86 citations · 333 across the 21 of their papers we have counts for
25 papers
Kinetic Mean-Field Planning via Schrödinger Bridges: Existence, Penalization, and Consistency Bounds
Erhan Bayraktar, Zhiyan Ding, Hiroaki Horikawa
We study a mean-field planning problem for a swarm of interacting, non-cooperative agents whose dynamics are stochastic and kinetic. The noise acts on the velocity only, and the in…
Quantitative homogenization of convex Hamilton-Jacobi equations in the Wasserstein space
Zhiyan Ding, Ibrahim Ekren, Yuxi Han +1
We study a homogenization problem for first-order Hamilton-Jacobi equations in the Wasserstein space with a convex Hamiltonian. We show that the solution , which is…
Swarm-based gradient descent meets simulated annealing
Zhiyan Ding, Martin Guerra, Qin Li +1
We introduce a novel method for non-convex optimization, called Swarm-based Simulated Annealing (SSA), which is at the interface between the swarm-based gradient-descent (SBGD) [J.…
Bayesian sampling using interacting particles
Shi Chen, Zhiyan Ding, Qin Li
Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classica…
Single-ancilla ground state preparation via Lindbladians
Zhiyan Ding, Chi-Fang Chen, Lin Lin
We design a quantum algorithm for ground state preparation in the early fault tolerant regime. As a Monte Carlo-style quantum algorithm, our method features a Lindbladian where the…
Robust ground-state energy estimation under depolarizing noise
Zhiyan Ding, Yulong Dong, Yu Tong +1
We present a novel ground-state energy estimation algorithm that is robust under global depolarizing error channels. Building upon the recently developed Quantum Exponential Least…
On optimal bases for multiscale PDEs and Bayesian homogenization
Shi Chen, Zhiyan Ding, Qin Li +1
PDE solutions are numerically represented by basis functions. Classical methods employ pre-defined bases that encode minimum desired PDE properties, which naturally cause redundant…
Convergence of variational Monte Carlo simulation and scale-invariant pre-training
Nilin Abrahamsen, Zhiyan Ding, Gil Goldshlager +1
We provide theoretical convergence bounds for the variational Monte Carlo (VMC) method as applied to optimize neural network wave functions for the electronic structure problem. We…
Simultaneous estimation of multiple eigenvalues with short-depth quantum circuit on early fault-tolerant quantum computers
Zhiyan Ding, Lin Lin
We introduce a multi-modal, multi-level quantum complex exponential least squares (MM-QCELS) method to simultaneously estimate multiple eigenvalues of a quantum Hamiltonian on earl…
Even shorter quantum circuit for phase estimation on early fault-tolerant quantum computers with applications to ground-state energy estimation
Zhiyan Ding, Lin Lin
We develop a phase estimation method with a distinct feature: its maximal runtime (which determines the circuit depth) is , where is the target precision, and the preconst…
High-frequency limit of the inverse scattering problem: asymptotic convergence from inverse Helmholtz to inverse Liouville
Shi Chen, Zhiyan Ding, Qin Li +1
We investigate the asymptotic relation between the inverse problems relying on the Helmholtz equation and the radiative transfer equation (RTE) as physical models, in the high-freq…
On the Global Convergence of Gradient Descent for multi-layer ResNets in the mean-field regime
Zhiyan Ding, Shi Chen, Qin Li +1
Finding the optimal configuration of parameters in ResNet is a nonconvex minimization problem, but first-order methods nevertheless find the global optimum in the overparameterized…
A reduced order Schwarz method for nonlinear multiscale elliptic equations based on two-layer neural networks
Shi Chen, Zhiyan Ding, Qin Li +1
Neural networks are powerful tools for approximating high dimensional data that have been used in many contexts, including solution of partial differential equations (PDEs). We des…
Overparameterization of deep ResNet: zero loss and mean-field analysis
Zhiyan Ding, Shi Chen, Qin Li +1
Finding parameters in a deep neural network (NN) that fit training data is a nonconvex optimization problem, but a basic first-order optimization method (gradient descent) finds a…
Constrained Ensemble Langevin Monte Carlo
Zhiyan Ding, Qin Li
The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a…
Random Coordinate Underdamped Langevin Monte Carlo
Zhiyan Ding, Qin Li, Jianfeng Lu +1
The Underdamped Langevin Monte Carlo (ULMC) is a popular Markov chain Monte Carlo sampling method. It requires the computation of the full gradient of the log-density at each itera…
Random Coordinate Langevin Monte Carlo
Zhiyan Ding, Qin Li, Jianfeng Lu +1
Langevin Monte Carlo (LMC) is a popular Markov chain Monte Carlo sampling method. One drawback is that it requires the computation of the full gradient at each iteration, an expens…
Langevin Monte Carlo: random coordinate descent and variance reduction
Zhiyan Ding, Qin Li
Langevin Monte Carlo (LMC) is a popular Bayesian sampling method. For the log-concave distribution function, the method converges exponentially fast, up to a controllable discretiz…
Variance reduction for Random Coordinate Descent-Langevin Monte Carlo
Zhiyan Ding, Qin Li
Sampling from a log-concave distribution function is one core problem that has wide applications in Bayesian statistics and machine learning. While most gradient free methods have…
Ensemble Kalman Inversion for nonlinear problems: weights, consistency, and variance bounds
Zhiyan Ding, Qin Li, Jianfeng Lu
Ensemble Kalman Inversion (EnKI) and Ensemble Square Root Filter (EnSRF) are popular sampling methods for obtaining a target posterior distribution. They can be seem as one step (t…
Error Lower Bounds of Constant Step-size Stochastic Gradient Descent
Zhiyan Ding, Yiding Chen, Qin Li +1
Stochastic Gradient Descent (SGD) plays a central role in modern machine learning. While there is extensive work on providing error upper bound for SGD, not much is known about SGD…
Ensemble Kalman Sampler: mean-field limit and convergence analysis
Zhiyan Ding, Qin Li
Ensemble Kalman Sampler (EKS) is a method to find approximately samples from a target distribution. As of today, why the algorithm works and how it converges is mostly unk…
On a Fractional Schrödinger equation in the presence of Harmonic potential
Zhiyan Ding, Hichem Hajaiej
In this paper, we establish the existence of ground state solutions for a fractional Schrödinger equation in the presence of a harmonic trapping potential. We also address the orbi…
Ensemble Kalman Inversion: mean-field limit and convergence analysis
Zhiyan Ding, Qin Li
Ensemble Kalman Inversion (EKI) has been a very popular algorithm used in Bayesian inverse problems. It samples particles from a prior distribution, and introduces a motion to move…