Works Published in 2020
Displaying works 1 - 20 of 164 in total
Sorted by most recent date added to the index first, which may not be the same as publication date order.
2020 journal article
TRAINABILITY OF ReLU NETWORKS AND DATA-DEPENDENT INITIALIZATION
Journal of Machine Learning for Modeling and Computing, 1(1), 39–74.
arxiv.org (repository)
Source: ORCID
Added: January 24, 2024
2020 journal article
On the Convergence of Physics Informed Neural Networks for Linear Second-Order Elliptic and Parabolic Type PDEs
Communications in Computational Physics, 28(5), 2042–2074.
Contributors: J. Darbon & G. Karniadakis
TL;DR:
This is the first theoretical work that shows the consistency of PINNs, and it is shown that the sequence of minimizers strongly converges to the PDE solution in $C^0$.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: January 24, 2024
2020 journal article
Dying ReLU and Initialization: Theory and Numerical Examples
Communications in Computational Physics, 28(5), 1671–1706.
Contributors: Y. Shin* , Y. Su & G. Karniadakis
TL;DR:
It is shown that even for rectified linear unit activation, deep and narrow neural networks (NNs) will converge to erroneous mean or median states of the target function depending on the loss with high probability.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: January 24, 2024
2020 journal article
A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral Cauchy data
Journal of Inverse and Ill-Posed Problems, 0(0).
Source: ORCID
Added: January 23, 2024
2020 journal article
Numerical solution of a linearized travel time tomography problem with incomplete data
SIAM Journal on Scientific Computing, 42(5), B1173–B1192.
Contributors: M. Klibanov, T. Le* & L. Nguyen
TL;DR:
A new numerical method is proposed to solve the linearized problem of the travel time tomography with incomplete data using the technique of the truncation of the Fourier series.
(via Semantic Scholar)
Source: ORCID
Added: January 23, 2024
2020 report
Scalable spatio-temporal modeling using a fast multipole method for 3D tracer concentration breakthrough data with magnetic resonance imaging.
Sandia National Lab.(SNL-NM), Albuquerque, NM (United States).
Source: ORCID
Added: November 1, 2023
2020 journal article
Parallelization of the inverse fast multipole method with an application to boundary element method
Computer Physics Communications, 247, 106975.
TL;DR:
An algorithm to parallelize the inverse fast multipole method (IFMM), which is an approximate direct solver for dense linear systems, based on a greedy coloring algorithm, which proved that when σ ≥ 6 , the workload associated with one color is embarrassingly parallel.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: November 1, 2023
2020 journal article
An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations
SIAM Journal on Matrix Analysis and Applications, 41(2), 715–746.
TL;DR:
This work proposes a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND -- sparsified Nested Dissection, based on nested dissection, sparsification and low-rank compression and demonstrates that a version using orthogonal factorization and block-diagonal scaling takes less CG iterations to converge than previous similar algorithms on various kinds of problems.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions
(OpenAlex)
Sources: ORCID, Crossref, NC State University Libraries
Added: November 1, 2023
2020 conference paper
A preconditioner based on sparsified nested dissection and low-rank approximation
XXI Householder Symposium on Numerical Linear Algebra, 128.
Source: ORCID
Added: November 1, 2023
2020 journal article
Stability of thin film flowing down the outer surface of a rotating non-uniformly heated vertical cylinder
Nonlinear Dynamics, 100(2), 1143–1172.
Contributors: A. Mukhopadhyay *, S. Chattopadhyay* & A. Barua *
Source: ORCID
Added: October 13, 2023
2020 chapter
Central-upwind scheme for a non-hydrostatic Saint-Venant system
In Hyperbolic problems: theory, numerics, applications (Vol. 10, pp. 25–41). Am. Inst. Math. Sci. (AIMS), Springfield, MO.
Source: ORCID
Added: September 19, 2023
2020 journal article
Physics-integrated machine learning: embedding a neural network in the Navier-Stokes equations. Part I
ArXiv. https://publons.com/wos-op/publon/58758828/
Contributors: A. S. Iskhakov & N. T. Dinh
Source: ORCID
Added: September 5, 2023
2020 journal article
EFFECTIVE <i>l <sup>2 DECOUPLING FOR THE PARABOLA
Mathematika, 66(3), 681–712.
Sources: Crossref, NC State University Libraries
Added: August 24, 2023
2020 journal article
Nonlinear power-like and SVD-like iterative schemes with applications to entangled bipartite rank-1 approximation
SIAM Journal on Scientific Computing, S448–S474.
Contributors: M. Chu* & M. Lin
TL;DR:
This work has shown that the distance between a mixed state and the convex set of separable states in a bipartite quantum mechanical system over the complex field is smaller than the total number of states in the system.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
9. Industry, Innovation and Infrastructure
(Web of Science)
Source: ORCID
Added: July 4, 2023
2020 journal article
Theory for undercompressive shocks in tears of wine
Physical Review Fluids, 5(3).
Sources: ORCID, Crossref, NC State University Libraries
Added: May 18, 2023
2020 journal article
Steady states and dynamics of a thin-film-type equation with non-conserved mass
European Journal of Applied Mathematics, 11, 1–34.
Source: ORCID
Added: May 18, 2023
2020 journal article
Modelling film flows down a fibre influenced by nozzle geometry
Journal of Fluid Mechanics, 901.
Sources: ORCID, Crossref, NC State University Libraries
Added: May 18, 2023
2020 conference paper
Crystal for Stable Grothendieck Polynomials
Proceedings of of the 32nd Conference on Formal Power Series and Algebraic Combinatorics. Presented at the 32nd Conference on Formal Power Series and Algebraic Combinatorics, Ramat Gan, Israel.
Event: 32nd Conference on Formal Power Series and Algebraic Combinatorics at Ramat Gan, Israel on July 13-17, 2020
Source: NC State University Libraries
Added: March 31, 2023
2020 journal article
A Crystal on Decreasing Factorizations in the 0-Hecke Monoid
The Electronic Journal of Combinatorics, 27(2).
TL;DR:
It is proved that under the residue map the $\star$-crystal intertwines with the crystal on set-valued tableaux recently introduced by Monical, Pechenik and Scrimshaw.
(via Semantic Scholar)
Sources: ORCID, Crossref, NC State University Libraries
Added: March 30, 2023
2020 journal article
A functional analysis approach to the static replication of European options
Quantitative Finance, 21(4), 637–655.
author keywords: Derivatives; Options; Static replication; Payoff; Integral equation; Functional analysis; Spectral theorem; Breeden-Litzenberger formula; Implied distribution
Sources: Crossref, NC State University Libraries
Added: February 18, 2023
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