4 papers
Adaptive Collocation Point Strategies For Physics Informed Neural Networks via the QR Discrete Empirical Interpolation Method
Adrian Celaya, David Fuentes, Beatrice Riviere
Physics-informed neural networks (PINNs) have gained significant attention for solving forward and inverse problems related to partial differential equations (PDEs). While advancem…
Pre- and Post-Treatment Glioma Segmentation with the Medical Imaging Segmentation Toolkit
Adrian Celaya, Tucker Netherton, Dawid Schellingerhout +3
Medical image segmentation continues to advance rapidly, yet rigorous comparison between methods remains challenging due to a lack of standardized and customizable tooling. In this…
A Priori Generalizability Estimate for a CNN
Cito Balsells, Beatrice Riviere, David Fuentes
We formulate truncated singular value decompositions of entire convolutional neural networks. We demonstrate the computed left and right singular vectors are useful in identifying…
Learning Discontinuous Galerkin Solutions to Elliptic Problems via Small Linear Convolutional Neural Networks
Adrian Celaya, Yimo Wang, David Fuentes +1
In recent years, there has been an increasing interest in using deep learning and neural networks to tackle scientific problems, particularly in solving partial differential equati…