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Efficient hyperparameter estimation in Bayesian inverse problems using sample average approximation. [PDF]
Philos Trans A Math Phys Eng SciChung J +3 more
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False Alarm: When Dropped Gallstones Mimic Malignant Recurrence. A Case Report and Literature Review. [PDF]
Case Rep Obstet GynecolObeidi N +3 more
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WF-PINNs: solving forward and inverse problems of burgers equation with steep gradients using weak-form physics-informed neural networks. [PDF]
Sci RepWang X, Yi S, Gu H, Xu J, Xu W.
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Optimal discretization of Ill-posed problems
Ukrainian Mathematical Journal, 2000Summary: We present a review of results obtained in the Institute of Mathematics of National Ukrainian Academy of Sciences when investigating the optimal digitization of ill-posed problems.
Pereverzev, S. V., Solodkij, S. G.
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2013
As previously mentioned, for problems in mathematical physics Hadamard [95] postulated three requirements: a solution should exist, the solution should be unique, and the solution should depend continuously on the data. The third postulate is motivated by the fact that in all applications the data will be measured quantities.
Fioralba Cakoni, David Colton
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As previously mentioned, for problems in mathematical physics Hadamard [95] postulated three requirements: a solution should exist, the solution should be unique, and the solution should depend continuously on the data. The third postulate is motivated by the fact that in all applications the data will be measured quantities.
Fioralba Cakoni, David Colton
openaire +1 more source
Stochastic Methods for Ill-Posed Problems
BIT Numerical Mathematics, 2000This paper considers the behaviour of ill-posed problems of the stochastic Euler method, semi-implicit Euler method and some new method. The new method shows improved stability for stiff problems. It has been shown that the applied regularization cannot be driven beyond a certain critical parameter level.
Burrage, K., Piskarev, S.
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Noise Models for Ill-Posed Problems
2010The standard view of noise in ill-posed problems is that it is either deterministic and small (strongly bounded noise) or random and large (not necessarily small). Following Eggerment, LaRiccia and Nashed (2009), a new noise model is investigated, wherein the noise is weakly bounded.
Eggermont, Paul N. +2 more
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