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Full-Text Articles in Physical Sciences and Mathematics
Wildfire Modeling With Data Assimilation, Andrew Johnston
Wildfire Modeling With Data Assimilation, Andrew Johnston
Theses and Dissertations
Wildfire modeling is a complex, computationally costly endeavor, but with droughts worsening and fires burning across the western United States, obtaining accurate wildfire predictions is more important than ever. In this paper, we present a novel approach to wildfire modeling using data assimiliation. We model wildfire spread with a modification of the partial differential equation model described by Mandel et al. in their 2008 paper. Specifically, we replace some constant parameter values with geospatial functions of fuel type. We combine deep learning and remote sensing to obtain real-time data for the model and employ the Nelder-Mead method to recover optimal …
Data Assimilation And Parameter Recovery For Rayleigh-Bénard Convection, Jacob William Murri
Data Assimilation And Parameter Recovery For Rayleigh-Bénard Convection, Jacob William Murri
Theses and Dissertations
Many problems in applied mathematics involve simulating the evolution of a system using differential equations with known initial conditions. But what if one records observations and seeks to determine the causal factors which produced them? This is known as an inverse problem. Some prominent inverse problems include data assimilation and parameter recovery, which use partial observations of a system of evolutionary, dissipative partial differential equations to estimate the state of the system and relevant physical parameters (respectively). Recently a set of procedures called nudging algorithms have shown promise in performing simultaneous data assimilation and parameter recovery for the Lorentz equations …
Mathematical And Statistical Modeling With Deep Neural Networks, Albert Romero
Mathematical And Statistical Modeling With Deep Neural Networks, Albert Romero
Theses and Dissertations
General adversarial networks (GANs) are a form of machine learning that includes two neural networks competing in a zero-sum game. One network produces artificial, while the other tries to distinguish artificial data from real. The Wasserstein general adversarial network with gradient penalty (WGAN-GP) variant of this technique is used to produce solutions for ordinary and partial differential equations.