Yingzhou Li

Yingzhou Li
Fudan University · School of Mathematical Sciences

PhD

About

49
Publications
6,003
Reads
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452
Citations
Additional affiliations
July 2017 - December 2020
Duke University
Position
  • Professor (Assistant)
Education
September 2012 - June 2017
Stanford University
Field of study
  • Computational Mathematics
September 2008 - July 2012
Fudan University
Field of study
  • Mathematics

Publications

Publications (49)
Article
We propose a quantum-classical hybrid variational algorithm, the quantum orbital minimization method (qOMM), for obtaining the ground state and low-lying excited states of a Hermitian operator. Given parametrized ansatz circuits representing eigenstates, qOMM implements quantum circuits to represent the objective function in the orbital minimizatio...
Preprint
Full-text available
KSSOLV (Kohn-Sham Solver) is a MATLAB toolbox for performing Kohn-Sham density functional theory (DFT) calculations with a plane-wave basis set. KSSOLV 2.0 preserves the design features of the original KSSOLV software to allow users and developers to easily set up a problem and perform ground-state calculations as well as to prototype and test new...
Article
Full-text available
KSSOLV (Kohn-Sham Solver) is a MATLAB toolbox for performing Kohn-Sham density functional theory (DFT) calculations with a plane-wave basis set. KSSOLV 2.0 preserves the design features of the original KSSOLV software to allow users and developers to easily set up a problem and perform ground-state calculations as well as to prototype and test new...
Preprint
We propose a quantum-classical hybrid variational algorithm, the quantum orbital minimization method (qOMM), for obtaining the ground state and low-lying excited states of a Hermitian operator. Given parameterized ansatz circuits representing eigenstates, qOMM implements quantum circuits to represent the objective function in the orbital minimizati...
Preprint
This paper proves the global convergence of a triangularized orthogonalization-free method (TriOFM). TriOFM, in general, applies a triangularization idea to the gradient of an objective function and removes the rotation invariance in minimizers. More precisely, in this paper, the TriOFM works as an eigensolver for sizeable sparse matrices and obtai...
Preprint
Full-text available
In this work, we analyze the global convergence property of coordinate gradient descent with random choice of coordinates and stepsizes for non-convex optimization problems. Under generic assumptions, we prove that the algorithm iterate will almost surely escape strict saddle points of the objective function. As a result, the algorithm is guarantee...
Article
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...
Article
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...
Preprint
We introduce a data distribution scheme for $\mathcal{H}$-matrices and a distributed-memory algorithm for $\mathcal{H}$-matrix-vector multiplication. Our data distribution scheme avoids an expensive $\Omega(P^2)$ scheduling procedure used in previous work, where $P$ is the number of processes, while data balancing is well-preserved. Based on the da...
Article
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 computational budget. The optimization problem coincides with that of the complete active...
Article
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...
Article
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 differe...
Preprint
Full-text available
A novel orthogonalization-free method together with two specific algorithms are proposed to solve extreme eigenvalue problems. On top of gradient-based algorithms, the proposed algorithms modify the multi-column gradient such that earlier columns are decoupled from later ones. Global convergence to eigenvectors instead of eigenspace is guaranteed a...
Preprint
Full-text available
First-principles electronic structure calculations are very widely used thanks to the many successful software packages available. Their traditional coding paradigm is monolithic, i.e., regardless of how modular its internal structure may be, the code is built independently from others, from the compiler up, with the exception of linear-algebra and...
Preprint
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 computational budget. The method effectively finds an optimal rotation matrix to compress...
Article
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 expensi...
Article
Full-text available
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...
Preprint
Full-text available
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 differe...
Preprint
Full-text available
Structured CNN designed using the prior information of problems potentially improves efficiency over conventional CNNs in various tasks in solving PDEs and inverse problems in signal processing. This paper introduces BNet2, a simplified Butterfly-Net and inline with the conventional CNN. Moreover, a Fourier transform initialization is proposed for...
Preprint
Full-text available
We consider universal approximations of symmetric and anti-symmetric functions, which are important for applications in quantum physics, as well as other scientific and engineering computations. We give constructive approximations with explicit bounds on the number of parameters with respect to the dimension and the target accuracy $\epsilon$. Whil...
Chapter
Generative Adversarial Networks (GANs) have found applications in natural image synthesis and begin to show promises generating synthetic medical images. In many cases, the ability to perform controlled image synthesis using masked priors such as shape and size of organs is desired. However, mask-guided image synthesis is challenging due to the pix...
Preprint
Recent advancements in conditional Generative Adversarial Networks (cGANs) have shown promises in label guided image synthesis. Semantic masks, such as sketches and label maps, are another intuitive and effective form of guidance in image synthesis. Directly incorporating the semantic masks as constraints dramatically reduces the variability and qu...
Preprint
Full-text available
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 energy landscape even when the tensor ring format is muc...
Preprint
Full-text available
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 train the network variationally via loss functions from the underlying physical models. Solve-training framework avoids expensiv...
Preprint
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 non-convex optimization problem, which is a reformulation of the full configuration interaction eigenvalue problem, via an adaptive coordinate descent meth...
Preprint
Full-text available
We propose in this work RBM-SVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and 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 i...
Preprint
Full-text available
Leading eigenvalue problems for large scale matrices arise in many applications. Coordinate-wise descent methods are considered in this work for such problems based on a reformulation of the leading eigenvalue problem as a non-convex optimization problem. The convergence of several coordinate-wise methods is analyzed and compared. Numerical example...
Preprint
Full-text available
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 hard-coded weights and sparse across-channel connections, which a...
Article
Full-text available
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 ar...
Article
Full-text available
Minority carrier diffusion length (LD) 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 LD, ranging from a few nanometers (such as α-Fe2O3 and TiO2) to a few tens of nanometers (s...
Article
Full-text available
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 significan...
Article
Full-text available
Low-rank approximations are popular techniques to reduce the high computational cost of large-scale kernel matrices, which are of significant interest in many applications. The success of low-rank methods hinges on the matrix rank, and in practice, these methods are effective even for high-dimensional datasets. The practical success has elicited th...
Article
Full-text available
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 elliptic operator and linear complexity for solving the associated...
Article
Full-text available
This paper proposes an efficient method for computing selected generalized eigenpairs of a sparse Hermitian definite matrix pencil (A, B). Based on Zolotarev's best rational function approximations of the signum function and conformal maps, we construct the best rational function approximation of a rectangular function supported on an arbitrary int...
Article
Full-text available
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 factorizati...
Article
Full-text available
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(log N) sparse matrices, each of which contains O(N) nonzero entries. We also p...
Article
Full-text available
Kernel matrices are popular in machine learning and scientific computing, but they are limited by their quadratic complexity in both construction and storage. It is well-known that as one varies the kernel parameter, e.g., the width parameter in radial basis function kernels, the kernel matrix changes from a smooth low-rank kernel to a diagonally-d...
Article
Full-text available
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 \times N...
Article
Full-text available
This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form $(\mathcal{L} f)(x) = \int_{\mathbb{R}^d}a(x,\xi) e^{2\pi \i \Phi(x,\xi)}\widehat{f}(\xi) d\xi$, where $\Phi(x,\xi)$ is a phase function, $a(x,\xi)$ is an amplitude function, and $f(x)$ is a given input. The frequency domain i...

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Project (1)
Project
Fast and scalable eigensolvers.