1,850 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
JAX-DIPS: Neural bootstrapping of finite discretization methods and application to elliptic problems with discontinuities
We present a scalable strategy for development of mesh-free hybrid
neuro-symbolic partial differential equation solvers based on existing
mesh-based numerical discretization methods. Particularly, this strategy can be
used to efficiently train neural network surrogate models of partial
differential equations by (i) leveraging the accuracy and convergence
properties of advanced numerical methods, solvers, and preconditioners, as well
as (ii) better scalability to higher order PDEs by strictly limiting
optimization to first order automatic differentiation. The presented neural
bootstrapping method (hereby dubbed NBM) is based on evaluation of the finite
discretization residuals of the PDE system obtained on implicit Cartesian cells
centered on a set of random collocation points with respect to trainable
parameters of the neural network. Importantly, the conservation laws and
symmetries present in the bootstrapped finite discretization equations inform
the neural network about solution regularities within local neighborhoods of
training points. We apply NBM to the important class of elliptic problems with
jump conditions across irregular interfaces in three spatial dimensions. We
show the method is convergent such that model accuracy improves by increasing
number of collocation points in the domain and predonditioning the residuals.
We show NBM is competitive in terms of memory and training speed with other
PINN-type frameworks. The algorithms presented here are implemented using
\texttt{JAX} in a software package named \texttt{JAX-DIPS}
(https://github.com/JAX-DIPS/JAX-DIPS), standing for differentiable interfacial
PDE solver. We open sourced \texttt{JAX-DIPS} to facilitate research into use
of differentiable algorithms for developing hybrid PDE solvers
University of Windsor Graduate Calendar 2023 Spring
https://scholar.uwindsor.ca/universitywindsorgraduatecalendars/1027/thumbnail.jp
University of Windsor Graduate Calendar 2023 Winter
https://scholar.uwindsor.ca/universitywindsorgraduatecalendars/1026/thumbnail.jp
Investigating different approaches and analyses of psychological variables to enhance sport and exercise
This thesis addresses the acquisition of knowledge through a logical step by step process during the PhD course, highlighting five research activities with a main focus on sport and exercise psychology. The ultimate goal for research looked at exploring wearable devices and associated digital technology to deliver interventions aimed to increase exercise while measuring psychological variables such as stress. A foundation was initially set with a systematic review and meta-analysis on correlations between physical activity and key variables such as self-efficacy, self-regulation, and anxiety measured using validated questionnaires. A continued interest in exploring psychometric tools and their validation in sport drove the analysis of a motivation scales and related parameters in a cohort of Italian rugby players. With the beginning of the COVID-19 pandemic, however, community-based sports activities stopped, and the way in which exercise was performed and measured rapidly changed, as I highlighted in the report “Physical activity: Benefits and challenges during the COVID-19 pandemic”. In this unexpected scenario, government agencies as well as private entities and academic institutions applied digital technology to deliver health and wellbeing messages. The use of novel tools was beneficial while facing increased sedentarism occurring during restrictions and lock-down periods. The study performed, involving office workers and electronically delivering exercise interventions in the form of active breaks, showed improvement in wellbeing and stress reduction. Finally, the last study presented can be viewed as a marker in time, as people return to normality, exercising and performing their normal routine but with a new emphasis in keeping track of their own health and wellbeing through wearable technology, following the change in measuring physical and psychological variables consolidated during the pandemic. The results met the intended goal to successfully provide a message-based, digitally delivered intervention aimed at increasing exercise and reducing stress among university students, using wearables to measure the outcome. Moreover, the comparison of wearable-associated stress (based on physiological stimuli) with self-reported stress using a validated questionnaire (e.g., Perceived Stress Scale-10) showed a promising connection. I intend to continue in this direction to further explore benefits and limitations of digital technology in sport and exercise psychology
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