Publications (180)
Localized Sparsifying Preconditioner for Periodic Indefinite Systems
Fei Liu, Lexing Ying
This paper introduces the localized sparsifying preconditioner for the pseudospectral approximations of indefinite systems on periodic structures. The work is built on top of the r…
Sweeping Preconditioner for the Helmholtz Equation: Hierarchical Matrix Representation
Björn Engquist, Lexing Ying
The paper introduces the sweeping preconditioner, which is highly efficient for iterative solutions of the variable coefficient Helmholtz equation including very high frequency pro…
Multimodal Sampling via Approximate Symmetries
Lexing Ying
Sampling from multimodal distributions is a challenging task in scientific computing. When a distribution has an exact symmetry between the modes, direct jumps among them can accel…
Generative Modeling via Tree Tensor Network States
Xun Tang, Yoonhaeng Hur, Yuehaw Khoo +1
In this paper, we present a density estimation framework based on tree tensor-network states. The proposed method consists of determining the tree topology with Chow-Liu algorithm,…
Computing localized representations of the kohn-sham subspace via randomization and refinement
Anil Damle, Lin Lin, Lexing Ying
Localized representation of the Kohn-Sham subspace plays an important role in quantum chemistry and materials science. The recently developed selected columns of the density matrix…
Importance Tempering: Group Robustness for Overparameterized Models
Yiping Lu, Wenlong Ji, Zachary Izzo +1
Although overparameterized models have shown their success on many machine learning tasks, the accuracy could drop on the testing distribution that is different from the training o…
Solving for high dimensional committor functions using artificial neural networks
Yuehaw Khoo, Jianfeng Lu, Lexing Ying
In this note we propose a method based on artificial neural network to study the transition between states governed by stochastic processes. In particular, we aim for numerical sch…
Element orbitals for Kohn-Sham density functional theory
Lin Lin, Lexing Ying
We present a method to discretize the Kohn-Sham Hamiltonian matrix in the pseudopotential framework by a small set of basis functions automatically contracted from a uniform basis…
Enterprise-Scale Search: Accelerating Inference for Sparse Extreme Multi-Label Ranking Trees
Philip A. Etter, Kai Zhong, Hsiang-Fu Yu +2
Tree-based models underpin many modern semantic search engines and recommender systems due to their sub-linear inference times. In industrial applications, these models operate at…
Sobolev Acceleration and Statistical Optimality for Learning Elliptic Equations via Gradient Descent
Yiping Lu, Jose Blanchet, Lexing Ying
In this paper, we study the statistical limits in terms of Sobolev norms of gradient descent for solving inverse problem from randomly sampled noisy observations using a general cl…
A note on continuous-time online learning
Lexing Ying
In online learning, the data is provided in a sequential order, and the goal of the learner is to make online decisions to minimize overall regrets. This note is concerned with con…
Fast Solvers for Discrete Diffusion Models: Theory and Applications of High-Order Algorithms
Yinuo Ren, Haoxuan Chen, Yuchen Zhu +5
Discrete diffusion models have emerged as a powerful generative modeling framework for discrete data with successful applications spanning from text generation to image synthesis.…
Top- eXtreme Contextual Bandits with Arm Hierarchy
Rajat Sen, Alexander Rakhlin, Lexing Ying +4
Motivated by modern applications, such as online advertisement and recommender systems, we study the top- extreme contextual bandits problem, where the total number of arms can…
Quantum Multiple Eigenvalue Gaussian filtered Search: an efficient and versatile quantum phase estimation method
Zhiyan Ding, Haoya Li, Lin Lin +3
Quantum phase estimation is one of the most powerful quantum primitives. This work proposes a new approach for the problem of multiple eigenvalue estimation: Quantum Multiple Eigen…
Directional Preconditioner for High Frequency Obstacle Scattering
Lexing Ying
The boundary integral method is an efficient approach for solving time-harmonic obstacle scattering problems by a bounded scatterer. This paper presents the directional preconditio…
Stable factorization for phase factors of quantum signal processing
Lexing Ying
This paper proposes a new factorization algorithm for computing the phase factors of quantum signal processing. The proposed algorithm avoids root finding of high degree polynomial…
Pole-based approximation of Fermi-Dirac function
Lin Lin, Jianfeng Lu, Lexing Ying +1
Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal mapping and the other…
Sampling on Metric Graphs
Rajat Vadiraj Dwaraknath, Lexing Ying
Metric graphs are structures obtained by associating edges in a standard graph with segments of the real line and gluing these segments at the vertices of the graph. The resulting…
Blind free deconvolution over one-parameter sparse families via eigenmatrix
Lexing Ying
This note considers the blind free deconvolution problems of sparse spectral measures from one-parameter families. These problems pose significant challenges since they involve non…
Discrete Symbol Calculus
Laurent Demanet, Lexing Ying
This paper deals with efficient numerical representation and manipulation of differential and integral operators as symbols in phase-space, i.e., functions of space and frequen…
Multidimensional unstructured sparse recovery via eigenmatrix
Lexing Ying
This note considers the multidimensional unstructured sparse recovery problems. Examples include Fourier inversion and sparse deconvolution. The eigenmatrix is a data-driven constr…
A sublinear-time randomized algorithm for column and row subset selection based on strong rank-revealing QR factorizations
Alice Cortinovis, Lexing Ying
In this work, we analyze a sublinear-time algorithm for selecting a few rows and columns of a matrix for low-rank approximation purposes. The algorithm is based on an initial unifo…
Hierarchical Interpolative Factorization Preconditioner for Parabolic Equations
Jordi Feliu-FabÃ, Lexing Ying
This note proposes an efficient preconditioner for solving linear and semi-linear parabolic equations. With the Crank-Nicholson time stepping method, the algebraic system of equati…
Analytical low-rank compression via proxy point selection
Xin Ye, Jianlin Xia, Lexing Ying
It has been known in potential theory that, for some kernels matrices corresponding to well-separated point sets, fast analytical low-rank approximation can be achieved via the use…
Variational inference and density estimation with non-negative tensor train
Xun Tang, Rajat Dwaraknath, Lexing Ying
This work proposes an efficient numerical approach for compressing a high-dimensional discrete distribution function into a non-negative tensor train (NTT) format. The two settings…
Efficient construction of tensor ring representations from sampling
Yuehaw Khoo, Jianfeng Lu, Lexing Ying
In this paper we propose an efficient method to compress a high dimensional function into a tensor ring format, based on alternating least-squares (ALS). Since the function has siz…
Pole expansion for solving a type of parametrized linear systems in electronic structure calculations
Anil Damle, Lin Lin, Lexing Ying
We present a new method for solving parametrized linear systems. Under certain assumptions on the parametrization, solutions to the linear systems for all parameters can be accurat…
An efficient algorithm for entropic optimal transport under martingale-type constraints
Xun Tang, Michael Shavlovsky, Holakou Rahmanian +2
This work introduces novel computational methods for entropic optimal transport (OT) problems under martingale-type conditions. The considered problems include the discrete marting…
A semigroup method for high dimensional committor functions based on neural network
Haoya Li, Yuehaw Khoo, Yinuo Ren +1
This paper proposes a new method based on neural networks for computing the high-dimensional committor functions that satisfy Fokker-Planck equations. Instead of working with parti…
Borrowing From the Future: An Attempt to Address Double Sampling
Yuhua Zhu, Lexing Ying
For model-free reinforcement learning, one of the main difficulty of stochastic Bellman residual minimization is the double sampling problem, i.e., while only one single sample for…
How Discrete and Continuous Diffusion Meet: Comprehensive Analysis of Discrete Diffusion Models via a Stochastic Integral Framework
Yinuo Ren, Haoxuan Chen, Grant M. Rotskoff +1
Discrete diffusion models have gained increasing attention for their ability to model complex distributions with tractable sampling and inference. However, the error analysis for d…
Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
Björn Engquist, Lexing Ying
This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the…
Approximation of High-Dimensional Gibbs Distributions with Functional Hierarchical Tensors
Nan Sheng, Xun Tang, Haoxuan Chen +1
The numerical representation of high-dimensional Gibbs distributions is challenging due to the curse of dimensionality manifesting through the intractable normalization constant ca…
Annealed importance sampling for Ising models with mixed boundary conditions
Lexing Ying
This note introduces a method for sampling Ising models with mixed boundary conditions. As an application of annealed importance sampling and the Swendsen-Wang algorithm, the metho…
On efficient quantum block encoding of pseudo-differential operators
Haoya Li, Hongkang Ni, Lexing Ying
Block encoding lies at the core of many existing quantum algorithms. Meanwhile, efficient and explicit block encodings of dense operators are commonly acknowledged as a challenging…
Additive Sweeping Preconditioner for the Helmholtz Equation
Fei Liu, Lexing Ying
We introduce a new additive sweeping preconditioner for the Helmholtz equation based on the perfect matched layer (PML). This method divides the domain of interest into thin layers…
Hierarchical interpolative factorization for elliptic operators: integral equations
Kenneth L. Ho, Lexing Ying
This paper introduces the hierarchical interpolative factorization for integral equations (HIF-IE) associated with elliptic problems in two and three dimensions. This factorization…
Computing Free Convolutions via Contour Integrals
Alice Cortinovis, Lexing Ying
This work proposes algorithms for computing additive and multiplicative free convolutions of two given measures. We consider measures with compact support whose free convolution re…
Synchrosqueezed Curvelet Transform for 2D Mode Decomposition
Haizhao Yang, Lexing Ying
This paper introduces the synchrosqueezed curvelet transform as an optimal tool for 2D mode decomposition of wavefronts or banded wave-like components. The synchrosqueezed curvelet…
Fast Computation of Partial Fourier Transforms
Lexing Ying, Sergey Fomel
We introduce two efficient algorithms for computing the partial Fourier transforms in one and two dimensions. Our study is motivated by the wave extrapolation procedure in reflecti…
A heuristic independent particle approximation to determinantal point processes
Lexing Ying
A determinantal point process is a stochastic point process that is commonly used to capture negative correlations. It has become increasingly popular in machine learning in recent…
Compressed representation of Kohn-Sham orbitals via selected columns of the density matrix
Anil Damle, Lin Lin, Lexing Ying
Given a set of Kohn-Sham orbitals from an insulating system, we present a simple, robust, efficient and highly parallelizable method to construct a set of, optionally orthogonal, l…
Multi-Level Fine-Tuning: Closing Generalization Gaps in Approximation of Solution Maps under a Limited Budget for Training Data
Zhihan Li, Yuwei Fan, Lexing Ying
In scientific machine learning, regression networks have been recently applied to approximate solution maps (e.g., potential-ground state map of Schrödinger equation). In this pap…
Tensor Network Skeletonization
Lexing Ying
We introduce a new coarse-graining algorithm, tensor network skeletonization, for the numerical computation of tensor networks. This approach utilizes a structure-preserving skelet…
Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
Lin Lin, Jianfeng Lu, Lexing Ying +1
Kohn-Sham density functional theory is one of the most widely used electronic structure theories. In the pseudopotential framework, uniform discretization of the Kohn-Sham Hamilton…
Statistical Spatially Inhomogeneous Diffusion Inference
Yinuo Ren, Yiping Lu, Lexing Ying +1
Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in b…
A note on spike localization for line spectrum estimation
Haoya Li, Hongkang Ni, Lexing Ying
This note considers the problem of approximating the locations of dominant spikes for a probability measure from noisy spectrum measurements under the condition of residue signal,…
Hierarchical interpolative factorization for elliptic operators: differential equations
Kenneth L. Ho, Lexing Ying
This paper introduces the hierarchical interpolative factorization for elliptic partial differential equations (HIF-DE) in two (2D) and three dimensions (3D). This factorization ta…
Convergence Analysis of Discrete Diffusion Model: Exact Implementation through Uniformization
Hongrui Chen, Lexing Ying
Diffusion models have achieved huge empirical success in data generation tasks. Recently, some efforts have been made to adapt the framework of diffusion models to discrete state s…
A simple solver for the fractional Laplacian in multiple dimensions
Victor Minden, Lexing Ying
We present a simple discretization scheme for the hypersingular integral representation of the fractional Laplace operator and solver for the corresponding fractional Laplacian pro…
Sparsify and sweep: an efficient preconditioner for the Lippmann-Schwinger equation
Fei Liu, Lexing Ying
This paper presents an efficient preconditioner for the Lippmann-Schwinger equation that combines the ideas of the sparsifying and the sweeping preconditioners. Following first the…
Solving the Fokker-Planck equation of discretized Dean-Kawasaki models with functional hierarchical tensor
Xun Tang, Lexing Ying
We introduce a novel numerical scheme for solving the Fokker-Planck equation of discretized Dean-Kawasaki models with a functional tensor network ansatz. The Dean-Kawasaki model de…
Monte Carlo Tree Search based Hybrid Optimization of Variational Quantum Circuits
Jiahao Yao, Haoya Li, Marin Bukov +2
Variational quantum algorithms stand at the forefront of simulations on near-term and future fault-tolerant quantum devices. While most variational quantum algorithms involve only…
BCR-Net: a neural network based on the nonstandard wavelet form
Yuwei Fan, Cindy Orozco Bohorquez, Lexing Ying
This paper proposes a novel neural network architecture inspired by the nonstandard form proposed by Beylkin, Coifman, and Rokhlin in [Communications on Pure and Applied Mathematic…
Heisenberg-limited Hamiltonian learning for interacting bosons
Haoya Li, Yu Tong, Hongkang Ni +2
We develop a protocol for learning a class of interacting bosonic Hamiltonians from dynamics with Heisenberg-limited scaling. For Hamiltonians with an underlying bounded-degree gra…
On adaptive low-depth quantum algorithms for robust multiple-phase estimation
Haoya Li, Hongkang Ni, Lexing Ying
This paper is an algorithmic study of quantum phase estimation with multiple eigenvalues. We present robust multiple-phase estimation (RMPE) algorithms with Heisenberg-limited scal…
Adaptively compressed polarizability operator for accelerating large scale \textit{ab initio} phonon calculations
Lin Lin, Ze Xu, Lexing Ying
Phonon calculations based on first principle electronic structure theory, such as the Kohn-Sham density functional theory, have wide applications in physics, chemistry and material…
Bayesian regularization of empirical MDPs
Samarth Gupta, Daniel N. Hill, Lexing Ying +1
In most applications of model-based Markov decision processes, the parameters for the unknown underlying model are often estimated from the empirical data. Due to noise, the policy…
Sparsifying preconditioner for the time-harmonic Maxwell's equations
Fei Liu, Lexing Ying
This paper presents the sparsifying preconditioner for the time-harmonic Maxwell's equations in the integral formulation. Following the work on sparsifying preconditioner for the L…
Quantum wave packet transforms with compact frequency support
Hongkang Ni, Lexing Ying
Different kinds of wave packet transforms are widely used for extracting multi-scale structures in signal processing tasks. This paper introduces the quantum circuit implementation…
Beyond the Quadratic Approximation: the Multiscale Structure of Neural Network Loss Landscapes
Chao Ma, Daniel Kunin, Lei Wu +1
A quadratic approximation of neural network loss landscapes has been extensively used to study the optimization process of these networks. Though, it usually holds in a very small…
Convex relaxation approaches for strictly correlated density functional theory
Yuehaw Khoo, Lexing Ying
In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxation…
A Multiscale Butterfly Algorithm for Multidimensional Fourier Integral Operators
Yingzhou Li, Haizhao Yang, Lexing Ying
This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form $(\mathcal{L} f)(x) = \int_{R^d}a(x,ξ) e^{2ÏıΦ(x,ξ)…
Multidimensional Butterfly Factorization
Yingzhou Li, Haizhao Yang, Lexing Ying
This paper introduces the multidimensional butterfly factorization as a data-sparse representation of multidimensional kernel matrices that satisfy the complementary low-rank prope…
Multi-Objective Optimization via Wasserstein-Fisher-Rao Gradient Flow
Yinuo Ren, Tesi Xiao, Tanmay Gangwani +4
Multi-objective optimization (MOO) aims to optimize multiple, possibly conflicting objectives with widespread applications. We introduce a novel interacting particle method for MOO…
Why resampling outperforms reweighting for correcting sampling bias with stochastic gradients
Jing An, Lexing Ying, Yuhua Zhu
A data set sampled from a certain population is biased if the subgroups of the population are sampled at proportions that are significantly different from their underlying proporti…
A Riemannian Mean Field Formulation for Two-layer Neural Networks with Batch Normalization
Chao Ma, Lexing Ying
The training dynamics of two-layer neural networks with batch normalization (BN) is studied. It is written as the training dynamics of a neural network without BN on a Riemannian m…
Distributed-memory Hierarchical Interpolative Factorization
Yingzhou Li, Lexing Ying
The hierarchical interpolative factorization (HIF) offers an efficient way for solving or preconditioning elliptic partial differential equations. By exploiting locality and low-ra…
High-dimensional density estimation with tensorizing flow
Yinuo Ren, Hongli Zhao, Yuehaw Khoo +1
We propose the tensorizing flow method for estimating high-dimensional probability density functions from the observed data. The method is based on tensor-train and flow-based gene…
Sparsifying preconditioner for soliton calculations
Jianfeng Lu, Lexing Ying
We develop a robust and efficient method for soliton calculations for nonlinear Schrödinger equations. The method is based on the recently developed sparsifying preconditioner com…
Sketch Tomography: Hybridizing Classical Shadow and Matrix Product State
Xun Tang, Haoxuan Chen, Yuehaw Khoo +1
We introduce Sketch Tomography, an efficient procedure for quantum state tomography based on the classical shadow protocol used for quantum observable estimations. The procedure ap…
Fast Phase Factor Finding for Quantum Signal Processing
Hongkang Ni, Lexing Ying
This paper presents two efficient and stable algorithms for recovering phase factors in quantum signal processing (QSP), a crucial component of many quantum algorithms. The first a…
Understanding the Generalization Benefits of Late Learning Rate Decay
Yinuo Ren, Chao Ma, Lexing Ying
Why do neural networks trained with large learning rates for a longer time often lead to better generalization? In this paper, we delve into this question by examining the relation…
Solving high-dimensional Kolmogorov backward equations with functional hierarchical tensor operators
Xun Tang, Leah Collis, Lexing Ying
Solving high-dimensional partial differential equations necessitates methods free of exponential scaling in the dimension of the problem. This work introduces a tensor network appr…
A perturbative analysis for noisy spectral estimation
Lexing Ying
Spectral estimation is a fundamental task in signal processing. Recent algorithms in quantum phase estimation are concerned with the large noise, large frequency regime of the spec…
Double Flip Move for Ising Models with Mixed Boundary Conditions
Lexing Ying
This note introduces the double flip move for accelerating the Swendsen-Wang algorithm for Ising models with mixed boundary conditions below the critical temperature. The double fl…
Pole recovery from noisy data on imaginary axis
Lexing Ying
This note proposes an algorithm for identifying the poles and residues of a meromorphic function from its noisy values on the imaginary axis. The algorithm uses Möbius transform a…
Sparse free deconvolution under unknown noise level via eigenmatrix
Lexing Ying
This note considers the spectral estimation problems of sparse spectral measures under unknown noise levels. The main technical tool is the eigenmatrix method for solving unstructu…
Accelerating Sinkhorn Algorithm with Sparse Newton Iterations
Xun Tang, Michael Shavlovsky, Holakou Rahmanian +4
Computing the optimal transport distance between statistical distributions is a fundamental task in machine learning. One remarkable recent advancement is entropic regularization a…
A Mean-field Analysis of Deep ResNet and Beyond: Towards Provable Optimization Via Overparameterization From Depth
Yiping Lu, Chao Ma, Yulong Lu +2
Training deep neural networks with stochastic gradient descent (SGD) can often achieve zero training loss on real-world tasks although the optimization landscape is known to be hig…
A multiscale neural network based on hierarchical nested bases
Yuwei Fan, Jordi Feliu-Faba, Lin Lin +2
In recent years, deep learning has led to impressive results in many fields. In this paper, we introduce a multi-scale artificial neural network for high-dimensional non-linear map…
Solving parametric PDE problems with artificial neural networks
Yuehaw Khoo, Jianfeng Lu, Lexing Ying
The curse of dimensionality is commonly encountered in numerical partial differential equations (PDE), especially when uncertainties have to be modeled into the equations as random…
Solving high-dimensional Hamilton-Jacobi-Bellman equation with functional hierarchical tensor
Xun Tang, Nan Sheng, Lexing Ying
This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting…
A Sharp Convergence Rate for the Asynchronous Stochastic Gradient Descent
Yuhua Zhu, Lexing Ying
We give a sharp convergence rate for the asynchronous stochastic gradient descent (ASGD) algorithms when the loss function is a perturbed quadratic function based on the stochastic…
Fast construction of hierarchical matrix representation from matrix-vector multiplication
Lin Lin, Jianfeng Lu, Lexing Ying
We develop a hierarchical matrix construction algorithm using matrix-vector multiplications, based on the randomized singular value decomposition of low-rank matrices. The algorith…
An efficient dynamical low-rank algorithm for the Boltzmann-BGK equation close to the compressible viscous flow regime
Lukas Einkemmer, Jingwei Hu, Lexing Ying
It has recently been demonstrated that dynamical low-rank algorithms can provide robust and efficient approximation to a range of kinetic equations. This is true especially if the…
On Linear Stability of SGD and Input-Smoothness of Neural Networks
Chao Ma, Lexing Ying
The multiplicative structure of parameters and input data in the first layer of neural networks is explored to build connection between the landscape of the loss function with resp…
Distributed-memory -matrix Algebra I: Data Distribution and Matrix-vector Multiplication
Yingzhou Li, Jack Poulson, Lexing Ying
We introduce a data distribution scheme for -matrices and a distributed-memory algorithm for -matrix-vector multiplication. Our data distribution scheme a…
Provably convergent quasistatic dynamics for mean-field two-player zero-sum games
Chao Ma, Lexing Ying
In this paper, we study the problem of finding mixed Nash equilibrium for mean-field two-player zero-sum games. Solving this problem requires optimizing over two probability distri…
A technique for updating hierarchical skeletonization-based factorizations of integral operators
Victor Minden, Anil Damle, Kenneth L. Ho +1
We present a method for updating certain hierarchical factorizations for solving linear integral equations with elliptic kernels. In particular, given a factorization corresponding…
A Simple Multiscale Method for Mean Field Games
Haoya Li, Yuwei Fan, Lexing Ying
This paper proposes a multiscale method for solving the numerical solution of mean field games which accelerates the convergence and addresses the problem of determining the initia…
Mirror Descent Algorithms for Minimizing Interacting Free Energy
Lexing Ying
This note considers the problem of minimizing interacting free energy. Motivated by the mirror descent algorithm, for a given interacting free energy, we propose a descent dynamics…
A parallel butterfly algorithm
Jack Poulson, Laurent Demanet, Nicholas Maxwell +1
The butterfly algorithm is a fast algorithm which approximately evaluates a discrete analogue of the integral transform \int K(x,y) g(y) dy at large numbers of target points when t…
How to Learn when Data Gradually Reacts to Your Model
Zachary Izzo, James Zou, Lexing Ying
A recent line of work has focused on training machine learning (ML) models in the performative setting, i.e. when the data distribution reacts to the deployed model. The goal in th…
Correcting Convexity Bias in Function and Functional Estimate
Chao Ma, Lexing Ying
A general framework with a series of different methods is proposed to improve the estimate of convex function (or functional) values when only noisy observations of the true input…
How to Learn when Data Reacts to Your Model: Performative Gradient Descent
Zachary Izzo, Lexing Ying, James Zou
Performative distribution shift captures the setting where the choice of which ML model is deployed changes the data distribution. For example, a bank which uses the number of open…
Continuous-in-time Limit for Bayesian Bandits
Yuhua Zhu, Zachary Izzo, Lexing Ying
This paper revisits the bandit problem in the Bayesian setting. The Bayesian approach formulates the bandit problem as an optimization problem, and the goal is to find the optimal…
Analytic continuation from limited noisy Matsubara data
Lexing Ying
This note proposes a new algorithm for estimating spectral function from limited noisy Matsubara data. We consider both the molecule and condensed matter cases. In each case, the a…
Initialization and training of matrix product state probabilistic models
Xun Tang, Yuehaw Khoo, Lexing Ying
Modeling probability distributions via the wave function of a quantum state is central to quantum-inspired generative modeling and quantum state tomography (QST). We investigate a…
Operator Shifting for Noisy Elliptic Systems
Philip A. Etter, Lexing Ying
In the computational sciences, one must often estimate model parameters from data subject to noise and uncertainty, leading to inaccurate results. In order to improve the accuracy…