisy estimators becomes independent of the characteristic speed

On the Fokker-Planck approximation to the Boltzmann collision operator

The Boltzmann equation (BE) is a mesoscopic model that provides a description of how gases undergoing a binary collision process evolve in time, however there is no general analytical approach for finding its solutions and direct numerical treatment using quadrature methods is prohibitively expensive due to the dimensions of the problem. For this reason, models that are able to capture the behaviour of solutions to the BE, but which are simpler to treat numerically and analytically are highly desirable. The Fokker-Planck collision operator is one such collision model, which is suited well to numerical solutions using stochastic particle methods, and is the subject of this thesis. The stochastic numerical solutions of the Fokker-Planck model suffer heavily from noise when the speed of the flow is low. We develop two methods that are able to reduced the variance of the estimators of the particle method. The first is a common random number method, which produces a correlated equilibrium solution where thermodynamic fields are known. The second is a importance sampling method, where weights are attached to the particles. This means that particles close to equilibrium do not contribute to the noise of the estimators. We also develop a randomised quasi-Monte Carlo scheme for solving the diffusion equation, which has a faster rate of convergence than simple Monte Carlo methods. The relative simplicity of the functional form of the Fokker-Planck collision operator makes it possible to find analytic solutions in simple cases. We consider a spatially homogeneous, isotropic gas with elastic collisions in the presence of forcing and dissipation and derive self-consistent non-equilibrium steady-state solutions. Previous numerical evidence exists that suggest such forcing and dissipation mechanisms, widely separated, give rise to steady-states of the BE that are close to Maxwellian, with a direct energy cascade and an inverse particle cascade. Using our analytic solutions, we are able to investigate the dependence of such solutions on the forcing and dissipation scales, and find that in the inertial range, the interaction is non-local. We then show that the “extreme driving” mechanism, responsible for a family of non-universal power-law solutions for inelastic granular gases, where the flux of energy is towards lower scales, is also able to produce inverse energy cascades for the elastic system

Hydrocarbon formation and oxidation in spark-ignition engines

This report summarizes the key results and conceptual findings from a three year research program on hydrocarbon formation and oxidation mechanisms in spark-ignition engines. Research was carried out in four areas: laminar flame quenching experimental and analytical studies; quench layer studies in a spark-ignition engine using a rapid-acting gas sampling valve; flow visualization studies in a transparent engine to determine quench layer and quench crevice gas motion; studies of heat transfer, mixing and HC oxidation in the exhaust port. More detailed descriptions of the individual research activities in these areas can be found in the theses and publications completed to date which form Volumes II to XI of the final report on this program.Final report on a research program funded by General Motors Research Laboratories, September 1976 to August 1979

SCHISTOX: An individual based model for the epidemiology and control of schistosomiasis.

A stochastic individual based model, SCHISTOX, has been developed for the study of schistosome transmission dynamics and the impact of control by mass drug administration. More novel aspects that can be investigated include individual level adherence and access to treatment, multiple communities, human sex population dynamics, and implementation of a potential vaccine. Many of the model parameters have been estimated within previous studies and have been shown to vary between communities, such as the age-specific contact rates governing the age profiles of infection. However, uncertainty remains as there are wide ranges for certain parameter values and a few remain relatively unknown. We analyse the model dynamics by parameterizing it with published parameter values. We also discuss the development of SCHISTOX in the form of a publicly available open-source GitHub repository. The next key development stage involves validating the model by calibrating to epidemiological data

Towards personalized guidelines: using machine-learning algorithms to guide antimicrobial selection.

BACKGROUND Electronic decision support systems could reduce the use of inappropriate or ineffective empirical antibiotics. We assessed the accuracy of an open-source machine-learning algorithm trained in predicting antibiotic resistance for three Gram-negative bacterial species isolated from patients' blood and urine within 48 h of hospital admission. METHODS This retrospective, observational study used routine clinical information collected between January 2010 and October 2016 in Birmingham, UK. Patients from whose blood or urine cultures Escherichia coli, Klebsiella pneumoniae or Pseudomonas aeruginosa was isolated were identified. Their demographic, microbiology and prescribing data were used to train an open-source machine-learning algorithm-XGBoost-in predicting resistance to co-amoxiclav and piperacillin/tazobactam. Multivariate analysis was performed to identify predictors of resistance and create a point-scoring tool. The performance of both methods was compared with that of the original prescribers. RESULTS There were 15 695 admissions. The AUC of the receiver operating characteristic curve for the point-scoring tools ranged from 0.61 to 0.67, and performed no better than medical staff in the selection of appropriate antibiotics. The machine-learning system performed statistically but marginally better (AUC 0.70) and could have reduced the use of unnecessary broad-spectrum antibiotics by as much as 40% among those given co-amoxiclav, piperacillin/tazobactam or carbapenems. A validation study is required. CONCLUSIONS Machine-learning algorithms have the potential to help clinicians predict antimicrobial resistance in patients found to have a Gram-negative infection of blood or urine. Prospective studies are required to assess performance in an unselected patient cohort, understand the acceptability of such systems to clinicians and patients, and assess the impact on patient outcome

Informing antimicrobial stewardship with explainable AI

The accuracy and flexibility of artificial intelligence (AI) systems often comes at the cost of a decreased ability to offer an intuitive explanation of their predictions. This hinders trust and discourage adoption of AI in healthcare, exacerbated by concerns over liabilities and risks to patients’ health in case of misdiagnosis. Providing an explanation for a model’s prediction is possible due to recent advances in the field of interpretable machine learning. We considered a data set of hospital admissions linked to records of antibiotic prescriptions and susceptibilities of bacterial isolates. An appropriately trained gradient boosted decision tree algorithm, supplemented by a Shapley explanation model, predicts the likely antimicrobial drug resistance, with the odds of resistance informed by characteristics of the patient, admission data, and historical drug treatments and culture test results. Applying this AI-based system, we found that it substantially reduces the risk of mismatched treatment compared with the observed prescriptions. The Shapley values provide an intuitive association between observations/data and outcomes; the associations identified are broadly consistent with expectations based on prior knowledge from health specialists. The results, and the ability to attribute confidence and explanations, support the wider adoption of AI in healthcare. Author summary Antimicrobial resistance is the ability of organisms (usually bacteria) that cause infections to survive antibiotic treatments. It is a major threat to health and is responsible for an increased risk of death and prolonged hospital stays. Artificial intelligence (AI) is starting to be used for early prediction of resistance to different antibiotics, but care is needed to safely and confidently incorporate this tool into clinical practice. To gain trust from both patients and the medical profession, AI output needs to be transparent and explainable. Here we use explainable AI to show how the characteristics of patients can be used to determine the chance of antimicrobial resistance. The identified patterns could potentially inform hospital practice. Our approach reports the level of certainty and uncertainty for each prediction. This can guide doctors on how much they should rely on it when making initial recommendations. We also show that following our AI predictions would have lowered the initial number of mismatched prescriptions compared to what happened in practice. These methods may therefore increase confidence in AI predictions, improve patient treatment and slow the increase in antimicrobial resistance by targeting antibiotics effectively

Informing antimicrobial stewardship with explainable AI

The accuracy and flexibility of artificial intelligence (AI) systems often comes at the cost of a decreased ability to offer an intuitive explanation of their predictions. This hinders trust and discourage adoption of AI in healthcare, exacerbated by concerns over liabilities and risks to patients’ health in case of misdiagnosis. Providing an explanation for a model’s prediction is possible due to recent advances in the field of interpretable machine learning. We considered a data set of hospital admissions linked to records of antibiotic prescriptions and susceptibilities of bacterial isolates. An appropriately trained gradient boosted decision tree algorithm, supplemented by a Shapley explanation model, predicts the likely antimicrobial drug resistance, with the odds of resistance informed by characteristics of the patient, admission data, and historical drug treatments and culture test results. Applying this AI-based system, we found that it substantially reduces the risk of mismatched treatment compared with the observed prescriptions. The Shapley values provide an intuitive association between observations/data and outcomes; the associations identified are broadly consistent with expectations based on prior knowledge from health specialists. The results, and the ability to attribute confidence and explanations, support the wider adoption of AI in healthcare

Informing antimicrobial stewardship with explainable AI.

The accuracy and flexibility of artificial intelligence (AI) systems often comes at the cost of a decreased ability to offer an intuitive explanation of their predictions. This hinders trust and discourage adoption of AI in healthcare, exacerbated by concerns over liabilities and risks to patients' health in case of misdiagnosis. Providing an explanation for a model's prediction is possible due to recent advances in the field of interpretable machine learning. We considered a data set of hospital admissions linked to records of antibiotic prescriptions and susceptibilities of bacterial isolates. An appropriately trained gradient boosted decision tree algorithm, supplemented by a Shapley explanation model, predicts the likely antimicrobial drug resistance, with the odds of resistance informed by characteristics of the patient, admission data, and historical drug treatments and culture test results. Applying this AI-based system, we found that it substantially reduces the risk of mismatched treatment compared with the observed prescriptions. The Shapley values provide an intuitive association between observations/data and outcomes; the associations identified are broadly consistent with expectations based on prior knowledge from health specialists. The results, and the ability to attribute confidence and explanations, support the wider adoption of AI in healthcare

The impact of overseas conflict on UK communities

Researchers and policymakers have limited understanding of how conflicts overseas affect UK communities, aside from when substantial flows of asylum seekers and migrants from conflict regions occur. Yet globalisation has intensified and changed UK communities’ international connections. This research studies the impact on UK communities of three areas of conflict: Afghanistan/Pakistan, the Great Lakes region of Africa, and the Western Balkans