Zobrazeno 1 - 10
of 30
pro vyhledávání: '"Hayden Schaeffer"'
Publikováno v:
Applied and Computational Harmonic Analysis. 62:310-330
Random feature methods have been successful in various machine learning tasks, are easy to compute, and come with theoretical accuracy bounds. They serve as an alternative approach to standard neural networks since they can represent similar function
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::693316dc38e82ddb04c2b708fc042776
https://doi.org/10.1016/j.acha.2022.08.003
https://doi.org/10.1016/j.acha.2022.08.003
Autor:
Hayden Schaeffer
Publikováno v:
Communications in Mathematical Sciences. 16:1757-1777
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ec4e4517064fe5e1bbfb9b2af883227c
https://doi.org/10.4310/cms.2018.v16.n7.a1
https://doi.org/10.4310/cms.2018.v16.n7.a1
Autor:
Hayden Schaeffer, Scott G. McCalla
We provide larger step-size restrictions for which gradient descent based algorithms (almost surely) avoid strict saddle points. In particular, consider a twice differentiable (non-convex) objective function whose gradient has Lipschitz constant L an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::3e51a919ac4754e8122298e64e36e8f2
Autor:
Thomas Y. Hou, Hayden Schaeffer
Publikováno v:
Journal of Scientific Computing. 69:556-580
We propose two numerical methods for accelerating the convergence of the standard fixed point method associated with a nonlinear and/or degenerate elliptic partial differential equation. The first method is linearly stable, while the second is provab
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::420ceaa14dc00345e6c6813a8a24e07b
https://doi.org/10.1007/s10915-016-0215-8
https://doi.org/10.1007/s10915-016-0215-8
Publikováno v:
Journal of Approximation Theory. 259:105472
Learning non-linear systems from noisy, limited, and/or dependent data is an important task across various scientific fields including statistics, engineering, computer science, mathematics, and many more. In general, this learning task is ill-posed;
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::571c53ea4f281eed0c8d0793f7479b35
https://doi.org/10.1016/j.jat.2020.105472
https://doi.org/10.1016/j.jat.2020.105472
Autor:
Hayden Schaeffer, Linan Zhang
The residual neural network (ResNet) is a popular deep network architecture which has the ability to obtain high-accuracy results on several image processing problems. In order to analyze the behavior and structure of ResNet, recent work has been on
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a8edba16d79c303f668125e660a3c4bf
http://arxiv.org/abs/1811.09885
http://arxiv.org/abs/1811.09885
Learning governing equations allows for deeper understanding of the structure and dynamics of data. We present a random sampling method for learning structured dynamical systems from under-sampled and possibly noisy state-space measurements. The lear
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::d17e71cbbb381f327da3d753246dfe57
http://arxiv.org/abs/1805.04158
http://arxiv.org/abs/1805.04158
Autor:
Hayden Schaeffer, Linan Zhang
One way to understand time-series data is to identify the underlying dynamical system which generates it. This task can be done by selecting an appropriate model and a set of parameters which best fits the dynamics while providing the simplest repres
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b45c29c0de4b6acc2f7d70ba84277267
Autor:
Linan Zhang, Hayden Schaeffer
Reconstructing images from ill-posed inverse problems often utilizes total variation regularization in order to recover discontinuities in the data while also removing noise and other artifacts. Total variation regularization has been successful in r
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::679ee6740fc69540f346674cc9640d02
Publikováno v:
Journal of Computational Physics. 288:150-166
For viscous conservation laws, solutions contain smooth but high-contrast features, which require the use of fine grids to properly resolve. On coarse grids, these high-contrast jumps resemble shocks rather than their true viscous profiles, which cou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8987350cf9c08e2b74125fbbac5414a5
https://doi.org/10.1016/j.jcp.2015.02.019
https://doi.org/10.1016/j.jcp.2015.02.019