Zobrazeno 1 - 10
of 402
pro vyhledávání: '"Ernst, Oliver P."'
Autor:
Blechta, Jan, Ernst, Oliver G.
We consider the identification of spatially distributed parameters under $H^1$ regularization. Solving the associated minimization problem by Gauss-Newton iteration results in linearized problems to be solved in each step that can be cast as boundary
Externí odkaz:
http://arxiv.org/abs/2209.02815
We present a machine learning method for model reduction which incorporates domain-specific physics through candidate functions. Our method estimates an effective probability distribution and differential equation model from stochastic simulations of
Externí odkaz:
http://arxiv.org/abs/2109.05053
Autor:
Blechschmidt, Jan, Ernst, Oliver G.
Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and their suitabil
Externí odkaz:
http://arxiv.org/abs/2102.11802
Autor:
Menon, Indu, Sych, Taras, Son, Yeeun, Morizumi, Takefumi, Lee, Joon, Ernst, Oliver P., Khelashvili, George, Sezgin, Erdinc, Levitz, Joshua, Menon, Anant K.
Publikováno v:
In Journal of Biological Chemistry February 2024 300(2)
We investigate the stationary diffusion equation with a coefficient given by a (transformed) L\'evy random field. L\'evy random fields are constructed by smoothing L\'evy noise fields with kernels from the Mat\'ern class. We show that L\'evy noise na
Externí odkaz:
http://arxiv.org/abs/2010.14912
Fibre Bragg Gratings have become widespread measurement devices in engineering and other fields of application. In all but a few cases, the relation between cause and effect is simplified to a proportional model. However, at its mathematical core lie
Externí odkaz:
http://arxiv.org/abs/2009.06509
Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori error esti
Externí odkaz:
http://arxiv.org/abs/2008.07186
When propagating uncertainty in the data of differential equations, the probability laws describing the uncertainty are typically themselves subject to uncertainty. We present a sensitivity analysis of uncertainty propagation for differential equatio
Externí odkaz:
http://arxiv.org/abs/2003.03129
This work is a follow-up to our previous contribution ("Convergence of sparse collocation for functions of countably many Gaussian random variables (with application to elliptic PDEs)", SIAM J. Numer. Anal., 2018), and contains further insights on so
Externí odkaz:
http://arxiv.org/abs/1906.01252
The moments of spatial probabilistic systems are often given by an infinite hierarchy of coupled differential equations. Moment closure methods are used to approximate a subset of low order moments by terminating the hierarchy at some order and repla
Externí odkaz:
http://arxiv.org/abs/1905.12122