Reactive transport equations in porous media are critical in various scientific and engineering disciplines,but solving these equations can be computationally expensive when exploring different scenarios,such as varyi...Reactive transport equations in porous media are critical in various scientific and engineering disciplines,but solving these equations can be computationally expensive when exploring different scenarios,such as varying porous structures and initial or boundary conditions.The deep operator network(DeepONet)has emerged as a popular deep learning framework for solving parametric partial differential equations.However,applying the DeepONet to porous media presents significant challenges due to its limited capability to extract representative features from intricate structures.To address this issue,we propose the Porous-DeepONet,a simple yet highly effective extension of the DeepONet framework that leverages convolutional neural networks(CNNs)to learn the solution operators of parametric reactive transport equations in porous media.By incorporating CNNs,we can effectively capture the intricate features of porous media,enabling accurate and efficient learning of the solution operators.We demonstrate the effectiveness of the Porous-DeepONet in accurately and rapidly learning the solution operators of parametric reactive transport equations with various boundary conditions,multiple phases,and multiphysical fields through five examples.This approach offers significant computational savings,potentially reducing the computation time by 50–1000 times compared with the finite-element method.Our work may provide a robust alternative for solving parametric reactive transport equations in porous media,paving the way for exploring complex phenomena in porous media.展开更多
Very short-term prediction of ship motion is critically important in many scenarios such as carrier aircraft landings and marine engineering operations.This paper introduces the newly developed functional deep learnin...Very short-term prediction of ship motion is critically important in many scenarios such as carrier aircraft landings and marine engineering operations.This paper introduces the newly developed functional deep learning model,named as Deep Operator networks neural network(DeepOnet)to predict very short-term ship motion in waves.It takes wave height as input and predicts ship motion as output,employing a cause-to-effect prediction approach.The modeling data for this study is derived from publicly available experimental data at the Iowa Institute of Hydraulic Research.Initially,the tuning of the hyperparameters within the neural network system was conducted to identify the optimal parameter combination.Subsequently,the DeepOnet model for wave height and multi-degree-of-freedom motion was established,and the impact of increasing time steps on prediction accuracy was analyzed.Lastly,a comparative analysis was performed between the DeepOnet model and the classical time series model,long short-term memory(LSTM).It was observed that the DeepOnet model exhibited a tenfold improvement in accuracy for roll and heave motions.Furthermore,as the forecast duration increased,the advantage of the DeepOnet model showed a trend of strengthening.As a functional prediction model,DeepOnet offers a novel and promising tool for very short-term ship motion prediction.展开更多
基金supported by the National Key Research and Development Program of China(2022YFA1503501)the National Natural Science Foundation of China(22378112,22278127,and 22078088)+1 种基金the Fundamental Research Funds for the Central Universities(2022ZFJH004)the Shanghai Rising-Star Program(21QA1401900).
文摘Reactive transport equations in porous media are critical in various scientific and engineering disciplines,but solving these equations can be computationally expensive when exploring different scenarios,such as varying porous structures and initial or boundary conditions.The deep operator network(DeepONet)has emerged as a popular deep learning framework for solving parametric partial differential equations.However,applying the DeepONet to porous media presents significant challenges due to its limited capability to extract representative features from intricate structures.To address this issue,we propose the Porous-DeepONet,a simple yet highly effective extension of the DeepONet framework that leverages convolutional neural networks(CNNs)to learn the solution operators of parametric reactive transport equations in porous media.By incorporating CNNs,we can effectively capture the intricate features of porous media,enabling accurate and efficient learning of the solution operators.We demonstrate the effectiveness of the Porous-DeepONet in accurately and rapidly learning the solution operators of parametric reactive transport equations with various boundary conditions,multiple phases,and multiphysical fields through five examples.This approach offers significant computational savings,potentially reducing the computation time by 50–1000 times compared with the finite-element method.Our work may provide a robust alternative for solving parametric reactive transport equations in porous media,paving the way for exploring complex phenomena in porous media.
基金Project supported by the National Natural Science Foundation of China(Grant No.51679021)supported by the Southern Marine Science and Engineering Guangdong Laboratory(Guangzhou)(Grant Nos.GML20240001,GML2024009).
文摘Very short-term prediction of ship motion is critically important in many scenarios such as carrier aircraft landings and marine engineering operations.This paper introduces the newly developed functional deep learning model,named as Deep Operator networks neural network(DeepOnet)to predict very short-term ship motion in waves.It takes wave height as input and predicts ship motion as output,employing a cause-to-effect prediction approach.The modeling data for this study is derived from publicly available experimental data at the Iowa Institute of Hydraulic Research.Initially,the tuning of the hyperparameters within the neural network system was conducted to identify the optimal parameter combination.Subsequently,the DeepOnet model for wave height and multi-degree-of-freedom motion was established,and the impact of increasing time steps on prediction accuracy was analyzed.Lastly,a comparative analysis was performed between the DeepOnet model and the classical time series model,long short-term memory(LSTM).It was observed that the DeepOnet model exhibited a tenfold improvement in accuracy for roll and heave motions.Furthermore,as the forecast duration increased,the advantage of the DeepOnet model showed a trend of strengthening.As a functional prediction model,DeepOnet offers a novel and promising tool for very short-term ship motion prediction.
