Non-intrusive reduced order modeling of nonlinear problems using neural networks

We develop a non-intrusive reduced basis (RB) method for parametrized steady-state partial differential equations (PDEs). The method extracts a reduced basis from a collection of high-fidelity solutions via a proper orthogonal decomposition (POD) and employs artificial neural networks (ANNs), particularly multi-layer perceptrons (MLPs), to accurately approxi- mate the coefficients of the reduced model. The search for the optimal number of neurons and the minimum amount of training samples to avoid overfitting is carried out in the offline phase through an automatic routine, relying upon a joint use of the latin hypercube sampling (LHS) and the Levenberg-Marquardt training algorithm. This guarantees a complete offline-online decoupling, leading to an efficient RB method - referred to as POD-NN - suitable also for general nonlinear problems with a non-affine parametric dependence. Numerical studies are presented for the nonlinear Poisson equation and for driven cavity viscous flows, modeled through the steady incompressible Navier-Stokes equations. Both physical and geometrical parametrizations are considered. Several results confirm the accuracy of the POD-NN method and show the substantial speed-up enabled at the online stage as compared to a traditional RB strategy

Kilometer-scale climate models: Prospects and challenges

Currently major efforts are underway toward refining the horizontal resolution (or grid spacing) of climate models to about 1 km, using both global and regional climate models (GCMs and RCMs). Several groups have succeeded in conducting kilometer-scale multiweek GCM simulations and decadelong continental-scale RCM simulations. There is the well-founded hope that this increase in resolution represents a quantum jump in climate modeling, as it enables replacing the parameterization of moist convection by an explicit treatment. It is expected that this will improve the simulation of the water cycle and extreme events and reduce uncertainties in climate change projections. While kilometer-scale resolution is commonly employed in limited-area numerical weather prediction, enabling it on global scales for extended climate simulations requires a concerted effort. In this paper, we exploit an RCM that runs entirely on graphics processing units (GPUs) and show examples that highlight the prospects of this approach. A particular challenge addressed in this paper relates to the growth in output volumes. It is argued that the data avalanche of high-resolution simulations will make it impractical or impossible to store the data. Rather, repeating the simulation and conducting online analysis will become more efficient. A prototype of this methodology is presented. It makes use of a bit-reproducible model version that ensures reproducible simulations across hardware architectures, in conjunction with a data virtualization layer as a common interface for output analyses. An assessment of the potential of these novel approaches will be provided

Psychometric properties of the Multidimensional Health Locus of Control Scale Form C in a non-Western culture

Form C of the Multidimensional Health Locus of Control Scales (MHLC-C) was designed to investigate health-related control beliefs of persons with an existing medical condition. The aim of the present study was to examine the psychometric properties of this instrument in a culture characterized by external control beliefs and learned helplessness—contrary to the societal context of original test development. Altogether, 374 Hungarian patients with cancer, irritable bowel syndrome, diabetes, and cardiovascular and musculoskeletal disorders were enrolled in the study. Besides the MHLC-C, instruments measuring general control beliefs, anxiety, depression, self-efficacy, and health behaviors were also administered to evaluate the validity of the scale. Both exploratory and confirmatory factor analytic techniques were used to investigate the factor structure of the scale. Our results showed that the Hungarian adaptation of the instrument had a slightly different structure than the one originally hypothesized: in the present sample, a three-factor structure emerged where the items of the Doctors and the Others subscales loaded onto a single common component. Internal reliability of all three subscales was adequate (alphas between .71 and .79). Data concerning the instrument's validity were comparable with previous results from Western countries. These findings may suggest that health locus of control can be construed very similarly to Western countries even in a post-communist society—regardless of the potential differences in general control beliefs

Multiple dimensions of health locus of control in a representative population sample: ordinal factor analysis and cross-validation of an existing three and a new four factor model

<p>Abstract</p> <p>Background</p> <p>Based on the general approach of locus of control, health locus of control (HLOC) concerns control-beliefs due to illness, sickness and health. HLOC research results provide an improved understanding of health related behaviour and patients' compliance in medical care. HLOC research distinguishes between beliefs due to Internality, Externality powerful Others (POs) and Externality Chance. However, evidences for differentiating the POs dimension were found. Previous factor analyses used selected and predominantly clinical samples, while non-clinical studies are rare. The present study is the first analysis of the HLOC structure based on a large representative general population sample providing important information for non-clinical research and public health care.</p> <p>Methods</p> <p>The standardised German questionnaire which assesses HLOC was used in a representative adult general population sample for a region in Northern Germany (N = 4,075). Data analyses used ordinal factor analyses in LISREL and Mplus. Alternative theory-driven models with one to four latent variables were compared using confirmatory factor analysis. Fit indices, chi-square difference tests, residuals and factor loadings were considered for model comparison. Exploratory factor analysis was used for further model development. Results were cross-validated splitting the total sample randomly and using the cross-validation index.</p> <p>Results</p> <p>A model with four latent variables (Internality, Formal Help, Informal Help and Chance) best represented the HLOC construct (three-dimensional model: normed chi-square = 9.55; RMSEA = 0.066; CFI = 0.931; SRMR = 0.075; four-dimensional model: normed chi-square = 8.65; RMSEA = 0.062; CFI = 0.940; SRMR = 0.071; chi-square difference test: p < 0.001). After excluding one item, the superiority of the four- over the three-dimensional HLOC construct became very obvious (three-dimensional model: normed chi-square = 7.74; RMSEA = 0.059; CFI = 0.950; SRMR = 0.079; four-dimensional model: normed chi-square = 5.75; RMSEA = 0.049; CFI = 0.965; SRMR = 0.065; chi-square difference test: p < 0.001). Results were confirmed by cross-validation. Results based on our large community sample indicated that western general populations separate health-related control-beliefs concerning formal and informal assistance.</p> <p>Conclusions</p> <p>Future non-clinical HLOC studies in western cultures should consider four dimensions of HLOC: Internality, Formal Help, Informal Help and Chance. However, the standardised German instrument needs modification. Therefore, confirmation of our results may be useful. Future research should compare HLOC structure between clinical and non-clinical samples as well as cross-culturally.</p

Spousal involvement and CPAP adherence: A dyadic perspective

Poor adherence to continuous positive airway pressure (CPAP) treatment is associated with substantial health care costs, morbidity and mortality, and has been a leading obstacle in the effective management of obstructive sleep apnea (OSA). Successful interventions to improve CPAP adherence may ultimately include a variety of components. For patients living with spouses (refers to all domestic partners), the spouse will likely be an integral component to any successful intervention. Developing understanding of the role of spouses in adherence to CPAP has been identified to be a critical research need. This review expands the investigation of CPAP adherence to a broader context, from an exclusive focus on individual patients to a dyadic perspective encompassing both patients and their spouses. A conceptual framework based on social support and social control theories is proposed to understand spousal involvement in CPAP adherence. Methodologies for future investigations are discussed, along with implications for developing interventions that engage both patients and their spouses to improve CPAP use