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Efficient algorithms and high-performance simulations for a class of deterministic and stochastic models
Reyes, Brandon C.
Reyes, Brandon C.
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2021
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2023-04-14
Abstract
Efficient numerical algorithms and high-performance computing (HPC) simulations are crucial for the understanding and discovery of complex biological and physical processes. The main focus of this thesis is on the development and HPC implementation of algorithms to address key challenges associated with these processes. These include numerical approaches for the identification of deterministic biological signaling pathways capable of switch-like behavior; efficient finite element method (FEM) based uncertainty quantification (UQ) algorithms for the reduction in computational resources to simulate stochastic-space-time physical models; and neural network (NN) based approximations of deterministic counterparts of the space-time models.
To showcase our efficient FEM constrained high-order multilevel UQ algorithmic developments for space-time physical processes with input uncertainties (in a class of phase-separation and quantum systems) and marked advantages on CPU-based HPC environments with message passing interface (MPI) implementations, we simulate high-stochastic dimensional systems governed by the Allen-Cahn (A-C) and Schrodinger equations, respectively defined on stationary and time-dependent domains. Using a physics constrained NN (PCNN) algorithm we simulate a data-driven inverse problem for parameters in a deterministic A-C model, and also demonstrate accuracy and GPU computational costs associated with our PCNN approach for the simulation of a class of oscillatory processes in moving domains, governed by the Schrodinger equation in three spatial dimensions. For the biological processes, we demonstrate the effectiveness of our optimization-based method for general detection of switch-like behavior on models describing a biterminal futile signaling cycle and a biterminal prion/double phosphorylation motif.
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