arXiv subjects

Hongsheng Liu

Publications and source records attributed to Hongsheng Liu.

36 records · Page 2Linked to original sources

arXiv2023

Learning to simulate partially known spatio-temporal dynamics with trainable difference operators

Recently, using neural networks to simulate spatio-temporal dynamics has received a lot of attention. However, most existing methods adopt pure data-driven black-box models, which have limited accuracy and interpretability. By combining trainable difference operators with black-box models, we propose a new hybrid architecture explicitly embedded with partial prior knowledge of the underlying PDEs named PDE-Net++. Furthermore, we introduce two distinct options called the trainable flipping difference layer (TFDL) and the trainable dynamic difference layer (TDDL) for the difference operators. Numerous numerical experiments have demonstrated that PDE-Net++ has superior prediction accuracy and better extrapolation performance than black-box models.

cs.LG↗

arXiv2023

Deep learning-based reduced order model for three-dimensional unsteady flow using mesh transformation and stitching

Artificial intelligence-based three-dimensional(3D) fluid modeling has gained significant attention in recent years. However, the accuracy of such models is often limited by the processing of irregular flow data. In order to bolster the credibility of near-wall flow prediction, this paper presents a deep learning-based reduced order model for three-dimensional unsteady flow using the transformation and stitching of multi-block structured meshes. To begin with, full-order flow data is provided by numerical simulations that rely on multi-block structured meshes. A mesh transformation technique is applied to convert each structured grid with data into a corresponding uniform and orthogonal grid, which is subsequently stitched and filled. The resulting snapshots in the transformed domain contain accurate flow information for multiple meshes and can be directly fed into a structured neural network without requiring any interpolation operation. Subsequently, a network model based on a fully convolutional neural network is constructed to predict flow dynamics accurately. To validate the strategy's feasibility, the flow around a sphere with Re=300 was investigated, and the results obtained using traditional Cartesian interpolation were used as the baseline for comparison. All the results demonstrate the preservation and accurate prediction of flow details near the wall, with the pressure correlation coefficient on the wall achieving an impressive value of 0.9985. Moreover, the periodic behavior of flow fields can be faithfully predicted during long-term inference.

physics.flu-dyn↗

arXiv2023

Analysis of the Decoder Width for Parametric Partial Differential Equations

Recently, Meta-Auto-Decoder (MAD) was proposed as a novel reduced order model (ROM) for solving parametric partial differential equations (PDEs), and the best possible performance of this method can be quantified by the decoder width. This paper aims to provide a theoretical analysis related to the decoder width. The solution sets of several parametric PDEs are examined, and the upper bounds of the corresponding decoder widths are estimated. In addition to the elliptic and the parabolic equations on a fixed domain, we investigate the advection equations that present challenges for classical linear ROMs, as well as the elliptic equations with the computational domain shape as a variable PDE parameter. The resulting fast decay rates of the decoder widths indicate the promising potential of MAD in addressing these problems.

math.NA↗

arXiv2023

Prediction of transonic flow over supercritical airfoils using geometric-encoding and deep-learning strategies

The Reynolds-averaged Navier-Stokes equation for compressible flow over supercritical airfoils under various flow conditions must be rapidly and accurately solved to shorten design cycles for such airfoils. Although deep-learning methods can effectively predict flow fields, the accuracy of these predictions near sensitive regions and their generalizability to large-scale datasets in engineering applications must be enhanced. In this study, a modified vision transformer-based encoder-decoder network is designed for the prediction of transonic flow over supercritical airfoils. In addition, four methods are designed to encode the geometric input with various information points and the performances of these methods are compared. The statistical results show that these methods generate accurate predictions over the complete flow field, with a mean absolute error on the order of 1e-4. To increase accuracy near the shock area, multilevel wavelet transformation and gradient distribution losses are introduced into the loss function. This results in the maximum error that is typically observed near the shock area decreasing by 50%. Furthermore, the models are pretrained through transfer learning on large-scale datasets and finetuned on small datasets to improve their generalizability in engineering applications. The results generated by various pretrained models demonstrate that transfer learning yields a comparable accuracy from a reduced training time.

physics.flu-dyn↗

arXiv2023

Solving Boltzmann equation with neural sparse representation

We consider the neural sparse representation to solve Boltzmann equation with BGK and quadratic collision model, where a network-based ansatz that can approximate the distribution function with extremely high efficiency is proposed. Precisely, fully connected neural networks are employed in the time and spatial space so as to avoid the discretization in space and time. The different low-rank representations are utilized in the microscopic velocity for the BGK and quadratic collision model, resulting in a significant reduction in the degree of freedom. We approximate the discrete velocity distribution in the BGK model using the canonical polyadic decomposition. For the quadratic collision model, a data-driven, SVD-based linear basis is built based on the BGK solution. All these will significantly improve the efficiency of the network when solving Boltzmann equation. Moreover, the specially designed adaptive-weight loss function is proposed with the strategies as multi-scale input and Maxwellian splitting applied to further enhance the approximation efficiency and speed up the learning process. Several numerical experiments, including 1D wave and Sod problems and 2D wave problem, demonstrate the effectiveness of these neural sparse representation methods.

math.NA↗

arXiv2022

Meta-Auto-Decoder for Solving Parametric Partial Differential Equations

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computation domains, etc. Recently, building learning-based numerical solvers for parametric PDEs has become an emerging new field. One category of methods such as the Deep Galerkin Method (DGM) and Physics-Informed Neural Networks (PINNs) aim to approximate the solution of the PDEs. They are typically unsupervised and mesh-free, but require going through the time-consuming network training process from scratch for each set of parameters of the PDE. Another category of methods such as Fourier Neural Operator (FNO) and Deep Operator Network (DeepONet) try to approximate the solution mapping directly. Being fast with only one forward inference for each PDE parameter without retraining, they often require a large corpus of paired input-output observations drawn from numerical simulations, and most of them need a predefined mesh as well. In this paper, we propose Meta-Auto-Decoder (MAD), a mesh-free and unsupervised deep learning method that enables the pre-trained model to be quickly adapted to equation instances by implicitly encoding (possibly heterogenous) PDE parameters as latent vectors. The proposed method MAD can be interpreted by manifold learning in infinite-dimensional spaces, granting it a geometric insight. Extensive numerical experiments show that the MAD method exhibits faster convergence speed without losing accuracy than other deep learning-based methods. The project page with code is available: https://gitee.com/mindspore/mindscience/tree/master/MindElec/.

cs.LG↗

arXiv2022

Statistical inference for piecewise normal distributions and stochastic variational inequalities

In this paper we first provide a method to compute confidence intervals for the center of a piecewise normal distribution given a sample from this distribution, under certain assumptions. We then extend this method to an asymptotic setting, and apply this method to compute confidence intervals for the true solution of a stochastic variational inequality based on a solution to a sample average approximation problem. The confidence intervals are computed with simple formulas. Performance of the proposed method is tested with numerical experiments.

math.OC↗

arXiv2022

StepDIRECT -- A Derivative-Free Optimization Method for Stepwise Functions

In this paper, we propose the StepDIRECT algorithm for derivative-free optimization (DFO), in which the black-box objective function has a stepwise landscape. Our framework is based on the well-known DIRECT algorithm. By incorporating the local variability to explore the flatness, we provide a new criterion to select the potentially optimal hyper-rectangles. In addition, we introduce a stochastic local search algorithm performing on potentially optimal hyper-rectangles to improve the solution quality and convergence speed. Global convergence of the StepDIRECT algorithm is provided. Numerical experiments on optimization for random forest models and hyper-parameter tuning are presented to support the efficacy of our algorithm. The proposed StepDIRECT algorithm shows competitive performance results compared with other state-of-the-art baseline DFO methods including the original DIRECT algorithm.

math.OC↗

arXiv2022

Eliminating edge electronic and phonon states of phosphorene nanoribbon by unique edge reconstruction

Edge termination plays a vital role in determining the properties of 2D materials. By performing compelling ab initio simulations, a lowest-energy U-edge [ZZ(U)] reconstruction is revealed in the bilayer phosphorene. Such reconstruction reduces 60% edge energy compared with the pristine one and occurs almost without energy barrier, implying it should be the dominating edge in reality. The electronic band structure of phosphorene nanoribbon with such reconstruction resembles that of intrinsic 2D layer, exhibiting nearly edgeless band characteristics. Although ZZ(U) changes the topology of phosphorene nanoribbon (PNR), simulated TEM, STEM and STM images indicates it is very hard to be identified. One possible identify method is IR/Raman analyses because ZZ(U) edge alters vibrational modes dramatically. Beyond, it also increases the thermal conductivity of PNR 1.4 and 2.3 times than the pristine and Klein edges.

cond-mat.mtrl-sci↗

arXiv2021

Solving Partial Differential Equations with Point Source Based on Physics-Informed Neural Networks

In recent years, deep learning technology has been used to solve partial differential equations (PDEs), among which the physics-informed neural networks (PINNs) emerges to be a promising method for solving both forward and inverse PDE problems. PDEs with a point source that is expressed as a Dirac delta function in the governing equations are mathematical models of many physical processes. However, they cannot be solved directly by conventional PINNs method due to the singularity brought by the Dirac delta function. We propose a universal solution to tackle this problem with three novel techniques. Firstly the Dirac delta function is modeled as a continuous probability density function to eliminate the singularity; secondly a lower bound constrained uncertainty weighting algorithm is proposed to balance the PINNs losses between point source area and other areas; and thirdly a multi-scale deep neural network with periodic activation function is used to improve the accuracy and convergence speed of the PINNs method. We evaluate the proposed method with three representative PDEs, and the experimental results show that our method outperforms existing deep learning-based methods with respect to the accuracy, the efficiency and the versatility.

cs.LG↗

arXiv2021

Parametrization of the Fe-Owater cross-interaction for a more accurate Fe3O4/water interface model and its application to a spherical Fe3O4 nanoparticle of realistic size

The accurate description of iron oxides/water interfaces requires reliable force field parameters that can be developed through the comparison with sophisticated quantum mechanical calculations. Here a set of CLASS2 force field parameters is optimized to describe the Fe-Owater cross interaction through comparison with hybrid density functional theory (HSE06) calculations of the potential energy function for a single water molecule adsorbed on the Fe3O4 (001) surface and with density functional tight binding (DFTB+U) molecular dynamics simulations for a water tri-layer on the same surface. The performance of the new parameters is assessed through the analysis of the number density profile of a water bulk (12 nm) sandwiched between two magnetite slabs of large surface area. Their transferability is tested for the water adsorption on the curved surface of a spherical Fe3O4 nanoparticle of realistic size (2.5 nm).

cond-mat.mtrl-sci↗

arXiv2020

"Inside Out" Growth Method for High-Quality Nitrogen-Doped Graphene

High-quality nitrogen-doped graphene on nickel is prepared by exploiting both the catalytic properties of nickel and the solubility of nitrogen atoms into its bulk. Following the standard chemical vapor deposition procedure, a previously nitrogen-doped nickel substrate is exposed to carbon-containing precursors so that nitrogen atoms, segregating to the surface, remain trapped in the growing graphene network. Morphological and chemical characterization by scanning tunneling microscopy and X-ray photoelectron spectroscopy demonstrates that the process yields a flat, wide, continuous nitrogen-doped graphene layer. Experimental results are combined with a thorough density functional theory investigation of possible structural models, to obtain a clear description at the atomic scale of the various configurations of the nitrogen atoms observed in the graphene mesh. This growth method is potentially scalable and suitable for the production of high-performance nano-devices with well-defined nitrogen centers, to be exploited as metal-free carbon-based catalysts in several applicative fields such as electrochemistry, energy storage, gas storage/sensing or wastewater treatment.

cond-mat.mtrl-sci↗

arXiv2020

Insight into the interface between Fe$_3$O$_4$(001) surface and water overlayers through multiscale molecular dynamics simulations

In this work we investigate the Fe$_3$O$_4$(001) surface/water interface by combining several theoretical approaches, ranging from a hybrid functional method (HSE06) to density-functional tight-binding (DFTB) to molecular mechanics (MM). First, we assess the accuracy of the DFTB method to reproduce correctly HSE06 results on structural details and energetics and available experimental data for the adsorption of isolated water, dimers, trimers, etc. up to a water monolayer. Secondly, we build two possible configurations of a second and a third overlayer and perform molecular dynamics simulations with DFTB, monitoring the water orientation, the H-bond network, and ordered water structures formation. To make our models more realistic, we then build a 12-nm thick water multilayer on top of the Fe$_3$O$_4$(001) surface slab model, which we investigate through MM molecular dynamics. The water layers structuring, revealed by the analysis of the atomic positions from a long MM-MD run for this large MM model, extends up to about 6-7 Å and nicely compares with that observed for a water trilayer model. However, MM and DFTB MD simulations show some discrepancy due to the poor description of the Fe--OH2 distance in MM that calls for further work in the parametrization of the model.

cond-mat.mtrl-sci↗

arXiv2019

Shaping Magnetite Nanoparticles from First-principles

Iron oxide magnetic nanoparticles (NPs) are stimuli-responsive materials at the forefront of nanomedicine. Their realistic finite temperature simulations are a formidable challenge for first-principles methods. Here, we use density functional tight binding to open up the required time and length scales and obtain global minimum structures of Fe3O4 NPs of realistic size (1400 atoms, 2.5 nm) and of different shapes, which we then refine with hybrid density functional theory methods to accomplish proper electronic and magnetic properties, which have never been accurately described in simulations. On this basis, we develop a general empirical formula and prove its predictive power for the evaluation of the total magnetic moment of Fe3O4 NPs. By converting the total magnetic moment into the macroscopic saturation magnetization, we rationalize the experimentally observed dependence with shape. We also reveal interesting reconstruction mechanisms and unexpected patterns of charge ordering.

cond-mat.mtrl-sci↗

arXiv2019

An efficient way to model complex magnetite: assessment of SCC-DFTB against DFT

Magnetite has attracted increasing attention in recent years due to its promising and diverse applications in biomedicine. Theoretical modelling can play an important role in understanding magnetite-based nanomaterials at the atomic scale for a deeper insight into the experimental observations. However, calculations based on density functional theory (DFT) are too costly for realistically large models of magnetite nanoparticles. Classical force field methods are very fast but lack of precision and of the description of electronic effects. Therefore, a cheap and efficient quantum mechanical simulation method with comparable accuracy than DFT is highly desired. Here, a less computational demanding DFT-based method, i.e. self-consistent charge density functional tight-binding (SCC-DFTB), is adopted to investigate magnetite bulk and low-index (001) surface with newly proposed parameters for Fe-O interactions. We report that SCC-DFTB with on-site Coulomb correction provides results in quantitatively comparable agreement with those obtained by DFT+U and hybrid functional methods. Therefore, SCC-DFTB is valued as an efficient and reliable method for the description magnetite. This assessment will promote SCC-DFTB computational studies on magnetite-based nanostructures that attract increasing attention for medical applications.

cond-mat.mtrl-sci↗

arXiv2018

Convergence of the Augmented Decomposition Algorithm

We study the convergence of the Augmented Decomposition Algorithm (ADA) proposed in [32] for solving multi-block separable convex minimization problems subject to linear constraints. We show that the global convergence rate of the exact ADA is o(1/k) under the assumption that there exists a saddle point. We consider the inexact Augmented Decomposition Algorithm (iADA) and establish global and local convergence results under some mild assumptions, by providing a stability result for the maximal monotone operator T associated with the perturbation from both primal and dual perspectives. This result implies the local linear convergence of the inexact ADA for many applications such as the lasso, total variation reconstruction, exchange problem and many other problems from statistics, machine learning and engineering with l1 regularization.

math.OC↗

arXiv2015

Point defects in epitaxial silicene on Ag(111) surface

Silicene, a counterpart of graphene, has achieved rapid development due to its exotic electronic properties and excellent compatibility with the mature silicon-based semiconductor technology. Its low room-temperature mobility of about 100 cm2V-1s-1, however, inhibits device applications such as in field-effect transistors. Generally, defects and grain boundaries would act as scattering centers and thus reduce the carrier mobility. In this paper, the morphologies of various point defects in epitaxial silicene on Ag(111) surfaces have been systematically investigated using first-principles calculations combined with experimental scanning tunneling microscope (STM) observations. The STM signatures for various defects in epitaxial silicene on Ag(111) surface are identified. In particular, the formation energies of point defects in Ag(111)-supported silicene sheets show an interesting dependence on the superstructures, which, in turn, may have implications for controlling the defect density during the synthesis of silicene. Through estimating the concentrations of various point defects in different silicene superstructures, the mystery of the defective appearance of v13*v13 silicene in experiments is revealed, and 4*4 silicene sheet is thought to be the most suitable structure for future device applications.

cond-mat.mtrl-sci↗

arXiv2014

Tuning the Band Gap in Silicene by Oxidation

Silicene monolayers grown on Ag(111) surfaces demonstrate a band gap that is tunable by oxygen adatoms from semimetallic to semiconducting type. By using low-temperature scanning tunneling microscopy, it is found that the adsorption configurations and amounts of oxygen adatoms on the silicene surface are critical for band-gap engineering, which is dominated by different buckled structures in R13xR13, 4x4, and 2R3x2R3 silicene layers. The Si-O-Si bonds are the most energy-favored species formed on R13xR13, 4x4, and 2R3x2R3 structures under oxidation, which is verified by in-situ Raman spectroscopy as well as first-principles calculations. The silicene monolayers retain their structures when fully covered by oxygen adatoms. Our work demonstrates the feasibility of tuning the band gap of silicene with oxygen adatoms, which, in turn, expands the base of available two-dimensional electronic materials for devices with properties that is hardly achieved with graphene oxide.

cond-mat.mtrl-sci↗