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 a...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 NSE.Moreover,solving inverse flow problems is often prohibitively expensive and requires complex and expensive formulations and new computer codes.Here,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.展开更多
This is the second part of our series works on failure-informed adaptive sampling for physic-informed neural networks(PINNs).In our previous work(SIAM J.Sci.Comput.45:A1971–A1994),we have presented an adaptive sampli...This is the second part of our series works on failure-informed adaptive sampling for physic-informed neural networks(PINNs).In our previous work(SIAM J.Sci.Comput.45:A1971–A1994),we have presented an adaptive sampling framework by using the failure probability as the posterior error indicator,where the truncated Gaussian model has been adopted for estimating the indicator.Here,we present two extensions of that work.The first extension consists in combining with a re-sampling technique,so that the new algorithm can maintain a constant training size.This is achieved through a cosine-annealing,which gradually transforms the sampling of collocation points from uniform to adaptive via the training progress.The second extension is to present the subset simulation(SS)algorithm as the posterior model(instead of the truncated Gaussian model)for estimating the error indicator,which can more effectively estimate the failure probability and generate new effective training points in the failure region.We investigate the performance of the new approach using several challenging problems,and numerical experiments demonstrate a significant improvement over the original algorithm.展开更多
In this paper, we use Physics-Informed Neural Networks (PINNs) to solve shape optimization problems. These problems are based on incompressible Navier-Stokes equations and phase-field equations. The phase-field functi...In this paper, we use Physics-Informed Neural Networks (PINNs) to solve shape optimization problems. These problems are based on incompressible Navier-Stokes equations and phase-field equations. The phase-field function is used to describe the state of the fluids, and the optimal shape optimization is obtained by using the shape sensitivity analysis based on the phase-field function. The sharp interface is also presented by a continuous function between zero and one with a large gradient. To avoid the numerical solutions falling into the trivial solution, the hard boundary condition is implemented for our PINNs’ training. Finally, numerical results are given to prove the feasibility and effectiveness of the proposed numerical method.展开更多
近几年来,深度学习无所不在,赋能于各个领域.尤其是人工智能与传统科学的结合(AI for science,AI4Science)引发广泛关注.在AI4Science领域,利用人工智能算法求解PDEs(AI4PDEs)已成为计算力学研究的焦点.AI4PDEs的核心是将数据与方程相融...近几年来,深度学习无所不在,赋能于各个领域.尤其是人工智能与传统科学的结合(AI for science,AI4Science)引发广泛关注.在AI4Science领域,利用人工智能算法求解PDEs(AI4PDEs)已成为计算力学研究的焦点.AI4PDEs的核心是将数据与方程相融合,并且几乎可以求解任何偏微分方程问题,由于其融合数据的优势,相较于传统算法,其计算效率通常提升数万倍.因此,本文全面综述了AI4PDEs的研究,总结了现有AI4PDEs算法、理论,并讨论了其在固体力学中的应用,包括正问题和反问题,展望了未来研究方向,尤其是必然会出现的计算力学大模型.现有AI4PDEs算法包括基于物理信息神经网络(physicsinformed neural network,PINNs)、深度能量法(deep energy methods,DEM)、算子学习(operator learning),以及基于物理神经网络算子(physics-informed neural operator,PINO).AI4PDEs在科学计算中有许多应用,本文聚焦于固体力学,正问题包括线弹性、弹塑性,超弹性、以及断裂力学;反问题包括材料参数,本构,缺陷的识别,以及拓朴优化.AI4PDEs代表了一种全新的科学模拟方法,通过利用大量数据在特定问题上提供近似解,然后根据具体的物理方程进行微调,避免了像传统算法那样从头开始计算,因此AI4PDEs是未来计算力学大模型的雏形,能够大大加速传统数值算法.我们相信,利用人工智能助力科学计算不仅仅是计算领域的未来重要方向,同时也是计算力学的未来,即是智能计算力学。展开更多
The core-surface flow is crucial for understanding the dynamics of the Earth's outer core and geomagnetic secular variations.Conventional core flow models often use a single set of spherical harmonic coefficients ...The core-surface flow is crucial for understanding the dynamics of the Earth's outer core and geomagnetic secular variations.Conventional core flow models often use a single set of spherical harmonic coefficients to represent the flow both inside and outside the tangent cylinder,inherently imposing continuity across the tangent cylinder around the solid inner core.To address this limitation,we present a core-surface flow inversion framework based on physics-informed neural networks.This framework employs distinct neural network representations for the flow inside and outside the tangent cylinder,allowing for discontinuities as the flow crosses the tangent cylinder.Additionally,it incorporates secular acceleration data to constrain the temporal evolution of the core flow.Using this inversion framework,we derive a new core-surface flow model spanning 2001 to 2024 from a geomagnetic model,incorporating the latest magnetic data from Swarm satellites and Macao Science Satellite-1.The recovered model reveals persistent large-scale circulation linked to westward drift,significant temporal variations in the equatorial Pacific,and distinct jet-like structures at the poles.The inversion also reveals a large-scale wave pattern in equatorial azimuthal flow acceleration,corresponding to observed geomagnetic jerks and likely resulting from quasi-geostrophic magneto-Coriolis waves.Additionally,the framework infers small-scale magnetic fields at the core-mantle boundary,highlighting split flux concentrations and localized high-latitude patches.展开更多
Dilatancy is referred to the phenomenon of volume increase that occurs when a material is deformed.Dilatancy theory originated in geomechanics for the study of the behavior of granular materials.Later it is expanded t...Dilatancy is referred to the phenomenon of volume increase that occurs when a material is deformed.Dilatancy theory originated in geomechanics for the study of the behavior of granular materials.Later it is expanded to the case of more brittle materials like rocks when it is subjected to the load of varying effective stress and starts to crack and deform,then named the dilatancy-diffusion hypothesis.This hypothesis was developed to explain the changes in rock volume and pore pressure that occur prior to and during fault slip,which can influence earthquake dynamics.Dilatancy-fluid diffusion is a significant concept in understanding the seismogenic process and has served as the major theoretical pillar for earthquake prediction by its classic definition.This paper starts with the recount of fundamental laboratory experiments on granular materials and rocks,then conducts review and examination of the history for using the dilatancy-diffusion hypothesis to interpret the‘prediction’of the 1975 Haicheng Earthquake and other events.The Haicheng Earthquake is the first significant event to be interpreted with the dilatancy-diffusion hypothesis in the world.As one pivotal figure in the development of the dilatancy-diffusion hypothesis for earthquake prediction Professor Amos Nur of Stanford University worked tirelessly to attract societal attention to this important scientific and humanistic issue.As a deterministic physical model the dilatancy-diffusion hypothesis intrinsically bears the deficit to interpret the stochastic seismogenic process.With the emergence of deep learning and its successful applications to many science and technology fields,we may see a possibility to overcome the shortcoming of the current state of the theory with the addition of empirical statistics to push the operational earthquake forecasting approach with the addition of the physicallyinformed neural networks which adopt the dilatancy-diffusion hypothesis as one of its embedded physical relations,to uplift the seismic risk reduction to a new level for saving lives and reducing the losses.展开更多
基金The research of the second author(ZM)was sup-539 ported by the National Natural Science Foundation of China(Grant 54012171404)The last author(GEK)would like to acknowledge support 541 by the Alexander von Humboldt fellowship.
文摘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 NSE.Moreover,solving inverse flow problems is often prohibitively expensive and requires complex and expensive formulations and new computer codes.Here,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.
基金supported by the NSF of China(No.12171085)This work was supported by the National Key R&D Program of China(2020YFA0712000)+2 种基金the NSF of China(No.12288201)the Strategic Priority Research Program of Chinese Academy of Sciences(No.XDA25010404)and the Youth Innovation Promotion Association(CAS).
文摘This is the second part of our series works on failure-informed adaptive sampling for physic-informed neural networks(PINNs).In our previous work(SIAM J.Sci.Comput.45:A1971–A1994),we have presented an adaptive sampling framework by using the failure probability as the posterior error indicator,where the truncated Gaussian model has been adopted for estimating the indicator.Here,we present two extensions of that work.The first extension consists in combining with a re-sampling technique,so that the new algorithm can maintain a constant training size.This is achieved through a cosine-annealing,which gradually transforms the sampling of collocation points from uniform to adaptive via the training progress.The second extension is to present the subset simulation(SS)algorithm as the posterior model(instead of the truncated Gaussian model)for estimating the error indicator,which can more effectively estimate the failure probability and generate new effective training points in the failure region.We investigate the performance of the new approach using several challenging problems,and numerical experiments demonstrate a significant improvement over the original algorithm.
文摘In this paper, we use Physics-Informed Neural Networks (PINNs) to solve shape optimization problems. These problems are based on incompressible Navier-Stokes equations and phase-field equations. The phase-field function is used to describe the state of the fluids, and the optimal shape optimization is obtained by using the shape sensitivity analysis based on the phase-field function. The sharp interface is also presented by a continuous function between zero and one with a large gradient. To avoid the numerical solutions falling into the trivial solution, the hard boundary condition is implemented for our PINNs’ training. Finally, numerical results are given to prove the feasibility and effectiveness of the proposed numerical method.
文摘近几年来,深度学习无所不在,赋能于各个领域.尤其是人工智能与传统科学的结合(AI for science,AI4Science)引发广泛关注.在AI4Science领域,利用人工智能算法求解PDEs(AI4PDEs)已成为计算力学研究的焦点.AI4PDEs的核心是将数据与方程相融合,并且几乎可以求解任何偏微分方程问题,由于其融合数据的优势,相较于传统算法,其计算效率通常提升数万倍.因此,本文全面综述了AI4PDEs的研究,总结了现有AI4PDEs算法、理论,并讨论了其在固体力学中的应用,包括正问题和反问题,展望了未来研究方向,尤其是必然会出现的计算力学大模型.现有AI4PDEs算法包括基于物理信息神经网络(physicsinformed neural network,PINNs)、深度能量法(deep energy methods,DEM)、算子学习(operator learning),以及基于物理神经网络算子(physics-informed neural operator,PINO).AI4PDEs在科学计算中有许多应用,本文聚焦于固体力学,正问题包括线弹性、弹塑性,超弹性、以及断裂力学;反问题包括材料参数,本构,缺陷的识别,以及拓朴优化.AI4PDEs代表了一种全新的科学模拟方法,通过利用大量数据在特定问题上提供近似解,然后根据具体的物理方程进行微调,避免了像传统算法那样从头开始计算,因此AI4PDEs是未来计算力学大模型的雏形,能够大大加速传统数值算法.我们相信,利用人工智能助力科学计算不仅仅是计算领域的未来重要方向,同时也是计算力学的未来,即是智能计算力学。
基金supported by the National Natural Science Foundation of China (12250012,42250101)the Macao Foundation。
文摘The core-surface flow is crucial for understanding the dynamics of the Earth's outer core and geomagnetic secular variations.Conventional core flow models often use a single set of spherical harmonic coefficients to represent the flow both inside and outside the tangent cylinder,inherently imposing continuity across the tangent cylinder around the solid inner core.To address this limitation,we present a core-surface flow inversion framework based on physics-informed neural networks.This framework employs distinct neural network representations for the flow inside and outside the tangent cylinder,allowing for discontinuities as the flow crosses the tangent cylinder.Additionally,it incorporates secular acceleration data to constrain the temporal evolution of the core flow.Using this inversion framework,we derive a new core-surface flow model spanning 2001 to 2024 from a geomagnetic model,incorporating the latest magnetic data from Swarm satellites and Macao Science Satellite-1.The recovered model reveals persistent large-scale circulation linked to westward drift,significant temporal variations in the equatorial Pacific,and distinct jet-like structures at the poles.The inversion also reveals a large-scale wave pattern in equatorial azimuthal flow acceleration,corresponding to observed geomagnetic jerks and likely resulting from quasi-geostrophic magneto-Coriolis waves.Additionally,the framework infers small-scale magnetic fields at the core-mantle boundary,highlighting split flux concentrations and localized high-latitude patches.
基金sponsored by the National Research Foundation of Korea(RS-2023-00220913).
文摘Dilatancy is referred to the phenomenon of volume increase that occurs when a material is deformed.Dilatancy theory originated in geomechanics for the study of the behavior of granular materials.Later it is expanded to the case of more brittle materials like rocks when it is subjected to the load of varying effective stress and starts to crack and deform,then named the dilatancy-diffusion hypothesis.This hypothesis was developed to explain the changes in rock volume and pore pressure that occur prior to and during fault slip,which can influence earthquake dynamics.Dilatancy-fluid diffusion is a significant concept in understanding the seismogenic process and has served as the major theoretical pillar for earthquake prediction by its classic definition.This paper starts with the recount of fundamental laboratory experiments on granular materials and rocks,then conducts review and examination of the history for using the dilatancy-diffusion hypothesis to interpret the‘prediction’of the 1975 Haicheng Earthquake and other events.The Haicheng Earthquake is the first significant event to be interpreted with the dilatancy-diffusion hypothesis in the world.As one pivotal figure in the development of the dilatancy-diffusion hypothesis for earthquake prediction Professor Amos Nur of Stanford University worked tirelessly to attract societal attention to this important scientific and humanistic issue.As a deterministic physical model the dilatancy-diffusion hypothesis intrinsically bears the deficit to interpret the stochastic seismogenic process.With the emergence of deep learning and its successful applications to many science and technology fields,we may see a possibility to overcome the shortcoming of the current state of the theory with the addition of empirical statistics to push the operational earthquake forecasting approach with the addition of the physicallyinformed neural networks which adopt the dilatancy-diffusion hypothesis as one of its embedded physical relations,to uplift the seismic risk reduction to a new level for saving lives and reducing the losses.
