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Physics-informed neural networks with residual/gradient-based adaptive sampling methods for solving partial differential equations with sharp solutions

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Applied Mathematics and Mechanics(English Edition) 2023年第7期44卷 1069-1084页

作者： zhiping mao Xuhui MENG School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamen 361005Fujian ProvinceChina Institute of Interdisciplinary Research for Mathematics and Applied Science School of Mathematics and StatisticsHuazhong University of Science and TechnologyWuhan 430074China

We consider solving the forward and inverse partial differential equations(PDEs)which have sharp solutions with physics-informed neural networks(PINNs)in this *** particular,to better capture the sharpness of the solution,we propose the adaptive sampling methods(ASMs)based on the residual and the gradient of the *** first present a residual only-based ASM denoted by ASMⅠ.In this approach,we first train the neural network using a small number of residual points and divide the computational domain into a certain number of sub-domains,then we add new residual points in the sub-domain which has the largest mean absolute value of the residual,and those points which have the largest absolute values of the residual in this sub-domain as new residual *** further develop a second type of ASM(denoted by ASMⅡ)based on both the residual and the gradient of the solution due to the fact that only the residual may not be able to efficiently capture the sharpness of the *** procedure of ASMⅡis almost the same as that of ASMⅠ,and we add new residual points which have not only large residuals but also large *** demonstrate the effectiveness of the present methods,we use both ASMⅠand ASMⅡto solve a number of PDEs,including the Burger equation,the compressible Euler equation,the Poisson equation over an Lshape domain as well as the high-dimensional Poisson *** has been shown from the numerical results that the sharp solutions can be well approximated by using either ASMⅠor ASMⅡ,and both methods deliver much more accurate solutions than the original PINNs with the same number of residual ***,the ASMⅡalgorithm has better performance in terms of accuracy,efficiency,and stability compared with the ASMⅠ*** means that the gradient of the solution improves the stability and efficiency of the adaptive sampling procedure as well as the accuracy of the ***,we also employ the similar adaptive sampling technique fo

关键词： physics-informed neural network(PINN) adaptive sampling high-dimension L-shape Poisson equation accuracy

柔性海泡石基气凝胶的制备及其保温隔热性能的研究

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化工新型材料 2024年第2期52卷 175-180页

作者：胡叶蕾续通毛志平徐红东华大学化学与化工学院生态纺织教育部重点实验室上海201620 上海电子信息技术学院中德工程学院上海201620 山东中康国创先进印染技术研究院有限公司国家先进印染技术创新中心泰安271000

以海泡石为基质,聚乙烯醇为有机增强相,硅烷偶联剂KH-560和聚乙烯亚胺为交联剂,经冷冻干燥制备了具有优异保温隔热性能的柔性海泡石基气凝胶。其导热系数低至0.0374W/(m·K),轴向在经过80%的压缩形变后能达到100%回弹,径向在经过50%的... 详细信息

以海泡石为基质,聚乙烯醇为有机增强相,硅烷偶联剂KH-560和聚乙烯亚胺为交联剂,经冷冻干燥制备了具有优异保温隔热性能的柔性海泡石基气凝胶。其导热系数低至0.0374W/(m·K),轴向在经过80%的压缩形变后能达到100%回弹,径向在经过50%的压缩形变后也能达到100%回弹。该气凝胶有望作为保温隔热材料应用于建筑、隔热帐篷等领域。

关键词：海泡石基气凝胶热稳定性力学性能保温隔热

铁-三联吡啶配合物活化高碘酸盐体系构建及其对染色废水的催化降解机制

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纺织学报 2024年第6期45卷 105-112页

作者：武守营黄启超张开封张琳萍钟毅徐红毛志平东华大学化学与化工学院上海201620 东华大学生态纺织教育部重点实验室上海201620 山东中康国创先进印染技术研究院有限公司国家先进印染技术创新中心山东泰安271000

为开发新型、高效的染色废水处理方法,通过铁-三联吡啶(Fe^(Ⅲ)(tpy)C_(l3))配合物活化高碘酸盐(PI)构建了Fe^(Ⅲ)(tpy)C_(l3)/PI催化氧化体系。在此基础上,采用酸性红1(AR1)作为染色废水模型污染物测试了该体系的催化降解性能,并通过... 详细信息

为开发新型、高效的染色废水处理方法,通过铁-三联吡啶(Fe^(Ⅲ)(tpy)C_(l3))配合物活化高碘酸盐(PI)构建了Fe^(Ⅲ)(tpy)C_(l3)/PI催化氧化体系。在此基础上,采用酸性红1(AR1)作为染色废水模型污染物测试了该体系的催化降解性能,并通过捕获和探针实验研究了Fe^(Ⅲ)(tpy)C_(l3)配合物活化PI降解酸性红1的机制。结果表明:Fe^(Ⅲ)(tpy)C_(l3)配合物能够高效活化PI实现酸性红1的快速降解,15 min内对AR1的去除率高达98%;Fe^(Ⅲ)(tpy)C_(l3)/PI体系对酸性红1的降解符合伪一级动力学模型,同时酸性红1的降解速率常数随Fe^(Ⅲ)(tpy)C_(l3)配合物和PI浓度的增加而呈线性增加;在Fe^(Ⅲ)(tpy)C_(l3)/PI体系中包含超氧自由基、单线态氧以及高价铁,这些活性物质共同促进酸性红1的降解;该体系不仅对多种有机物的降解表现出普适性,同时催化降解过程不受溶液pH值以及常见无机盐离子的干扰。

关键词：配合物高碘酸盐染色废水降解催化机制废水处理铁-三联吡啶

Analysis and Approximation of Gradient Flows Associated with a Fractional Order Gross-Pitaevskii Free Energy

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Communications on Applied Mathematics and Computation 2019年第1期1卷 5-19页

作者： Mark Ainsworth zhiping mao Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA

We establish the well-posedness of the fractional PDE which arises by considering the gradient flow associated with a fractional Gross-Pitaevskii free energy functional and some basic properties of the *** equation reduces to the Allen-Cahn or Cahn-Hilliard equations in the case where the mass tends to zero and an integer order derivative is used in the *** study how the presence of a non-zero mass affects the nature of the solutions compared with the Cahn-Hilliard *** particular,we show that,analogous to the Cahn-Hilliard case,the solutions consist of regions in which the solution is a piecewise constant(whose value depends on the mass and the fractional order)separated by an interface whose width is independent of the mass and the fractional ***,if the average value of the initial data exceeds some threshold(which we determine explic让ly),then the solution will tend to a single constant steady state.

关键词： Fractional differential equation Non-local energy Well-posedness Fourier spectral method

基于有机硅弹性体及石墨烯涂层的疏水光热棉织物的制备及性能

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印染 2024年第8期50卷 12-15页

作者：董政钟毅隋晓锋毛志平冯雪凌生态纺织教育部重点实验室东华大学化学与化工学院上海201620 山东中康国创先进印染技术研究院有限公司山东泰安271000 国家染整工程技术研究中心上海201620

通过简单的丝网印花工艺,将磷酸(PA)、石墨烯(Graphene)及微晶纤维素(MCC)混合物涂覆在棉织物上,制备具有光热转换效果的石墨烯涂层棉织物。光学显微镜观察发现石墨烯在磷酸与微晶纤维素中具有优异的分散性,扫描电子显微镜观察到导电棉... 详细信息

通过简单的丝网印花工艺,将磷酸(PA)、石墨烯(Graphene)及微晶纤维素(MCC)混合物涂覆在棉织物上,制备具有光热转换效果的石墨烯涂层棉织物。光学显微镜观察发现石墨烯在磷酸与微晶纤维素中具有优异的分散性,扫描电子显微镜观察到导电棉织物上石墨烯-微晶纤维素涂层的生成。采用0.6%石墨烯分散液两次涂覆工艺制备的复合织物,在一个太阳光强度下迅速升温至65℃,具备良好的光热转换性能。为使复合织物可以适应复杂的应用环境,在复合织物上覆盖有机硅弹性体薄膜,使其接触角达到105.75°,表现出良好的疏水效果。

关键词：功能整理光热转换疏水磷酸石墨烯有机硅弹性体棉织物

Efficient and Accurate Numerical Methods Using the Accelerated Spectral Deferred Correction for Solving Fractional Differential Equations

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Numerical Mathematics(Theory,Methods and Applications) 2022年第4期15卷 876-902页

作者： Xuejuan Chen zhiping mao George Em Karniadakis School of Science Jimei UniversityXiamen 361021China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamenChina Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA

We develop an efficient and accurate spectral deferred correction(SDC)method for fractional differential equations(FDEs)by extending the algorithm in[14]for classical ordinary differential equations(ODEs).Specifically,we discretize the resulted Picard integral equation by the SDC method and accelerate the convergence of the SDC iteration by using the generalized minimal residual algorithm(GMRES).We first derive the correction matrix of the SDC method for FDEs and analyze the convergence region of the SDC *** then present several numerical examples for stiff and non-stiff FDEs including fractional linear and nonlinear ODEs as well as fractional phase field models,demonstrating that the accelerated SDC method is much more efficient than the original SDC method,especially for stiff ***,we resolve the issue of low accuracy arising from the singularity of the solutions by using a geometric mesh,leading to highly accurate solutions compared to uniform mesh solutions at almost the same computational ***,for long-time integration of FDEs,using the geometric mesh leads to great computational savings as the total number of degrees of freedom required is relatively small.

关键词： Stiff problem generalized minimal residual geometric mesh refinement long time evolution fractional phase field models

基于二氧化钛纳米颗粒的辐射制冷织物的制备及其性能

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印染 2024年第9期50卷 1-4,17页

作者：李彤彤耿雨钟毅毛志平冯雪凌生态纺织教育部重点试验室东华大学化学与化工学院上海201620 山东中康国创先进印染技术研究院有限公司山东泰安271000 国家染整工程技术研究中心上海201620

利用磷酸-微晶纤维素法(PA-MCC),将二氧化钛纳米颗粒(TiO_(2)-NP)制成均匀的分散液,再使用丝网印花方式将分散液整理到棉织物表面,制备了表面负载TiO_(2)-NP的辐射制冷(RC)织物。通过扫描电子显微镜(SEM)观察MCC-TiO_(2)-NP制冷层表面... 详细信息

利用磷酸-微晶纤维素法(PA-MCC),将二氧化钛纳米颗粒(TiO_(2)-NP)制成均匀的分散液,再使用丝网印花方式将分散液整理到棉织物表面,制备了表面负载TiO_(2)-NP的辐射制冷(RC)织物。通过扫描电子显微镜(SEM)观察MCC-TiO_(2)-NP制冷层表面和截面的形貌;采用紫外可见近红外分光光度计测得RC织物在0.3~2.5μm太阳光波段的最高反射率为0.9;采用傅里叶红外光谱仪得到RC织物在8~14μm的中红外波段的平均发射率为0.98;一个标准太阳光照下,RC织物下的温度比棉织物平均低1.59℃,比室温平均低9.48℃;不同弯折次数下的降温效果证明织物辐射制冷性能的耐久性;接触角测试测得RC织物的吸水性能仍然较佳;室外测试证明了RC织物能成功调节人体温度。

关键词：辐射制冷二氧化钛丝网印花棉织物

High Order Conservative Finite Difference/Fourier Spectral Methods for Inviscid Surface Quasi-Geostrophic Flows

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Communications in Computational Physics 2022年第10期32卷 1474-1509页

作者： Nan Zhang zhiping mao Tao Xiong School of Mathematical Sciences Xiamen UniversityXiamenFujian361005P.R.China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific ComputingXiamen UniversityXiamenFujian361005P.R.China

In this paper,we develop an effective conservative high order finite difference scheme with a Fourier spectral method for solving the inviscid surface quasigeostrophic equations,which include a spectral fractional Laplacian determining the vorticity for the transport velocity of the potential *** fractional Laplacian is approximated by a Fourier-Galerkin spectral method,while the time evolution of the potential temperature is discretized by a high order conservative finite difference *** essentially non-oscillatory(WENO)reconstructions are also considered for *** to a low regularity of problems involving such a fractional Laplacian,especially in the critical or supercritical regime,directly applying the Fourier spectral method leads to a very oscillatory transport velocity associated with the gradient of the vorticity,*** smooth *** of using an artificial filter,we propose to reconstruct the velocity from the vorticity with central difference *** results are performed to demonstrate the good performance of our proposed approach.

关键词： Finite difference WENO Fourier spectral fractional Laplacian surface quasigeostrophic flow

Physics-informed neural networks(PINNs)for fluidmechanics:a review

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Acta Mechanica Sinica 2021年第12期37卷 1727-1738页

作者： Shengze Cai zhiping mao Zhicheng Wang Minglang Yin George Em Karniadakis Division of Applied Mathematics Brown UniversityProvidenceRI 02912USA School of Mathematical Sciences Xiamen University 361005 China Laboratory of Ocean Energy Utilization of Ministry of Education Dalian University of TechnologyDalian116024China School of Engineering Brown UniversityProvidenceRI 02912USA Center for Biomedical Engineering Brown UniversityProvidenceRI 02912USA

Despite the significant progress over the last 50 years in simulating flow problems using numerical discretization of the Navier–Stokes equations(NSE),we still cannot incorporate seamlessly noisy data into existing algorithms,mesh-generation is complex,and we cannot tackle high-dimensional problems governed by parametrized ***,solving inverse flow problems is often prohibitively expensive and requires complex and expensive formulations and new computer ***,we review flow physics-informed learning,integrating seamlessly data and mathematical models,and implement them using physics-informed neural networks(PINNs).We demonstrate the effectiveness of PINNs for inverse problems related to three-dimensional wake flows,supersonic flows,and biomedical flows.

关键词： Physics-informed learning PINNs Inverse problems Supersonic flows Biomedical flows