arXiv subjects

Feng Bao

Publications and source records attributed to Feng Bao.

62 records · Page 4Linked to original sources

arXiv2020

An efficient numerical algorithm for solving data driven feedback control problems

The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an Itô type stochastic differential equation with control process entering both in the drift and the diffusion, and is observed partially. The optimal control of feedback form is determined based on the available observational data. We call this type of control problems the data driven feedback control. The computational framework that we introduce to solve such type of problems aims to find the best estimate for the optimal control as a conditional expectation given the observational information. To make our method feasible in providing timely feedback to the controlled system from data, we develop an efficient stochastic optimization algorithm to implement our computational framework.

math.OC↗

arXiv2020

Reconstruction of effective potential from statistical analysis of dynamic trajectories

The broad incorporation of microscopic methods is yielding a wealth of information on atomic and mesoscale dynamics of individual atoms, molecules, and particles on surfaces and in open volumes. Analysis of such data necessitates statistical frameworks to convert observed dynamic behaviors to effective properties of materials. Here we develop a method for stochastic reconstruction of effective acting potentials from observed trajectories. Using the Silicon vacancy defect in graphene as a model, we develop a statistical framework to reconstruct the free energy landscape from calculated atomic displacements.

cond-mat.mes-hall↗

arXiv2019

Analytic Continuation of Noisy Data Using Adams Bashforth ResNet

We propose a data-driven learning framework for the analytic continuation problem in numerical quantum many-body physics. Designing an accurate and efficient framework for the analytic continuation of imaginary time using computational data is a grand challenge that has hindered meaningful links with experimental data. The standard Maximum Entropy (MaxEnt)-based method is limited by the quality of the computational data and the availability of prior information. Also, the MaxEnt is not able to solve the inversion problem under high level of noise in the data. Here we introduce a novel learning model for the analytic continuation problem using a Adams-Bashforth residual neural network (AB-ResNet). The advantage of this deep learning network is that it is model independent and, therefore, does not require prior information concerning the quantity of interest given by the spectral function. More importantly, the ResNet-based model achieves higher accuracy than MaxEnt for data with higher level of noise. Finally, numerical examples show that the developed AB-ResNet is able to recover the spectral function with accuracy comparable to MaxEnt where the noise level is relatively small.

physics.comp-ph↗

arXiv2018

Backward SDE Filter for Jump Diffusion Processes and Its Applications in Material Sciences

The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward doubly stochastic differential equations are expressed in terms of conditional law of a partially observed Markov diffusion process. It then follows that the adjoint time-inverse forward backward doubly stochastic differential equations governs the evolution of the unnormalized filtering density in the optimal filtering problem.

math.NA↗

arXiv2018

Single atom force measurements: mapping potential energy landscapes via electron beam induced single atom dynamics

In the last decade, the atomically focused beam of a scanning transmission electron microscope (STEM) was shown to induce a broad set of transformations of material structure, open pathways for probing atomic-scale reactions and atom-by-atom matter assembly. However, the mechanisms of beam-induced transformations remain largely unknown, due to an extreme mismatch between the energy and time scales of electron passage through solids and atomic and molecular motion. Here, we demonstrate that a single dopant Si atom in the graphene lattice can be used as an atomic scale force sensor, providing information on the random force exerted by the beam on chemically-relevant time scales. Using stochastic reconstruction of molecular dynamic simulations, we recover the potential energy landscape of the atom and use it to determine the beam-induced effects in the thermal (i.e. white noise) approximation. We further demonstrate that the moving atom under beam excitation can be used to map potential energy along step edges, providing information about atomic-scale potentials in solids. These studies open the pathway for quantitative studies of beam-induced atomic dynamics, elementary mechanisms of solid-state transformations, and predictive atom-by-atom fabrication.

cond-mat.mtrl-sci↗

arXiv2017

Forward Backward Doubly Stochastic Differential Equations and the Optimal Filtering of Diffusion Processes

math.PR↗

arXiv2015

An Efficient Meshfreee Implicit Filter for Nonlinear Filtering Problems

In this paper, we propose a meshfree approximation method for the implicit filter developed in [2], which is a novel numerical algorithm for nonlinear filtering problems. The implicit filter approximates conditional distributions in the optimal filter over a deterministic state space grid and is developed from samples of the current state obtained by solving the state equation implicitly. The purpose of the meshfree approximation is to improve the efficiency of the implicit filter in moderately high-dimensional problems. The construction of the algorithm includes generation of random state space points and a meshfree interpolation method. Numerical experiments show the effectiveness and efficiency of our algorithm.

math.NA↗

arXiv2005

Efficient Authenticated Encryption Schemes with Public Verifiability

An authenticated encryption scheme allows messages to be encrypted and authenticated simultaneously. In 2003, Ma and Chen proposed such a scheme with public verifiability. That is, in their scheme the receiver can efficiently prove to a third party that a message is indeed originated from a specific sender. In this paper, we first identify two security weaknesses in the Ma-Chen authenticated encryption scheme. Then, based on the Schnorr signature, we proposed an efficient and secure improved scheme such that all the desired security requirements are satisfied.

cs.CR↗