Physics Model Calibration via Functional Kernel Regression and Multilevel Modeling
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Ohene-Obeng, Kwesi Appau [Sandia National Laborato↗
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Results for “Multilevel Regression”
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Do Piperonyl Butoxide Long-Lasting Insecticide Treated Nets Provide Additional Protection Against Malaria Infections Compared with Conventional Nets in an Operational Setting in Western Kenya?
Malaria control in sub-Saharan Africa has stagnated despite widespread adoption of control measures such as long-lasting insecticidal nets (LLINs). Progress has stalled, in part, because of pyrethroid insecticide resistance, driving the need for retooling to increase the effectiveness of bed nets. Consequently, LLINs have been treated with the chemical synergist piperonyl butoxide (PBO). Piperonyl butoxide LLINs have been shown to be efficacious in controlled settings; however, their effectiveness in real-world settings warrants investigation. In Bungoma County, Western Kenya, a cohort of 768 participants was followed from June 2017 to December 2023 via active and passive surveillance. Household visits were conducted monthly, during which LLIN use for nets distributed in 2017 and 2021 was recorded, and symptomatic malaria cases were identified using rapid diagnostic tests (RDTs). The comparative effectiveness of PBO versus conventional LLINs was assessed in terms of malaria infections. A multilevel logistic regression model was fit with monthly RDT results as the dependent variable. The study results indicate that PBO LLINs provide greater protection against malaria at the individual level than conventional LLINs (odds ratio: 0.70; 95% CI: 0.47–1.03), although the findings were not statistically significant. The added protection against malaria infections provided by PBO LLINs compared with conventional LLINs observed in the current study aligns with findings from most previous studies, although this finding was not statistically significant. In areas with documented pyrethroid resistance, the use of LLINs with an added synergist, such as PBO, can provide additional protection against malaria infections (compared with pyrethroid-only LLINs) and should be considered for scaled-up scenarios despite the additional cost.
60 APPLIED LIFE SCIENCES↗
Multilevel-in-width training for deep neural network regression
A common challenge in regression is that for many problems, the degrees of freedom required for a high-quality solution also allows for overfitting. Regularization is a class of strategies that seek to restrict the range of possible solutions so as to discourage overfitting while still enabling good solutions, and different regularization strategies impose different types of restrictions. In this paper, we present a multilevel regularization strategy that constructs and trains a hierarchy of neural networks, each of which has layers that are wider versions of the previous network's layers. Here, we draw intuition and techniques from the field of Algebraic Multigrid (AMG), traditionally used for solving linear and nonlinear systems of equations, and specifically adapt the Full Approximation Scheme (FAS) for nonlinear systems of equations to the problem of deep learning. Training through V-cycles then encourage the neural networks to build a hierarchical understanding of the problem. We refer to this approach as multilevel-in-width to distinguish from prior multilevel works which hierarchically alter the depth of neural networks. The resulting approach is a highly flexible framework that can be applied to a variety of layer types, which we demonstrate with both fully connected and convolutional layers. We experimentally show with PDE regression problems that our multilevel training approach is an effective regularizer, improving the generalize performance of the neural networks studied.
97 MATHEMATICS AND COMPUTING↗
Urban Flood Modeling: Uncertainty Quantification and Physics‐Informed Gaussian Processes Regression Forecasting
Abstract Estimating uncertainty in flood model predictions is important for many applications, including risk assessment and flood forecasting. We focus on uncertainty in physics‐based urban flooding models. We consider the effects of the model's complexity and uncertainty in key input parameters. The effect of rainfall intensity on the uncertainty in water depth predictions is also studied. As a test study, we choose the Interconnected Channel and Pond Routing (ICPR) model of a part of the city of Minneapolis. The uncertainty in the ICPR model's predictions of the floodwater depth is quantified in terms of the ensemble variance using the multilevel Monte Carlo (MC) simulation method. Our results show that uncertainties in the studied domain are highly localized. Model simplifications, such as disregarding the groundwater flow, lead to overly confident predictions, that is, predictions that are both less accurate and uncertain than those of the more complex model. We find that for the same number of uncertain parameters, increasing the model resolution reduces uncertainty in the model predictions (and increases the MC method's computational cost). We employ the multilevel MC method to reduce the cost of estimating uncertainty in a high‐resolution ICPR model. Finally, we use the ensemble estimates of the mean and covariance of the flood depth for real‐time flood depth forecasting using the physics‐informed Gaussian process regression method. We show that even with few measurements, the proposed framework results in a more accurate forecast than that provided by the mean prediction of the ICPR model.
Kohanpur, Amir H.↗
MFNets: Multifidelity data-driven networks for Bayesian learning and prediction
This paper presents a multifidelity uncertainty quantification framework called MFNets. We seek to address three existing challenges that arise when experimental and simulation data from different sources are used to enhance statistical estimation and prediction with quantified uncertainty. Specifically, we demonstrate that MFNets can (1) fuse heterogeneous data sources arising from simulations with different parameterizations, e.g simulation models with different uncertain parameters or data sets collected under different environmental conditions; (2) encode known relationships among data sources to reduce data requirements; and (3) improve the robustness of existing multi-fidelity approaches to corrupted data. MFNets construct a network of latent variables (LVs) to facilitate the fusion of data from an ensemble of sources of varying credibility and cost. These LVs are posited as explanatory variables that provide the source of correlation in the observed data. Furthermore, MFNets provide a way to encode prior physical knowledge to enable efficient estimation of statistics and/or construction of surrogates via conditional independence relations on the LVs. We highlight the utility of our framework with a number of theoretical results which assess the quality of the posterior mean as a frequentist estimator and compare it to standard sampling approaches that use single fidelity, multilevel, and control variate Monte Carlo estimators. We also use the proposed framework to derive the Monte Carlo-based control variate estimator entirely from the use of Bayes rule and linear-Gaussian models -- to our knowledge the first such derivation. Finally, we demonstrate the ability to work with different uncertain parameters across different models.
97 MATHEMATICS AND COMPUTING↗