Zobrazeno 1 - 10
of 64
pro vyhledávání: '"Gulian, Mamikon"'
In complex large-scale systems such as climate, important effects are caused by a combination of confounding processes that are not fully observable. The identification of sources from observations of system state is vital for attribution and predict
Externí odkaz:
http://arxiv.org/abs/2303.11379
Deep operator learning has emerged as a promising tool for reduced-order modelling and PDE model discovery. Leveraging the expressive power of deep neural networks, especially in high dimensions, such methods learn the mapping between functional stat
Externí odkaz:
http://arxiv.org/abs/2204.10909
Nonlocal vector calculus, which is based on the nonlocal forms of gradient, divergence, and Laplace operators in multiple dimensions, has shown promising applications in fields such as hydrology, mechanics, and image processing. In this work, we stud
Externí odkaz:
http://arxiv.org/abs/2112.05317
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior with greate
Externí odkaz:
http://arxiv.org/abs/2110.11531
Partition of unity networks (POU-Nets) have been shown capable of realizing algebraic convergence rates for regression and solution of PDEs, but require empirical tuning of training parameters. We enrich POU-Nets with a Gaussian noise model to obtain
Externí odkaz:
http://arxiv.org/abs/2107.03066
Many active matter systems are known to perform L\'{e}vy walks during migration or foraging. Such superdiffusive transport indicates long-range correlated dynamics. These behavior patterns have been observed for microswimmers such as bacteria in micr
Externí odkaz:
http://arxiv.org/abs/2104.07117
Approximation theorists have established best-in-class optimal approximation rates of deep neural networks by utilizing their ability to simultaneously emulate partitions of unity and monomials. Motivated by this, we propose partition of unity networ
Externí odkaz:
http://arxiv.org/abs/2101.11256
Autor:
D'Elia, Marta, Gulian, Mamikon
We analyze the well-posedness of an anisotropic, nonlocal diffusion equation. Establishing an equivalence between weighted and unweighted anisotropic nonlocal diffusion operators in the vein of unified nonlocal vector calculus, we apply our analysis
Externí odkaz:
http://arxiv.org/abs/2101.04289
We develop a framework for Gaussian processes regression constrained by boundary value problems. The framework may be applied to infer the solution of a well-posed boundary value problem with a known second-order differential operator and boundary co
Externí odkaz:
http://arxiv.org/abs/2012.11857
Second-order optimizers hold intriguing potential for deep learning, but suffer from increased cost and sensitivity to the non-convexity of the loss surface as compared to gradient-based approaches. We introduce a coordinate descent method to train d
Externí odkaz:
http://arxiv.org/abs/2006.10123