Publications

(2024). Evaluating nAI and Quadrature Based Neural Networks. SIAM Undergraduate Research Online, Under Review, 2024.

(2024). Unified hp-HDG Frameworks for Friedrichs PDE systems. Computer & Mathematics with Applications, Volume 154, Pages 236-266, 15 January 2024.

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(2024). Model-constrained deep learning approaches for inverse problems. SIAM Journal of Scientific Computing, 41(1), C77-C100, January 2024.

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(2023). Model-constrained uncertainty quantification for scientific deep learning of inverse solutions. The XLIV Iberto-Latin American Congress on Computational Mechanics in Engineering, Refereeed Conference Proceedings, 2023.

(2023). A Multilevel Block Preconditioner for the HDG Trace System Applied to Incompressible Resistive MHD. Computer Methods in Applied Mechanics and Engineering, 401 , 115775, February 1, 2023..

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(2023). A Model-Constrained Tangent Manifold Learning Approach for Dynamical Systems. International Journal of Computational Fluid Dynamics, 36(7) , 655-685, February 10, 2023..

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(2023). TNet: A Model-Constrained Tikhonov Network Approach for Inverse Problems. SIAM Journal of Scientific Computing, In Production , 2023.

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(2022). A Unified and Constructive Framework for the Universality of Neural Networks. The IMA Journal of Applied Mathematics, hxad032, November, 2023.

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(2021). High-speed simulation of the 3D behavior of myocardium using a neural network PDE approach. International Conference on Functional Imaging and Modeling of the Heart.

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(2021). Data-Informed Regularization for Inverse and Imaging Problems. Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging, 1-38.

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