Ainsworth, Mark

1. Galerkin Neural Networks: A Framework for Approximating Variational Equations with Error Control
   2021/05/28 by Mark Ainsworth, Ainsworth, Mark, Justin Dong +1 · 5 citations
   Computer Science · Environmental Science · Physics and Astronomy · #35A15 (secondary) #68T07 (primary) #FOS: Computer and information sciences #FOS: Mathematics #Hydrological Forecasting Using AI #Machine Learning (cs.LG) #Model Reduction and Neural Networks #Neural Networks and Applications #Numerical Analysis (math.NA)
2. Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations
   2017/06/19 by Ainsworth, Mark, Fu, Guosheng · 1 citation
   #FOS: Mathematics #Numerical Analysis (math.NA)
3. Plateau Phenomenon in Gradient Descent Training of ReLU networks: Explanation, Quantification and Avoidance
   2020/07/14 by Ainsworth, Mark, Shin, Yeonjong · 1 citation
   #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Numerical Analysis (math.NA)
4. Statically Condensed Iterated Penalty Method for High Order Finite Element Discretizations of Incompressible Flow
   2023/01/04 by Mark Ainsworth, Charles Thomas Parker, Ainsworth, Mark +1 · 1 citation
   Computer Science · Engineering · Mathematics · #65N12 #65N30 #76M10 #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
5. Two and three dimensional H²-conforming finite element approximations without C¹-elements
   2024/06/01 by Mark Ainsworth, Ainsworth, Mark, Charles Parker +1 · 1 citation
   Engineering · #65N30 65N12 #Composite Structure Analysis and Optimization #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Topology Optimization in Engineering
6. Extended Galerkin neural network approximation of singular variational problems with error control
   2024/05/01 by Mark Ainsworth, Justin Dong, Ainsworth, Mark +1 · 1 citation
   Computer Science · Mathematics · #Neural Networks and Applications #Numerical methods in inverse problems