In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate...In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate solution in terms of the automatic differentiation(AD)algorithm.To overcome the deficiency of CAT that demands high computation cost for implementation,a set of ordinary differential equations(ODEs)entailed from CAT based discretized population balance equation(PBE)are solved by using the AD based high-order Taylor expansion.Moreover,an AD based trust-region reflective(TRR)algorithm and another interior-point(IP)algorithm are established for estimating the kinetic parameters associated with particle growth,aggregation and breakage.As a result,the estimation accuracy can be further improved while the computation cost can be significantly reduced,compared to the existing algorithms.Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT,TRR and IP algorithms in comparison with the existing algorithms.Moreover,seeded batch cooling crystallization experiments ofβform L-glutamic acid are performed to validate the proposed method.展开更多
In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD）...In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD） is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.展开更多
A systematic methodology for formulating,implementing,solving and verifying discrete adjoint of the compressible Reynolds-averaged Navier-Stokes（RANS） equations for aerodynamic design optimization on unstructured me...A systematic methodology for formulating,implementing,solving and verifying discrete adjoint of the compressible Reynolds-averaged Navier-Stokes（RANS） equations for aerodynamic design optimization on unstructured meshes is proposed.First,a general adjoint formulation is constructed for the entire optimization problem,including parameterization,mesh deformation,flow solution and computation of the objective function,which is followed by detailed formulations of matrix-vector products arising in the adjoint model.According to this formulation,procedural components of implementing the required matrix-vector products are generated by means of automatic differentiation（AD） in a structured and modular manner.Furthermore,a duality-preserving iterative algorithm is employed to solve flow adjoint equations arising in the adjoint model,ensuring identical convergence rates for the tangent and the adjoint models.A three-step strategy is adopted to verify the adjoint computation.The proposed method has several remarkable features：the use of AD techniques avoids tedious and error-prone manual derivation and programming;duality is strictly preserved so that consistent and highly accurate discrete sensitivities can be obtained;and comparable efficiency to hand-coded implementation can be achieved.Upon the current discrete adjoint method,a gradient-based optimization framework has been developed and applied to a drag reduction problem.展开更多
Soil moisture plays a crucial role in drought monitoring,flood forecasting,and water resource management.Data assimilation methods can integrate the strengths of land surface models(LSM)and remote sensing data to gene...Soil moisture plays a crucial role in drought monitoring,flood forecasting,and water resource management.Data assimilation methods can integrate the strengths of land surface models(LSM)and remote sensing data to generate highprecision and spatio-temporally continuous soil moisture products.However,one of the challenges of the land data assimilation system(LDAS)is how to accurately estimate model and observation errors.To address this,we had previously proposed a dualcycle assimilation algorithm that can simultaneously estimate the model and observation errors,LSM parameters,and observation operator parameters.However,this algorithm requires a large ensemble size to guarantee stable parameter estimates,resulting in low efficiency and limiting its large-scale applications.To address this limitation,the authors employed the following approaches:(1)using automatic differentiation to compute the Jacobian matrix of LSM instead of constructing a tangent linear model of LSM,and(2)replacing the ensemble Kalman filter framework with the extended Kalman filter(EKF)framework to improve the efficiency of parameter optimization for the dual-cycle algorithm.The EKF-based dual-cycle algorithm accelerated the parameter estimation efficiency near 60 times during a 90-day time period with a model integration time step of 1 h.To evaluate the dual-cycle LDAS at the regional-scale,it was applied to assimilate the SMAP soil moisture over the Tibetan Plateau,and soil moisture estimates were validated using in situ observations from four different climatic areas.The results showed that the EKF-based dual-cycle LDAS corrected biases in both the model and observations and produced more accurate estimates of soil moisture,land surface temperature,and evapotranspiration than did the open loop with default parameters.Furthermore,the spatial distribution of soil parameters(sand content,clay content,and porosity)obtained from the LDAS was more reasonable than those of default values.The EKF-based dual-cycle algorithm developed in this study is expected to improve the assimilation skills of land surface,ecological,and hydrological studies.展开更多
This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeabi...This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeability,and fluid components,like viscosity.The primary aim is to deduce either constant pressure head or pressure profiles,given the known velocity field at a steady-state flow through a conduit containing obstacles,including walls,spheres,and grains.The lattice Boltzmann method(LBM)combined with automatic differentiation(AD)(AD-LBM)is employed,with the help of the GPU-capable Taichi programming language.A lightweight tape is used to generate gradients for the entire LBM simulation,enabling end-to-end backpropagation.Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media,leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity.The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency,making it a powerful tool for solving inverse fluid flow problems in various applications.展开更多
In artificial intelligence(AI)for science,the AI-empowered topology optimization methods have garnered sustained attention from researchers and achieved significant development.In this paper,we introduce the implicit ...In artificial intelligence(AI)for science,the AI-empowered topology optimization methods have garnered sustained attention from researchers and achieved significant development.In this paper,we introduce the implicit neural representation(INR)from AI and the material point method(MPM)from the field of computational mechanics into topology optimization,resulting in a novel differentiable and fully mesh-independent topology optimization framework named MI-TONR,and it is then applied to nonlinear topology optimization(NTO)design.Within MI-TONR,the INR is combined with the topology description function to construct the design model,while implicit MPM is employed for physical response analysis.A skillful integration is achieved between the design model based on the continuous implicit representation field and the analysis model based on the Lagrangian particles.Along with updating parameters of the neural network(i.e.,design variables),the structural topologies iteratively evolve according to the responses analysis results and optimization functions.The computational differentiability is ensured at every step of MI-TONR,enabling sensitivity analysis using automatic differentiation.In addition,we introduce the augmented Lagrangian Method to handle multiple constraints in topology optimization and adopt a learning rate adaptive adjustment scheme to enhance the robustness of the optimization process.Numerical examples demonstrate that MI-TONR can effectively conduct NTO design under large loads without any numerical techniques to mitigate numerical instabilities.Meanwhile,its natural satisfaction with the no-penetration condition facilitates the NTO design of considering contact.The infinite spatial resolution characteristic facilitates the generation of structural topology at multiple resolutions with clear and continuous boundaries.展开更多
In this article, the least program behavior decomposition method (LPBD) is put forward from a program structure point of view. This method can be extensively used both in algorithms of automatic differentiation (AD) a...In this article, the least program behavior decomposition method (LPBD) is put forward from a program structure point of view. This method can be extensively used both in algorithms of automatic differentiation (AD) and in tools design, and does not require programs to be evenly separable but the cost in terms of operations count and memory is similar to methods using checkpointing. This article starts by summarizing the rules of adjointization and then presents the implementation of LPBD. Next, the definition of the separable program space, based on the fundamental assumptions (FA) of automatic differentiation, is given and the differentiation cost functions are derived. Also, two constants of fundamental importance in AD, s and m, are derived under FA. Under the assumption of even separability, the adjoint cost of simple and deep decomposition is subsequently discussed quantitatively using checkpointing. Finally, the adjoint costs in terms of operations count and memory through the LPBD method are shown to be uniformly dependent on the depth of structure or decomposition.展开更多
Three model configurations are presented for multi-step time series predictions of the heat absorbed by thewater and steam in a thermal power plant. The models predict over horizons of 2, 4, and 6 steps into thefuture...Three model configurations are presented for multi-step time series predictions of the heat absorbed by thewater and steam in a thermal power plant. The models predict over horizons of 2, 4, and 6 steps into thefuture, where each step is a 5-minute increment. The evaluated models are a pure machine learning model, anovel hybrid machine learning and physics-based model, and the hybrid model with an incomplete dataset. Thehybrid model deconstructs the machine learning into individual boiler heat absorption units: economizer, waterwall, superheater, and reheater. Each configuration uses a gated recurrent unit (GRU) or a GRU-based encoder–decoder as the deep learning architecture. Mean squared error is used to evaluate the models compared totarget values. The encoder–decoder architecture is over 11% more accurate than the GRU only models. Thehybrid model with the incomplete dataset highlights the importance of the manipulated variables to the system.The hybrid model, compared to the pure machine learning model, is over 10% more accurate on averageover 20 iterations of each model. Automatic differentiation is applied to the hybrid model to perform a localsensitivity analysis to identify the most impactful of the 72 manipulated variables on the heat absorbed in theboiler. The models and sensitivity analyses are used in a discussion about optimizing the thermal power plant.展开更多
In this paper, the state-feedback Nash game based mixed H2/H∞ design^（[1, 2]）has been extended for output feedback case. The algorithm is applied to control bioreactor system with a Laguerre-Wavelet Network（LWN）^...In this paper, the state-feedback Nash game based mixed H2/H∞ design^（[1, 2]）has been extended for output feedback case. The algorithm is applied to control bioreactor system with a Laguerre-Wavelet Network（LWN）^（[3, 4]）model of the bioreactor.This is achieved by using the LWN model as a deviation model and by successively linearising the deviation model along the state trajectory. For reducing the approximation error and to improve the controller performance, symbolic derivation algorithm, viz.,automatic differentiation is employed. A cautionary note is also given on the fragility of the output feedback mixed H2/H∞ model predictive controller^（[4, 5]）due to its sensitivity to its own parametric changes.展开更多
The adjoint code generator （ADG） is developed to produce the adjoint codes, which are used to analytically calculate gradients and the Hessian-vector products with the costs independent of the number of the independ...The adjoint code generator （ADG） is developed to produce the adjoint codes, which are used to analytically calculate gradients and the Hessian-vector products with the costs independent of the number of the independent variables.Different from other automatic differentiation tools, the implementation of ADG has advantages of using the least program behavior decomposition method and several static dependence analysis techniques.In this paper we first address the concerned concepts and fundamentals, and then introduce the functionality and the features of ADG.In particular, we also discuss the design architecture of ADG and implementation details including the recomputation and storing strategy and several techniques for code optimization.Some experimental results in several applications are presented at the end.展开更多
基金supported in part by the National Natural Science Foundation of China(61633006)the Fundamental Research Funds for the Central Universities of China(DUT2018TB06)National Key Research and Development Program of China(2017YFA0700300)。
文摘In this paper,a cell average technique(CAT)based parameter estimation method is proposed for cooling crystallization involved with particle growth,aggregation and breakage,by establishing a more efficient and accurate solution in terms of the automatic differentiation(AD)algorithm.To overcome the deficiency of CAT that demands high computation cost for implementation,a set of ordinary differential equations(ODEs)entailed from CAT based discretized population balance equation(PBE)are solved by using the AD based high-order Taylor expansion.Moreover,an AD based trust-region reflective(TRR)algorithm and another interior-point(IP)algorithm are established for estimating the kinetic parameters associated with particle growth,aggregation and breakage.As a result,the estimation accuracy can be further improved while the computation cost can be significantly reduced,compared to the existing algorithms.Benchmark examples from the literature are used to illustrate the accuracy and efficiency of the AD-based CAT,TRR and IP algorithms in comparison with the existing algorithms.Moreover,seeded batch cooling crystallization experiments ofβform L-glutamic acid are performed to validate the proposed method.
文摘In order to slove the large-scale nonlinear programming （NLP） problems efficiently, an efficient optimization algorithm based on reduced sequential quadratic programming （rSQP） and automatic differentiation （AD） is presented in this paper. With the characteristics of sparseness, relatively low degrees of freedom and equality constraints utilized, the nonlinear programming problem is solved by improved rSQP solver. In the solving process, AD technology is used to obtain accurate gradient information. The numerical results show that the combined algorithm, which is suitable for large-scale process optimization problems, can calculate more efficiently than rSQP itself.
基金supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions of China
文摘A systematic methodology for formulating,implementing,solving and verifying discrete adjoint of the compressible Reynolds-averaged Navier-Stokes（RANS） equations for aerodynamic design optimization on unstructured meshes is proposed.First,a general adjoint formulation is constructed for the entire optimization problem,including parameterization,mesh deformation,flow solution and computation of the objective function,which is followed by detailed formulations of matrix-vector products arising in the adjoint model.According to this formulation,procedural components of implementing the required matrix-vector products are generated by means of automatic differentiation（AD） in a structured and modular manner.Furthermore,a duality-preserving iterative algorithm is employed to solve flow adjoint equations arising in the adjoint model,ensuring identical convergence rates for the tangent and the adjoint models.A three-step strategy is adopted to verify the adjoint computation.The proposed method has several remarkable features：the use of AD techniques avoids tedious and error-prone manual derivation and programming;duality is strictly preserved so that consistent and highly accurate discrete sensitivities can be obtained;and comparable efficiency to hand-coded implementation can be achieved.Upon the current discrete adjoint method,a gradient-based optimization framework has been developed and applied to a drag reduction problem.
基金supported by the Second Tibetan Plateau Scientific Expedition and Research Program(Grant No.2019QZKK0206)the National Key Research and Development Program of China(Grant No.2022YFC3002901)+1 种基金the National Natural Science Foundation of China(Grant No.42271491)the International Partnership Program of Chinese Academy of Sciences(Grant No.183311KYSB20200015)。
文摘Soil moisture plays a crucial role in drought monitoring,flood forecasting,and water resource management.Data assimilation methods can integrate the strengths of land surface models(LSM)and remote sensing data to generate highprecision and spatio-temporally continuous soil moisture products.However,one of the challenges of the land data assimilation system(LDAS)is how to accurately estimate model and observation errors.To address this,we had previously proposed a dualcycle assimilation algorithm that can simultaneously estimate the model and observation errors,LSM parameters,and observation operator parameters.However,this algorithm requires a large ensemble size to guarantee stable parameter estimates,resulting in low efficiency and limiting its large-scale applications.To address this limitation,the authors employed the following approaches:(1)using automatic differentiation to compute the Jacobian matrix of LSM instead of constructing a tangent linear model of LSM,and(2)replacing the ensemble Kalman filter framework with the extended Kalman filter(EKF)framework to improve the efficiency of parameter optimization for the dual-cycle algorithm.The EKF-based dual-cycle algorithm accelerated the parameter estimation efficiency near 60 times during a 90-day time period with a model integration time step of 1 h.To evaluate the dual-cycle LDAS at the regional-scale,it was applied to assimilate the SMAP soil moisture over the Tibetan Plateau,and soil moisture estimates were validated using in situ observations from four different climatic areas.The results showed that the EKF-based dual-cycle LDAS corrected biases in both the model and observations and produced more accurate estimates of soil moisture,land surface temperature,and evapotranspiration than did the open loop with default parameters.Furthermore,the spatial distribution of soil parameters(sand content,clay content,and porosity)obtained from the LDAS was more reasonable than those of default values.The EKF-based dual-cycle algorithm developed in this study is expected to improve the assimilation skills of land surface,ecological,and hydrological studies.
文摘This study presents a method for the inverse analysis of fluid flow problems.The focus is put on accurately determining boundary conditions and characterizing the physical properties of granular media,such as permeability,and fluid components,like viscosity.The primary aim is to deduce either constant pressure head or pressure profiles,given the known velocity field at a steady-state flow through a conduit containing obstacles,including walls,spheres,and grains.The lattice Boltzmann method(LBM)combined with automatic differentiation(AD)(AD-LBM)is employed,with the help of the GPU-capable Taichi programming language.A lightweight tape is used to generate gradients for the entire LBM simulation,enabling end-to-end backpropagation.Our AD-LBM approach accurately estimates the boundary conditions for complex flow paths in porous media,leading to observed steady-state velocity fields and deriving macro-scale permeability and fluid viscosity.The method demonstrates significant advantages in terms of prediction accuracy and computational efficiency,making it a powerful tool for solving inverse fluid flow problems in various applications.
基金supported by the National Natural Science Foundation of China(Grant No.92371206)the Post-graduate Scientific Research Innovation Project of Hunan Province(Grant No.CX20220059)。
文摘In artificial intelligence(AI)for science,the AI-empowered topology optimization methods have garnered sustained attention from researchers and achieved significant development.In this paper,we introduce the implicit neural representation(INR)from AI and the material point method(MPM)from the field of computational mechanics into topology optimization,resulting in a novel differentiable and fully mesh-independent topology optimization framework named MI-TONR,and it is then applied to nonlinear topology optimization(NTO)design.Within MI-TONR,the INR is combined with the topology description function to construct the design model,while implicit MPM is employed for physical response analysis.A skillful integration is achieved between the design model based on the continuous implicit representation field and the analysis model based on the Lagrangian particles.Along with updating parameters of the neural network(i.e.,design variables),the structural topologies iteratively evolve according to the responses analysis results and optimization functions.The computational differentiability is ensured at every step of MI-TONR,enabling sensitivity analysis using automatic differentiation.In addition,we introduce the augmented Lagrangian Method to handle multiple constraints in topology optimization and adopt a learning rate adaptive adjustment scheme to enhance the robustness of the optimization process.Numerical examples demonstrate that MI-TONR can effectively conduct NTO design under large loads without any numerical techniques to mitigate numerical instabilities.Meanwhile,its natural satisfaction with the no-penetration condition facilitates the NTO design of considering contact.The infinite spatial resolution characteristic facilitates the generation of structural topology at multiple resolutions with clear and continuous boundaries.
文摘In this article, the least program behavior decomposition method (LPBD) is put forward from a program structure point of view. This method can be extensively used both in algorithms of automatic differentiation (AD) and in tools design, and does not require programs to be evenly separable but the cost in terms of operations count and memory is similar to methods using checkpointing. This article starts by summarizing the rules of adjointization and then presents the implementation of LPBD. Next, the definition of the separable program space, based on the fundamental assumptions (FA) of automatic differentiation, is given and the differentiation cost functions are derived. Also, two constants of fundamental importance in AD, s and m, are derived under FA. Under the assumption of even separability, the adjoint cost of simple and deep decomposition is subsequently discussed quantitatively using checkpointing. Finally, the adjoint costs in terms of operations count and memory through the LPBD method are shown to be uniformly dependent on the depth of structure or decomposition.
基金funded by the United States Department of Energy project DE-FE0031754.
文摘Three model configurations are presented for multi-step time series predictions of the heat absorbed by thewater and steam in a thermal power plant. The models predict over horizons of 2, 4, and 6 steps into thefuture, where each step is a 5-minute increment. The evaluated models are a pure machine learning model, anovel hybrid machine learning and physics-based model, and the hybrid model with an incomplete dataset. Thehybrid model deconstructs the machine learning into individual boiler heat absorption units: economizer, waterwall, superheater, and reheater. Each configuration uses a gated recurrent unit (GRU) or a GRU-based encoder–decoder as the deep learning architecture. Mean squared error is used to evaluate the models compared totarget values. The encoder–decoder architecture is over 11% more accurate than the GRU only models. Thehybrid model with the incomplete dataset highlights the importance of the manipulated variables to the system.The hybrid model, compared to the pure machine learning model, is over 10% more accurate on averageover 20 iterations of each model. Automatic differentiation is applied to the hybrid model to perform a localsensitivity analysis to identify the most impactful of the 72 manipulated variables on the heat absorbed in theboiler. The models and sensitivity analyses are used in a discussion about optimizing the thermal power plant.
文摘In this paper, the state-feedback Nash game based mixed H2/H∞ design^（[1, 2]）has been extended for output feedback case. The algorithm is applied to control bioreactor system with a Laguerre-Wavelet Network（LWN）^（[3, 4]）model of the bioreactor.This is achieved by using the LWN model as a deviation model and by successively linearising the deviation model along the state trajectory. For reducing the approximation error and to improve the controller performance, symbolic derivation algorithm, viz.,automatic differentiation is employed. A cautionary note is also given on the fragility of the output feedback mixed H2/H∞ model predictive controller^（[4, 5]）due to its sensitivity to its own parametric changes.
基金Supported by the National Natural Science Foundation of China (Grant Nos 60503031, 10871014)the National Basic Research Programof China (Grant No 2004CB418304)
文摘The adjoint code generator （ADG） is developed to produce the adjoint codes, which are used to analytically calculate gradients and the Hessian-vector products with the costs independent of the number of the independent variables.Different from other automatic differentiation tools, the implementation of ADG has advantages of using the least program behavior decomposition method and several static dependence analysis techniques.In this paper we first address the concerned concepts and fundamentals, and then introduce the functionality and the features of ADG.In particular, we also discuss the design architecture of ADG and implementation details including the recomputation and storing strategy and several techniques for code optimization.Some experimental results in several applications are presented at the end.
