%% Papers Published
@article{fds353875,
Author = {Li, Y and Cheng, X and Lu, J},
Title = {Butterfly-net: Optimal function representation based on
convolutional neural networks},
Journal = {Communications in Computational Physics},
Volume = {28},
Number = {5},
Pages = {1838-1885},
Publisher = {Global Science Press},
Year = {2020},
Month = {November},
url = {http://dx.doi.org/10.4208/CICP.OA-2020-0214},
Abstract = {© 2020 Global-Science Press Deep networks, especially
convolutional neural networks (CNNs), have been successfully
applied in various areas of machine learning as well as to
challenging problems in other scientific and engineering
fields. This paper introduces Butterfly-net, a
low-complexity CNN with structured and sparse cross-channel
connections, together with a Butterfly initialization
strategy for a family of networks. Theoretical analysis of
the approximation power of Butterfly-net to the Fourier
representation of input data shows that the error decays
exponentially as the depth increases. Combining
Butterfly-net with a fully connected neural network, a large
class of problems are proved to be well approximated with
network complexity depending on the effective frequency
bandwidth instead of the input dimension. Regular CNN is
covered as a special case in our analysis. Numerical
experiments validate the analytical results on the
approximation of Fourier kernels and energy functionals of
Poisson's equations. Moreover, all experiments support that
training from Butterfly initialization outperforms training
from random initialization. Also, adding the remaining
cross-channel connections, although significantly increases
the parameter number, does not much improve the
post-training accuracy and is more sensitive to data
distribution.},
Doi = {10.4208/CICP.OA-2020-0214},
Key = {fds353875}
}
@article{fds350486,
Author = {Yu, VWZ and Campos, C and Dawson, W and García, A and Havu, V and Hourahine, B and Huhn, WP and Jacquelin, M and Jia, W and Keçeli, M and Laasner, R and Li, Y and Lin, L and Lu, J and Moussa, J and Roman, JE and Vázquez-Mayagoitia, Á and Yang, C and Blum, V},
Title = {ELSI — An open infrastructure for electronic structure
solvers},
Journal = {Computer Physics Communications},
Volume = {256},
Pages = {107459-107459},
Publisher = {Elsevier BV},
Year = {2020},
Month = {November},
url = {http://dx.doi.org/10.1016/j.cpc.2020.107459},
Abstract = {© 2020 Elsevier B.V. Routine applications of electronic
structure theory to molecules and periodic systems need to
compute the electron density from given Hamiltonian and, in
case of non-orthogonal basis sets, overlap matrices. System
sizes can range from few to thousands or, in some examples,
millions of atoms. Different discretization schemes (basis
sets) and different system geometries (finite non-periodic
vs. infinite periodic boundary conditions) yield matrices
with different structures. The ELectronic Structure
Infrastructure (ELSI) project provides an open-source
software interface to facilitate the implementation and
optimal use of high-performance solver libraries covering
cubic scaling eigensolvers, linear scaling
density-matrix-based algorithms, and other reduced scaling
methods in between. In this paper, we present recent
improvements and developments inside ELSI, mainly covering
(1) new solvers connected to the interface, (2) matrix
layout and communication adapted for parallel calculations
of periodic and/or spin-polarized systems, (3) routines for
density matrix extrapolation in geometry optimization and
molecular dynamics calculations, and (4) general utilities
such as parallel matrix I/O and JSON output. The ELSI
interface has been integrated into four electronic structure
code projects (DFTB+, DGDFT, FHI-aims, SIESTA), allowing us
to rigorously benchmark the performance of the solvers on an
equal footing. Based on results of a systematic set of
large-scale benchmarks performed with Kohn–Sham
density-functional theory and density-functional
tight-binding theory, we identify factors that strongly
affect the efficiency of the solvers, and propose a decision
layer that assists with the solver selection process.
Finally, we describe a reverse communication interface
encoding matrix-free iterative solver strategies that are
amenable, e.g., for use with planewave basis sets. Program
summary: Program title: ELSI Interface CPC Library link to
program files: http://dx.doi.org/10.17632/473mbbznrs.1
Licensing provisions: BSD 3-clause Programming language:
Fortran 2003, with interface to C/C++ External
routines/libraries: BLACS, BLAS, BSEPACK (optional),
EigenExa (optional), ELPA, FortJSON, LAPACK, libOMM, MPI,
MAGMA (optional), MUMPS (optional), NTPoly, ParMETIS
(optional), PETSc (optional), PEXSI, PT-SCOTCH (optional),
ScaLAPACK, SLEPc (optional), SuperLU_DIST Nature of problem:
Solving the electronic structure from given Hamiltonian and
overlap matrices in electronic structure calculations.
Solution method: ELSI provides a unified software interface
to facilitate the use of various electronic structure
solvers including cubic scaling dense eigensolvers, linear
scaling density matrix methods, and other
approaches.},
Doi = {10.1016/j.cpc.2020.107459},
Key = {fds350486}
}
@article{fds355105,
Author = {Gu, H and Shi, G and Chen, HC and Xie, S and Li, Y and Tong, H and Yang, C and Zhu, C and Mefford, JT and Xia, H and Chueh, WC and Chen, HM and Zhang,
L},
Title = {Strong Catalyst-Support Interactions in Electrochemical
Oxygen Evolution on Ni-Fe Layered Double
Hydroxide},
Journal = {Acs Energy Letters},
Volume = {5},
Number = {10},
Pages = {3185-3194},
Year = {2020},
Month = {October},
url = {http://dx.doi.org/10.1021/acsenergylett.0c01584},
Abstract = {Copyright © 2020 American Chemical Society. Strong
catalyst-support interaction plays a key role in
heterogeneous catalysis, as has been well-documented in
high-temperature gas-phase chemistry, such as the water gas
shift reaction. Insight into how catalyst-support
interactions can be exploited to optimize the catalytic
activity in aqueous electrochemistry, however, is still
lacking. In this work, we show the rationally designed
electrocatalyst/support interface can greatly impact the
overall electrocatalytic activity of Ni-Fe layered double
hydroxide (NiFeLDH) in water oxidation. In particular, the
use of Co as a non-noble metal support greatly improves the
activity of NiFeLDH 10-fold compared to the traditional
electrocatalytic supports such as fluorine-/indium-doped tin
oxide (FTO/ITO) and glassy carbon. We attribute the activity
enhancement of NiFeLDH/Co to the in situ formation of a
porous NiFeCoOxHy layer via Co incorporation, which
dramatically promotes the redox chemistry of metal centers
on the outer surface and enhances the electrical
conductivity of the catalyst over 2 orders of magnitude.
This new discovery highlights the importance of a rationally
designed electrocatalyst/support interface and offers a new
paradigm for designing and developing highly active
electrocatalytic systems via marrying catalyst and support
and creating synergy.},
Doi = {10.1021/acsenergylett.0c01584},
Key = {fds355105}
}
@article{fds351480,
Author = {Li, Y and Lu, J},
Title = {Optimal Orbital Selection for Full Configuration Interaction
(OptOrbFCI): Pursuing the Basis Set Limit under a
Budget.},
Journal = {Journal of Chemical Theory and Computation},
Volume = {16},
Number = {10},
Pages = {6207-6221},
Year = {2020},
Month = {October},
url = {http://dx.doi.org/10.1021/acs.jctc.0c00613},
Abstract = {Full configuration interaction (FCI) solvers are limited to
small basis sets due to their expensive computational costs.
An optimal orbital selection for FCI (OptOrbFCI) is proposed
to boost the power of existing FCI solvers to pursue the
basis set limit under a computational budget. The
optimization problem coincides with that of the complete
active space SCF method (CASSCF), while OptOrbFCI is
algorithmically quite different. OptOrbFCI effectively finds
an optimal rotation matrix via solving a constrained
optimization problem directly to compress the orbitals of
large basis sets to one with a manageable size, conducts FCI
calculations only on rotated orbital sets, and produces a
variational ground-state energy and its wave function.
Coupled with coordinate descent full configuration
interaction (CDFCI), we demonstrate the efficiency and
accuracy of the method on the carbon dimer and nitrogen
dimer under basis sets up to cc-pV5Z. We also benchmark the
binding curve of the nitrogen dimer under the cc-pVQZ basis
set with 28 selected orbitals, which provide consistently
lower ground-state energies than the FCI results under the
cc-pVDZ basis set. The dissociation energy in this case is
found to be of higher accuracy.},
Doi = {10.1021/acs.jctc.0c00613},
Key = {fds351480}
}
@article{fds350710,
Author = {Oliveira, MJT and Papior, N and Pouillon, Y and Blum, V and Artacho, E and Caliste, D and Corsetti, F and de Gironcoli, S and Elena, AM and García, A and García-Suárez, VM and Genovese, L and Huhn, WP and Huhs, G and Kokott, S and Küçükbenli, E and Larsen, AH and Lazzaro,
A and Lebedeva, IV and Li, Y and López-Durán, D and López-Tarifa, P and Lüders, M and Marques, MAL and Minar, J and Mohr, S and Mostofi, AA and O'Cais, A and Payne, MC and Ruh, T and Smith, DGA and Soler, JM and Strubbe, DA and Tancogne-Dejean, N and Tildesley, D and Torrent, M and Yu, VW-Z},
Title = {The CECAM electronic structure library and the modular
software development paradigm.},
Journal = {The Journal of Chemical Physics},
Volume = {153},
Number = {2},
Pages = {024117},
Publisher = {AIP Publishing},
Year = {2020},
Month = {July},
url = {http://dx.doi.org/10.1063/5.0012901},
Abstract = {First-principles electronic structure calculations are now
accessible to a very large community of users across many
disciplines, thanks to many successful software packages,
some of which are described in this special issue. The
traditional coding paradigm for such packages is monolithic,
i.e., regardless of how modular its internal structure may
be, the code is built independently from others, essentially
from the compiler up, possibly with the exception of
linear-algebra and message-passing libraries. This model has
endured and been quite successful for decades. The
successful evolution of the electronic structure methodology
itself, however, has resulted in an increasing complexity
and an ever longer list of features expected within all
software packages, which implies a growing amount of
replication between different packages, not only in the
initial coding but, more importantly, every time a code
needs to be re-engineered to adapt to the evolution of
computer hardware architecture. The Electronic Structure
Library (ESL) was initiated by CECAM (the European Centre
for Atomic and Molecular Calculations) to catalyze a
paradigm shift away from the monolithic model and promote
modularization, with the ambition to extract common tasks
from electronic structure codes and redesign them as
open-source libraries available to everybody. Such libraries
include "heavy-duty" ones that have the potential for a high
degree of parallelization and adaptation to novel hardware
within them, thereby separating the sophisticated computer
science aspects of performance optimization and
re-engineering from the computational science done by, e.g.,
physicists and chemists when implementing new ideas. We
envisage that this modular paradigm will improve overall
coding efficiency and enable specialists (whether they be
computer scientists or computational scientists) to use
their skills more effectively and will lead to a more
dynamic evolution of software in the community as well as
lower barriers to entry for new developers. The model comes
with new challenges, though. The building and compilation of
a code based on many interdependent libraries (and their
versions) is a much more complex task than that of a code
delivered in a single self-contained package. Here, we
describe the state of the ESL, the different libraries it
now contains, the short- and mid-term plans for further
libraries, and the way the new challenges are faced. The ESL
is a community initiative into which several pre-existing
codes and their developers have contributed with their
software and efforts, from which several codes are already
benefiting, and which remains open to the
community.},
Doi = {10.1063/5.0012901},
Key = {fds350710}
}
@article{fds348748,
Author = {Li, Y and Lu, J and Mao, A},
Title = {Variational training of neural network approximations of
solution maps for physical models},
Journal = {Journal of Computational Physics},
Volume = {409},
Year = {2020},
Month = {May},
url = {http://dx.doi.org/10.1016/j.jcp.2020.109338},
Abstract = {© 2020 Elsevier Inc. A novel solve-training framework is
proposed to train neural network in representing low
dimensional solution maps of physical models. Solve-training
framework uses the neural network as the ansatz of the
solution map and trains the network variationally via loss
functions from the underlying physical models.
Solve-training framework avoids expensive data preparation
in the traditional supervised training procedure, which
prepares labels for input data, and still achieves effective
representation of the solution map adapted to the input data
distribution. The efficiency of solve-training framework is
demonstrated through obtaining solution maps for linear and
nonlinear elliptic equations, and maps from potentials to
ground states of linear and nonlinear Schrödinger
equations.},
Doi = {10.1016/j.jcp.2020.109338},
Key = {fds348748}
}
@article{fds348343,
Author = {Hu, W and Liu, J and Li, Y and Ding, Z and Yang, C and Yang,
J},
Title = {Accelerating Excitation Energy Computation in Molecules and
Solids within Linear-Response Time-Dependent Density
Functional Theory via Interpolative Separable Density
Fitting Decomposition.},
Journal = {Journal of Chemical Theory and Computation},
Volume = {16},
Number = {2},
Pages = {964-973},
Year = {2020},
Month = {February},
url = {http://dx.doi.org/10.1021/acs.jctc.9b01019},
Abstract = {We present an efficient way to compute the excitation
energies in molecules and solids within linear-response
time-dependent density functional theory (LR-TDDFT).
Conventional methods to construct and diagonalize the
LR-TDDFT Hamiltonian require ultrahigh computational cost,
limiting its optoelectronic applications to small systems.
Our new method is based on the interpolative separable
density fitting (ISDF) decomposition combined with
implicitly constructing and iteratively diagonalizing the
LR-TDDFT Hamiltonian and only requires low computational
cost to accelerate the LR-TDDFT calculations in the
plane-wave basis sets under the periodic boundary condition.
We show that this method accurately reproduces excitation
energies in a fullerene (C60) molecule and bulk silicon Si64
system with significantly reduced computational cost
compared to conventional direct and iterative calculations.
The efficiency of this ISDF method enables us to investigate
the excited-state properties of liquid water absorption on
MoS2 and phosphorene by using the LR-TDDFT calculations. Our
computational results show that an aqueous environment has a
weak effect on low excitation energies but a strong effect
on high excitation energies of 2D semiconductors for
photocatalytic water splitting.},
Doi = {10.1021/acs.jctc.9b01019},
Key = {fds348343}
}
@article{fds349468,
Author = {Li, L and Li, Y and Liu, JG and Liu, Z and Lu, J},
Title = {A stochastic version of stein variational gradient descent
for efficient sampling},
Journal = {Communications in Applied Mathematics and Computational
Science},
Volume = {15},
Number = {1},
Pages = {37-63},
Publisher = {Mathematical Sciences Publishers},
Year = {2020},
Month = {January},
url = {http://dx.doi.org/10.2140/camcos.2020.15.37},
Abstract = {© Mathematical Sciences Publishers. We propose in this work
RBM-SVGD, a stochastic version of the Stein variational
gradient descent (SVGD) method for efficiently sampling from
a given probability measure, which is thus useful for
Bayesian inference. The method is to apply the random batch
method (RBM) for interacting particle systems proposed by
Jin et al. to the interacting particle systems in SVGD.
While keeping the behaviors of SVGD, it reduces the
computational cost, especially when the interacting kernel
has long range. We prove that the one marginal distribution
of the particles generated by this method converges to the
one marginal of the interacting particle systems under
Wasserstein-2 distance on fixed time interval T0; T U.
Numerical examples verify the efficiency of this new version
of SVGD.},
Doi = {10.2140/camcos.2020.15.37},
Key = {fds349468}
}
@article{fds352465,
Author = {CHEN, Z and LI, Y and LU, J},
Title = {Tensor ring decomposition: Optimization landscape and
one-loop convergence of alternating least
squares},
Journal = {Siam Journal on Matrix Analysis and Applications},
Volume = {41},
Number = {3},
Pages = {1416-1442},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2020},
Month = {January},
url = {http://dx.doi.org/10.1137/19M1270689},
Abstract = {© 2020 Society for Industrial and Applied Mathematics. In
this work, we study the tensor ring decomposition and its
associated numerical algorithms. We establish a sharp
transition of algorithmic difficulty of the optimization
problem as the bond dimension increases: On one hand, we
show the existence of spurious local minima for the
optimization landscape even when the tensor ring format is
much overparameterized, i.e., with bond dimension much
larger than that of the true target tensor. On the other
hand, when the bond dimension is further increased, we
establish one-loop convergence for the alternating least
squares algorithm for the tensor ring decomposition. The
theoretical results are complemented by numerical
experiments for both local minima and the one-loop
convergence for the alternating least squares
algorithm.},
Doi = {10.1137/19M1270689},
Key = {fds352465}
}
@article{fds355106,
Author = {Zhu, C and Zhang, Z and Zhong, L and Hsu, CS and Xu, X and Li, Y and Zhao, S and Chen, S and Yu, J and Wu, M and Gao, P and Li, S and Chen, HM and Liu, K and Zhang, L},
Title = {Product-Specific Active Site Motifs of Cu for
Electrochemical CO2 Reduction},
Journal = {Chem},
Year = {2020},
Month = {January},
url = {http://dx.doi.org/10.1016/j.chempr.2020.10.018},
Abstract = {© 2020 Elsevier Inc. Aqueous electrochemical CO2 reduction
(CO2R) on Cu can generate a variety of valuable fuels, yet
challenges remain in the improvement of electrosynthesis
pathways for highly selective fuel production.
Mechanistically, understanding CO2R on Cu, particularly
identifying the product-specific active sites, is crucial.
Herein, we rationally designed and fabricated nine
large-area single-crystal Cu foils with various surface
orientations as electrocatalysts and identified the voltage-
and facet-dependent CO2R selectivities. Operando grazing
incidence X-ray diffraction (GIXRD) and electron
back-scattered diffraction (EBSD) were applied to track the
top-surface reconstructions of Cu, and we correlate the
structural evolution with the change of product
selectivities. We extracted three distinct structural
descriptors, including crystal facet, atomic coordination
number, and step-terrace angle, to reveal the intrinsic
structure-function relationships and uniquely identify the
specific product-producing sites for CO2R. Our work guides
the rational design of Cu-based CO2R electrocatalysts and,
more importantly, establishes a paradigm to understand the
structure-function correlation in catalysis.},
Doi = {10.1016/j.chempr.2020.10.018},
Key = {fds355106}
}
@article{fds342765,
Author = {Wang, Z and Li, Y and Lu, J},
Title = {Coordinate Descent Full Configuration Interaction.},
Journal = {Journal of Chemical Theory and Computation},
Volume = {15},
Number = {6},
Pages = {3558-3569},
Year = {2019},
Month = {June},
url = {http://dx.doi.org/10.1021/acs.jctc.9b00138},
Abstract = {We develop an efficient algorithm, coordinate descent FCI
(CDFCI), for the electronic structure ground-state
calculation in the configuration interaction framework.
CDFCI solves an unconstrained nonconvex optimization
problem, which is a reformulation of the full configuration
interaction eigenvalue problem, via an adaptive coordinate
descent method with a deterministic compression strategy.
CDFCI captures and updates appreciative determinants with
different frequencies proportional to their importance. We
show that CDFCI produces accurate variational energy for
both static and dynamic correlation by benchmarking the
binding curve of nitrogen dimer in the cc-pVDZ basis with
10<sup>-3</sup> mHa accuracy. We also demonstrate the
efficiency and accuracy of CDFCI for strongly correlated
chromium dimer in the Ahlrichs VDZ basis and produce
state-of-the-art variational energy.},
Doi = {10.1021/acs.jctc.9b00138},
Key = {fds342765}
}
@article{fds341433,
Author = {Li, Y and Lu, J},
Title = {Bold diagrammatic Monte Carlo in the lens of stochastic
iterative methods},
Journal = {Transactions of Mathematics and Its Applications},
Volume = {3},
Number = {1},
Pages = {1-17},
Publisher = {Oxford University Press (OUP)},
Year = {2019},
Month = {February},
url = {http://dx.doi.org/10.1093/imatrm/tnz001},
Abstract = {<jats:title>Abstract</jats:title> <jats:p>This work aims at
understanding of bold diagrammatic Monte Carlo (BDMC)
methods for stochastic summation of Feynman diagrams from
the angle of stochastic iterative methods. The convergence
enhancement trick of the BDMC is investigated from the
analysis of condition number and convergence of the
stochastic iterative methods. Numerical experiments are
carried out for model systems to compare the BDMC with
related stochastic iterative approaches.</jats:p>},
Doi = {10.1093/imatrm/tnz001},
Key = {fds341433}
}
@article{fds341424,
Author = {Li, Y and Lin, L},
Title = {Globally constructed adaptive local basis set for spectral
projectors of second order differential operators},
Journal = {Multiscale Modeling & Simulation},
Volume = {17},
Number = {1},
Pages = {92-116},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2019},
Month = {January},
url = {http://dx.doi.org/10.1137/17M1140236},
Abstract = {© 2019 Society for Industrial and Applied Mathematics.
Spectral projectors of second order differential operators
play an important role in quantum physics and other
scientific and engineering applications. In order to resolve
local features and to obtain converged results, typically
the number of degrees of freedom needed is much larger than
the rank of the spectral projector. This leads to
significant cost in terms of both computation and storage.
In this paper, we develop a method to construct a basis set
that is adaptive to the given differential operator. The
basis set is systematically improvable, and the local
features of the projector is built into the basis set. As a
result the required number of degrees of freedom is only a
small constant times the rank of the projector. The
construction of the basis set uses a randomized procedure
and only requires applying the differential operator to a
small number of vectors on the global domain, while each
basis function itself is supported on strictly local domains
and is discontinuous across the global domain. The spectral
projector on the global domain is systematically
approximated from such a basis set using the discontinuous
Galerkin method. The global construction procedure is very
flexible and allows a local basis set to be consistently
constructed even if the operator contains a nonlocal
potential term. We verify the effectiveness of the globally
constructed adaptive local basis set using one-, two-and
three-dimensional linear problems with local potentials, as
well as a one dimensional nonlinear problem with nonlocal
potentials resembling the Hartree-Fock problem in quantum
physics.},
Doi = {10.1137/17M1140236},
Key = {fds341424}
}
@article{fds345879,
Author = {Yingzhou, LI and Jianfeng, LU and Wang, AZHE},
Title = {Coordinatewise descent methods for leading eigenvalue
problem},
Journal = {Siam Journal on Scientific Computing},
Volume = {41},
Number = {4},
Pages = {A2681-A2716},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2019},
Month = {January},
url = {http://dx.doi.org/10.1137/18M1202505},
Abstract = {© 2019 Society for Industrial and Applied Mathematics
Leading eigenvalue problems for large scale matrices arise
in many applications. Coordinatewise descent methods are
considered in this work for such problems based on a
reformulation of the leading eigenvalue problem as a
nonconvex optimization problem. The convergence of several
coordinatewise methods is analyzed and compared. Numerical
examples of applications to quantum many-body problems
demonstrate the efficiency and provide benchmarks of the
proposed coordinatewise descent methods.},
Doi = {10.1137/18M1202505},
Key = {fds345879}
}
@article{fds347983,
Author = {Wang, R and Li, Y and Mahoney, MW and Darve, E},
Title = {Block basis factorization for scalable kernel
evaluation},
Journal = {Siam Journal on Matrix Analysis and Applications},
Volume = {40},
Number = {4},
Pages = {1497-1526},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2019},
Month = {January},
url = {http://dx.doi.org/10.1137/18M1212586},
Abstract = {© 2019 Society for Industrial and Applied Mathematics
Kernel methods are widespread in machine learning; however,
they are limited by the quadratic complexity of the
construction, application, and storage of kernel matrices.
Low-rank matrix approximation algorithms are widely used to
address this problem and reduce the arithmetic and storage
cost. However, we observed that for some datasets with wide
intraclass variability, the optimal kernel parameter for
smaller classes yields a matrix that is less
well-approximated by low-rank methods. In this paper, we
propose an efficient structured low-rank approximation
method-the block basis factorization (BBF)-and its fast
construction algorithm to approximate radial basis function
kernel matrices. Our approach has linear memory cost and
floating point operations for many machine learning kernels.
BBF works for a wide range of kernel bandwidth parameters
and extends the domain of applicability of low-rank
approximation methods significantly. Our empirical results
demonstrate the stability and superiority over the
state-of-the-art kernel approximation algorithms.},
Doi = {10.1137/18M1212586},
Key = {fds347983}
}
@article{fds328965,
Author = {Li, Y and Yang, H and Ying, L},
Title = {Multidimensional butterfly factorization},
Journal = {Applied and Computational Harmonic Analysis},
Volume = {44},
Number = {3},
Pages = {737-758},
Publisher = {Elsevier BV},
Year = {2018},
Month = {May},
url = {http://dx.doi.org/10.1016/j.acha.2017.04.002},
Abstract = {© 2017 Elsevier Inc. This paper introduces the
multidimensional butterfly factorization as a data-sparse
representation of multidimensional kernel matrices that
satisfy the complementary low-rank property. This
factorization approximates such a kernel matrix of size N×N
with a product of O(logN) sparse matrices, each of which
contains O(N) nonzero entries. We also propose efficient
algorithms for constructing this factorization when either
(i) a fast algorithm for applying the kernel matrix and its
adjoint is available or (ii) every entry of the kernel
matrix can be evaluated in O(1) operations. For the kernel
matrices of multidimensional Fourier integral operators, for
which the complementary low-rank property is not satisfied
due to a singularity at the origin, we extend this
factorization by combining it with either a polar coordinate
transformation or a multiscale decomposition of the
integration domain to overcome the singularity. Numerical
results are provided to demonstrate the efficiency of the
proposed algorithms.},
Doi = {10.1016/j.acha.2017.04.002},
Key = {fds328965}
}
@article{fds340826,
Author = {Wang, R and Li, Y and Darve, E},
Title = {On the Numerical Rank of Radial Basis Function Kernels in
High Dimensions},
Journal = {Siam Journal on Matrix Analysis and Applications},
Volume = {39},
Number = {4},
Pages = {1810-1835},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2018},
Month = {January},
url = {http://dx.doi.org/10.1137/17m1135803},
Doi = {10.1137/17m1135803},
Key = {fds340826}
}
@article{fds329936,
Author = {Li, Y and Ying, L},
Title = {Distributed-memory hierarchical interpolative
factorization},
Journal = {Research in Mathematical Sciences},
Volume = {4},
Number = {1},
Publisher = {Springer Nature},
Year = {2017},
Month = {December},
url = {http://dx.doi.org/10.1186/s40687-017-0100-6},
Abstract = {© 2017, The Author(s). The hierarchical interpolative
factorization (HIF) offers an efficient way for solving or
preconditioning elliptic partial differential equations. By
exploiting locality and low-rank properties of the
operators, the HIF achieves quasi-linear complexity for
factorizing the discrete positive definite elliptic operator
and linear complexity for solving the associated linear
system. In this paper, the distributed-memory HIF (DHIF) is
introduced as a parallel and distributed-memory
implementation of the HIF. The DHIF organizes the processes
in a hierarchical structure and keeps the communication as
local as possible. The computation complexity is O(NlogNP)
and O(NP) for constructing and applying the DHIF,
respectively, where N is the size of the problem and P is
the number of processes. The communication complexity is
O(Plog3P)α+O(N2/3P)β where α is the latency and β is the
inverse bandwidth. Extensive numerical examples are
performed on the NERSC Edison system with up to 8192
processes. The numerical results agree with the complexity
analysis and demonstrate the efficiency and scalability of
the DHIF.},
Doi = {10.1186/s40687-017-0100-6},
Key = {fds329936}
}
@article{fds329937,
Author = {Zhang, L and Sun, L and Guan, Z and Lee, S and Li, Y and Deng, HD and Li, Y and Ahlborg, NL and Boloor, M and Melosh, NA and Chueh,
WC},
Title = {Quantifying and Elucidating Thermally Enhanced Minority
Carrier Diffusion Length Using Radius-Controlled Rutile
Nanowires.},
Journal = {Nano Letters},
Volume = {17},
Number = {9},
Pages = {5264-5272},
Year = {2017},
Month = {September},
url = {http://dx.doi.org/10.1021/acs.nanolett.7b01504},
Abstract = {The minority carrier diffusion length (L<sub>D</sub>) is a
crucial property that determines the performance of light
absorbers in photoelectrochemical (PEC) cells. Many
transition-metal oxides are stable photoanodes for solar
water splitting but exhibit a small to moderate
L<sub>D</sub>, ranging from a few nanometers (such as
α-Fe<sub>2</sub>O<sub>3</sub> and TiO<sub>2</sub>) to a few
tens of nanometers (such as BiVO<sub>4</sub>). Under
operating conditions, the temperature of PEC cells can
deviate substantially from ambient, yet the temperature
dependence of L<sub>D</sub> has not been quantified. In this
work, we show that measuring the photocurrent as a function
of both temperature and absorber dimensions provides a
quantitative method for evaluating the temperature-dependent
minority carrier transport. By measuring photocurrents of
nonstoichiometric rutile TiO<sub>2-x</sub> nanowires as a
function of wire radius (19-75 nm) and temperature (10-70
°C), we extract the minority carrier diffusion length along
with its activation energy. The minority carrier diffusion
length in TiO<sub>2-x</sub> increases from 5 nm at 25 °C to
10 nm at 70 °C, implying that enhanced carrier mobility
outweighs the increase in the recombination rate with
temperature. Additionally, by comparing the
temperature-dependent photocurrent in BiVO<sub>4</sub>,
TiO<sub>2</sub>, and α-Fe<sub>2</sub>O<sub>3</sub>, we
conclude that the ratio of the minority carrier diffusion
length to the depletion layer width determines the extent of
temperature enhancement, and reconcile the widespread
temperature coefficients, which ranged from 0.6 to 1.7%
K<sup>-1</sup>. This insight provides a general design rule
to select light absorbers for large thermally activated
photocurrents and to predict PEC cell characteristics at a
range of temperatures encountered during realistic device
operation.},
Doi = {10.1021/acs.nanolett.7b01504},
Key = {fds329937}
}
@article{fds328966,
Author = {Li, Y and Yang, H},
Title = {Interpolative butterfly factorization},
Journal = {Siam Journal on Scientific Computing},
Volume = {39},
Number = {2},
Pages = {A503-A531},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2017},
Month = {January},
url = {http://dx.doi.org/10.1137/16M1074941},
Abstract = {© 2017 Societ y for Industrial and Applied Mathematics.
This paper introduces the interpolative butterfly
factorization for nearly optimal implementation of several
transforms in harmonic analysis, when their explicit
formulas satisfy certain analytic properties and the matrix
representations of these transforms satisfy a complementary
low-rank property. A preliminary interpolative butterfly
factorization is constructed based on interpolative low-rank
approximations of the complementary low-rank matrix. A novel
sweeping matrix compression technique further compresses the
preliminary interpolative butterfly factorization via a
sequence of structure-preserving low-rank approximations.
The sweeping procedure propagates the low-rank property
among neighboring matrix factors to compress dense
submatrices in the preliminary butterfly factorization to
obtain an optimal one in the butterfly scheme. For an N×N
matrix, it takes O(N logN) operations and complexity to
construct the factorization as a product of O(logN) sparse
matrices, each with O(N) nonzero entries. Hence, it can be
applied rapidly in O(N log N) operations. Numerical results
are provided to demonstrate the effectiveness of this
algorithm.},
Doi = {10.1137/16M1074941},
Key = {fds328966}
}
@article{fds328967,
Author = {Li, Y and Yang, H and Martin, ER and Ho, KL and Ying,
L},
Title = {Butterfly factorization},
Journal = {Multiscale Modeling & Simulation},
Volume = {13},
Number = {2},
Pages = {714-732},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2015},
Month = {January},
url = {http://dx.doi.org/10.1137/15M1007173},
Abstract = {© 2015 Society for Industrial and Applied Mathematics. The
paper introduces the butterfly factorization as a
data-sparse approximation for the matrices that satisfy a
complementary low-rank property. The factorization can be
constructed efficiently if either fast algorithms for
applying the matrix and its adjoint are available or the
entries of the matrix can be sampled individually. For an N
× N matrix, the resulting factorization is a product of
O(logN) sparse matrices, each with O(N) nonzero entries.
Hence, it can be applied rapidly in O(N logN) operations.
Numerical results are provided to demonstrate the
effectiveness of the butterfly factorization and its
construction algorithms.},
Doi = {10.1137/15M1007173},
Key = {fds328967}
}
@article{fds328968,
Author = {Li, Y and Yang, H and Ying, L},
Title = {A multiscale butterfly algorithm for multidimensional
fourier integral operators},
Journal = {Multiscale Modeling & Simulation},
Volume = {13},
Number = {2},
Pages = {614-631},
Publisher = {Society for Industrial & Applied Mathematics
(SIAM)},
Year = {2015},
Month = {January},
url = {http://dx.doi.org/10.1137/140997658},
Abstract = {© 2015 Society for Industrial and Applied Mathematics. This
paper presents an efficient multiscale butterfly algorithm
for computing Fourier integral operators (FIOs) of the form
(Lf)(x) =∫ <inf>ℝ d</inf>a(x, ξ)e<sup>2πiΦ(x,ξ)</sup>f(ξ)dξ,
where Φ(x, ξ) is a phase function, a(x, ξ) is an
amplitude function, and f(x) is a given input. The frequency
domain is hierarchically decomposed into a union of
Cartesian coronas. The integral kernel a(x,
ξ)e<sup>2πiΦ(x,ξ)</sup>in each corona satisfies a
special low-rank property that enables the application of a
butterfly algorithm on the Cartesian phase-space grid. This
leads to an algorithm with quasi-linear operation complexity
and linear memory complexity. Different from previous
butterfly methods for the FIOs, this new approach is simple
and reduces the computational cost by avoiding extra
coordinate transformations. Numerical examples in two and
three dimensions are provided to demonstrate the practical
advantages of the new algorithm.},
Doi = {10.1137/140997658},
Key = {fds328968}
}
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Mathematics Department