相关论文: On Divergence- and Gradient-Preserving Coarse-Grai…
A number of results have recently demonstrated the benefits of incorporating various constraints when training deep architectures in vision and machine learning. The advantages range from guarantees for statistical generalization to better…
For a much-studied model of random copolymer at a selective interface we prove that the slope of the critical curve in the weak-disorder limit is strictly smaller than 1, which is the value given by the annealed inequality. The proof is…
Mathematical descriptions of flow phenomena usually come in the form of partial differential equations. The differential operators used in these equations may have properties such as symmetry, skew-symmetry, positive or negative…
The coupled mechanics of fluid-filled granular media controls the behavior of many natural systems such as saturated soils, fault gouge, and landslides. The grain motion and the fluid pressure influence each other: It is well established…
Spin foams are models of quantum gravity and therefore quantum space time. A key open issue is to determine the possible continuum phases of these models. Progress on this issue has been prohibited by the complexity of the full…
During an earthquake, slip occurs in a localised shear zone that features a heavily granulated fault core that can be characterised as a shear band. We study the formation of this fault core in a granular rock such as sandstone by…
To date, the only way to argue polynomial lower bounds for dynamic algorithms is via fine-grained complexity arguments. These arguments rely on strong assumptions about specific problems such as the Strong Exponential Time Hypothesis (SETH)…
Water retention is one of the key soil characteristics. Available models of soil water retention relate to the curve-fitting type. The objective of this work is to suggest a physical model of water retention (drying branch) for soils with a…
Prediction of flow profiles of slowly sheared granular materials is a major geophysical and industrial challenge. Understanding the role of gravity is particularly important for future planetary exploration in varying gravitational…
Recent success in the field of single image super-resolution (SISR) is achieved by optimizing deep convolutional neural networks (CNNs) in the image space with the L1 or L2 loss. However, when trained with these loss functions, models…
Data-driven discovery of "hidden physics" -- i.e., machine learning of differential equation models underlying observed data -- has recently been approached by embedding the discovery problem into a Gaussian Process regression of spatial…
Finite volume methods for problems involving second order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality…
Coarse-graining is a powerful tool for extending the reach of dynamic models of proteins and other biological macromolecules. Topological coarse-graining, in which biomolecules or sets thereof are represented via graph structures, is a…
Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…
Several recent works have explored stochastic gradient methods for variational inference that exploit the geometry of the variational-parameter space. However, the theoretical properties of these methods are not well-understood and these…
Multiphase flow through a porous medium involves complex interactions between gravity, wettability and capillarity during drainage process. In contrast to these factors, the effect of pore distribution on liquid retention is less…
We extend the exact coarse-graining result of Disertori, Merkl and Rolles~\cite{MR4517733} for the random field of $H^{2|2}$-model to the random Schr\"odinger operator representation of the $H^{2|2}$-model. We also introduce a fine-graining…
Small inter-class and large intra-class variations are the main challenges in fine-grained visual classification. Objects from different classes share visually similar structures and objects in the same class can have different poses and…
Local grid refinement aims to optimise the relationship between accuracy of the results and number of grid nodes. In the context of the finite volume method no single local refinement criterion has been globally established as optimum for…
We present a general purpose method for solving partial differential equations on a closed surface, based on a technique for discretizing the surface introduced by Wenjun Ying and Wei-Cheng Wang [J. Comput. Phys. 252 (2013), pp. 606-624]…