partial differential equations

Neural Networks to Accelerate Scientific Computing

Development and application of neural networks to accelerate scientific computing in areas of mechanistic simulation, parameter estimation, model selection, and optimization of materials and structures.

Residual-based error corrector operator to enhance accuracy and reliability of neural operator surrogates of nonlinear variational boundary-value problems

This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating appropriate …

Mutual-Information Based Optimal Experimental Design for Hyperpolarized 13C-Pyruvate MRI

A key parameter of interest recovered from hyperpolarized (HP) MRI measurements is the apparent pyruvate-to-lactate exchange rate, kPL, for measuring tumor metabolism. This manuscript presents an information-theory-based optimal experimental design …