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pro vyhledávání: '"Walton, Steven"'
The stochastic finite volume method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. Still, it struggles with the curse of dimensionality when dealing with multiple stochastic variables. We introduce th
Externí odkaz:
http://arxiv.org/abs/2404.06574
Autor:
Walton, Steven, Tran, Minh-Binh
In our previous work, numerical schemes for a simplified version of 3-wave kinetic equations, in which only the simple forward-cascade terms of the collision operators are kept, have been successfully designed, especially to capture the long time dyn
Externí odkaz:
http://arxiv.org/abs/2402.17481
Autor:
Choi, Brian, Walton, Steven
In this paper, it is shown that all non-trivial solutions of a wide class of dispersive equations, defined by a dispersion relation with minimal hypotheses on its regularity, are compactly supported for at most one time element. With plane waves of d
Externí odkaz:
http://arxiv.org/abs/2301.06288
Image generation has been a long sought-after but challenging task, and performing the generation task in an efficient manner is similarly difficult. Often researchers attempt to create a "one size fits all" generator, where there are few differences
Externí odkaz:
http://arxiv.org/abs/2211.05770
Bayesian optimal experimental design is a sub-field of statistics focused on developing methods to make efficient use of experimental resources. Any potential design is evaluated in terms of a utility function, such as the (theoretically well-justifi
Externí odkaz:
http://arxiv.org/abs/2210.03283
We present a deep learning approximation, stochastic optimization based, method for wave kinetic equations. To build confidence in our approach, we apply the method to a Smoluchowski coagulation equation with multiplicative kernel for which an analyt
Externí odkaz:
http://arxiv.org/abs/2209.12341
We present Neighborhood Attention (NA), the first efficient and scalable sliding-window attention mechanism for vision. NA is a pixel-wise operation, localizing self attention (SA) to the nearest neighboring pixels, and therefore enjoys a linear time
Externí odkaz:
http://arxiv.org/abs/2204.07143
Autor:
Jain, Jitesh, Singh, Anukriti, Orlov, Nikita, Huang, Zilong, Li, Jiachen, Walton, Steven, Shi, Humphrey
Finetuning a pretrained backbone in the encoder part of an image transformer network has been the traditional approach for the semantic segmentation task. However, such an approach leaves out the semantic context that an image provides during the enc
Externí odkaz:
http://arxiv.org/abs/2112.12782
Autor:
Walton, Steven
We consider the null-controllability of a non-local heat equation by interior $L^2(\Omega)$ controls. We confirm a conjecture of Lissy and Zuazua by showing that it is enough to assume that the kernel $k(x,\xi)$ is symmetric and $k(x,\xi)\in L^2(\Ome
Externí odkaz:
http://arxiv.org/abs/2111.09965