196 citations · 1.6k across the 143 of their papers we have counts for
19 papers · 1 filter
Neural-Network Quantum States for Periodic Systems in Continuous Space
Gabriel Pescia, Jiequn Han, Alessandro Lovato +2
We introduce a family of neural quantum states for the simulation of strongly interacting systems in the presence of spatial periodicity. Our variational state is parameterized in…
Geometry of backflow transformation ansatz for quantum many-body fermionic wavefunctions
Hang Huang, J. M. Landsberg, Jianfeng Lu
Wave function ansatz based on the backflow transformation are widely used to parametrize anti-symmetric multivariable functions for many-body quantum problems. We study the geometr…
Machine Learning For Elliptic PDEs: Fast Rate Generalization Bound, Neural Scaling Law and Minimax Optimality
Yiping Lu, Haoxuan Chen, Jianfeng Lu +2
In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method…
Low-rank approximation for multiscale PDEs
Ke Chen, Shi Chen, Qin Li +2
Historically, analysis for multiscale PDEs is largely unified while numerical schemes tend to be equation-specific. In this paper, we propose a unified framework for computing mult…
Optimal artificial boundary conditions based on second-order correctors for three dimensional random elliptic media
Jianfeng Lu, Felix Otto, Lihan Wang
We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale in an infinite heterogeneous medium, in a…
On the closedness and geometry of tensor network state sets
Thomas Barthel, Jianfeng Lu, Gero Friesecke
Tensor network states (TNS) are a powerful approach for the study of strongly correlated quantum matter. The curse of dimensionality is addressed by parametrizing the many-body sta…
Algebraic localization of Wannier functions implies Chern triviality in non-periodic insulators
Jianfeng Lu, Kevin D. Stubbs
For gapped periodic systems (insulators), it has been established that the insulator is topologically trivial (i.e., its Chern number is equal to ) if and only if its Fermi proj…
On the Representation of Solutions to Elliptic PDEs in Barron Spaces
Ziang Chen, Jianfeng Lu, Yulong Lu
Numerical solutions to high-dimensional partial differential equations (PDEs) based on neural networks have seen exciting developments. This paper derives complexity estimates of t…
Edge state dynamics along curved interfaces
Guillaume Bal, Simon Becker, Alexis Drouot +3
We study the propagation of wavepackets along weakly curved interfaces between topologically distinct media. Our Hamiltonian is an adiabatic modulation of Dirac operators omniprese…
A Priori Generalization Error Analysis of Two-Layer Neural Networks for Solving High Dimensional Schrödinger Eigenvalue Problems
Jianfeng Lu, Yulong Lu
This paper analyzes the generalization error of two-layer neural networks for computing the ground state of the Schrödinger operator on a -dimensional hypercube. We prove that t…
Inclusion-Exclusion Principle for Open Quantum Systems with Bosonic Bath
Siyao Yang, Zhenning Cai, Jianfeng Lu
We present two fast algorithms which apply inclusion-exclusion principle to sum over the bosonic diagrams in bare diagrammatic quantum Monte Carlo (dQMC) and inchworm Monte Carlo m…
Structure-preserving numerical schemes for Lindblad equations
Yu Cao, Jianfeng Lu
We study a family of structure-preserving deterministic numerical schemes for Lindblad equations. This family of schemes has a simple form and can systemically achieve arbitrary hi…
A Grid-free Approach for Simulating Sweep and Cyclic Voltammetry
Alec J. Coffman, Jianfeng Lu, Joseph E. Subotnik
We present a new computational approach to simulate linear sweep and cyclic voltammetry experiments that does not require a discretized grid in space to quantify diffusion. By usin…
Actor-Critic Method for High Dimensional Static Hamilton--Jacobi--Bellman Partial Differential Equations based on Neural Networks
Mo Zhou, Jiequn Han, Jianfeng Lu
We propose a novel numerical method for high dimensional Hamilton--Jacobi--Bellman (HJB) type elliptic partial differential equations (PDEs). The HJB PDEs, reformulated as optimal…
Neural Collapse with Cross-Entropy Loss
Jianfeng Lu, Stefan Steinerberger
We consider the variational problem of cross-entropy loss with feature vectors on a unit hypersphere in . We prove that when , the global minimum is…
Algebraic localization implies exponential localization in non-periodic insulators
Jianfeng Lu, Kevin D. Stubbs
Exponentially-localized Wannier functions are a basis of the Fermi projection of a Hamiltonian consisting of functions which decay exponentially fast in space. In two and three spa…
A Priori Generalization Analysis of the Deep Ritz Method for Solving High Dimensional Elliptic Equations
Jianfeng Lu, Yulong Lu, Min Wang
This paper concerns the a priori generalization analysis of the Deep Ritz Method (DRM) [W. E and B. Yu, 2017], a popular neural-network-based method for solving high dimensional pa…
On the global convergence of randomized coordinate gradient descent for non-convex optimization
Ziang Chen, Yingzhou Li, Jianfeng Lu
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…
Locality of the windowed local density of states
Terry A. Loring, Jianfeng Lu, Alexander B. Watson
We introduce a generalization of local density of states which is "windowed" with respect to position and energy, called the windowed local density of states (wLDOS). This definiti…