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
In this paper,we propose a DeepONet structure with causality to represent causal linear operators between Banach spaces of time-dependent signals.The theorem of universal approximations to nonlinear operators proposed...In this paper,we propose a DeepONet structure with causality to represent causal linear operators between Banach spaces of time-dependent signals.The theorem of universal approximations to nonlinear operators proposed in[5]is extended to operators with causalities,and the proposed Causality-DeepONet implements the physical causality in its framework.The proposed Causality-DeepONet considers causality(the state of the system at the current time is not affected by that of the future,but only by its current state and past history)and uses a convolution-type weight in its design.To demonstrate its effectiveness in handling the causal response of a physical system,the Causality-DeepONet is applied to learn the operator representing the response of a building due to earthquake ground accelerations.Extensive numerical tests and comparisons with some existing variants of DeepONet are carried out,and the Causality-DeepONet clearly shows its unique capability to learn the retarded dynamic responses of the seismic response operator with good accuracy.展开更多
Delivering energy flexibility at the district scale entails coordinating control actions across many buildings to shape aggregate demand;this coordination depends on training and deploying control policies and optimiz...Delivering energy flexibility at the district scale entails coordinating control actions across many buildings to shape aggregate demand;this coordination depends on training and deploying control policies and optimization routines,which in turn require predictive models that can be queried efficiently over large building clusters.However,conventional physics-based simulators are computationally prohibitive for large-scale control training,and simple data-driven surrogates often lack the generalization needed for heterogeneous clusters.This paper introduces ScaleONet,a deep operator network framework designed for scalable,control-oriented modeling of building-cluster thermal dynamics.ScaleONet leverages the DeepONet paradigm to decouple and share learning across buildings:an LSTM-based branch network encodes outdoor climate and individual HVAC control signals,while a multilayer perceptron(MLP)-based trunk network embeds prediction timestamps,enabling fast predictions for growing clusters with negligible extra cost for each additional building or timestep.To the authors’knowledge,this is the first operator-learning method tailored to indoor air temperature forecasting in heterogeneous building clusters.Validation on thirty Belgian buildings(GenkNet)simulated in Dymola shows that,although a non-operator-learning LSTM baseline slightly outperforms ScaleONet for single-building cases,its error grows monotonically with cluster size.In contrast,ScaleONet’s median per-building-per-day RMSE decreases from 0.59°C at three buildings to 0.53°C at ten and 0.47°C at thirty,compared to 0.95°C for the LSTM at thirty buildings-a 51%reduction in prediction error.Error analysis across envelope heat-loss coefficients(UAbuilding)further reveals that while the LSTM’s RMSE increases for high-𝑈𝐴structures,ScaleONet maintains uniformly low error.With millisecond-scale inference(approximately 4 ms per sample for thirty buildings),ScaleONet is well suited for large-scale reinforcement learning,receding-horizon optimization,and real-time model predictive control.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
Strip foundations,as a widely applied form of shallow foundation,involve foundation displacements and soil deformations under loading,which are critical issues in geotechnical engineering.Traditional limit analysis me...Strip foundations,as a widely applied form of shallow foundation,involve foundation displacements and soil deformations under loading,which are critical issues in geotechnical engineering.Traditional limit analysis methods can only provide solutions for ultimate bearing capacity,while numerical methods require remeshing and remodeling for different scenarios.To address these challenges,this study proposes a deep learning approach based on the DeepONet neural operator for rapid and accurate predictions of load–displacement curves and vertical displacement fields of strip foundations under various conditions.A dataset with randomly distributed parameters was generated using finite element method,with the training set employed to train the neural network.Validation on the test set shows that the proposed method not only accurately predicts ultimate bearing capacity but also captures the nonlinear characteristics of high-dimensional data.As an offline model alternative to finite element methods,the proposed approach holds promise for efficient and real-time prediction of the mechanical behavior of shallow foundations under loading.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supported by the US National Science Foundation grant DMS-2207449supported by OSD/AFOSR MURI grant FA9550-20-1-0358。
文摘In this paper,we propose a DeepONet structure with causality to represent causal linear operators between Banach spaces of time-dependent signals.The theorem of universal approximations to nonlinear operators proposed in[5]is extended to operators with causalities,and the proposed Causality-DeepONet implements the physical causality in its framework.The proposed Causality-DeepONet considers causality(the state of the system at the current time is not affected by that of the future,but only by its current state and past history)and uses a convolution-type weight in its design.To demonstrate its effectiveness in handling the causal response of a physical system,the Causality-DeepONet is applied to learn the operator representing the response of a building due to earthquake ground accelerations.Extensive numerical tests and comparisons with some existing variants of DeepONet are carried out,and the Causality-DeepONet clearly shows its unique capability to learn the retarded dynamic responses of the seismic response operator with good accuracy.
基金supported by KU Leuven,Belgium through the TECHPED-C2 project(C24M/21/021)which investigates tech-nically feasible and effective solutions for Positive Energy Districts.Additional support was provided by the National University of Singa-pore,Singapore through the Start-Up Grant(A-0009876-00-00)the Ministry of Education,Singapore,under the Academic Research Fund Tier 1(A-8003235-00-00).
文摘Delivering energy flexibility at the district scale entails coordinating control actions across many buildings to shape aggregate demand;this coordination depends on training and deploying control policies and optimization routines,which in turn require predictive models that can be queried efficiently over large building clusters.However,conventional physics-based simulators are computationally prohibitive for large-scale control training,and simple data-driven surrogates often lack the generalization needed for heterogeneous clusters.This paper introduces ScaleONet,a deep operator network framework designed for scalable,control-oriented modeling of building-cluster thermal dynamics.ScaleONet leverages the DeepONet paradigm to decouple and share learning across buildings:an LSTM-based branch network encodes outdoor climate and individual HVAC control signals,while a multilayer perceptron(MLP)-based trunk network embeds prediction timestamps,enabling fast predictions for growing clusters with negligible extra cost for each additional building or timestep.To the authors’knowledge,this is the first operator-learning method tailored to indoor air temperature forecasting in heterogeneous building clusters.Validation on thirty Belgian buildings(GenkNet)simulated in Dymola shows that,although a non-operator-learning LSTM baseline slightly outperforms ScaleONet for single-building cases,its error grows monotonically with cluster size.In contrast,ScaleONet’s median per-building-per-day RMSE decreases from 0.59°C at three buildings to 0.53°C at ten and 0.47°C at thirty,compared to 0.95°C for the LSTM at thirty buildings-a 51%reduction in prediction error.Error analysis across envelope heat-loss coefficients(UAbuilding)further reveals that while the LSTM’s RMSE increases for high-𝑈𝐴structures,ScaleONet maintains uniformly low error.With millisecond-scale inference(approximately 4 ms per sample for thirty buildings),ScaleONet is well suited for large-scale reinforcement learning,receding-horizon optimization,and real-time model predictive control.
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.
基金supported by Natural Science Foundation of Shanghai(Grant No:23ZR1468500).
文摘Strip foundations,as a widely applied form of shallow foundation,involve foundation displacements and soil deformations under loading,which are critical issues in geotechnical engineering.Traditional limit analysis methods can only provide solutions for ultimate bearing capacity,while numerical methods require remeshing and remodeling for different scenarios.To address these challenges,this study proposes a deep learning approach based on the DeepONet neural operator for rapid and accurate predictions of load–displacement curves and vertical displacement fields of strip foundations under various conditions.A dataset with randomly distributed parameters was generated using finite element method,with the training set employed to train the neural network.Validation on the test set shows that the proposed method not only accurately predicts ultimate bearing capacity but also captures the nonlinear characteristics of high-dimensional data.As an offline model alternative to finite element methods,the proposed approach holds promise for efficient and real-time prediction of the mechanical behavior of shallow foundations under loading.
