Rapid and reliable onboard optimization of bank angle profiles is crucial for mitigating uncertainties during Mars atmospheric entry.This paper presents a neural-network-accelerated methodology for optimizing parametr...Rapid and reliable onboard optimization of bank angle profiles is crucial for mitigating uncertainties during Mars atmospheric entry.This paper presents a neural-network-accelerated methodology for optimizing parametric bank angle profiles in Mars atmospheric entry missions.The methodology includes a universal approach to handling path constraints and a reliable solution method based on the Particle Swarm Optimization(PSO)algorithm.For illustrative purposes,a mission with the objective of maximizing terminal altitude is considered.The original entry optimization problem is converted into optimizing three coefficients for the bank angle profiles with terminal constraints by formulating a parametric Mars entry bank angle profile and constraint handling methods.The parameter optimization problem is addressed using the PSO algorithm,with reliability enhanced by increasing the PSO swarm size.To improve computational efficiency,an enhanced Deep Operator Network(Deep ONet)is used as a dynamics solver to predict terminal states under various bank angle profiles rapidly.Numerical simulations demonstrate that the proposed methodology ensures reliable convergence with a sufficiently large PSO swarm while maintaining high computational efficiency facilitated by the neural-network-based dynamics solver.Compared to the existing methodologies,this methodology offers a streamlined process,the reduced sensitivity to initial guesses,and the improved computational efficiency.展开更多
Wave propagation problems are typically formulated as partial differential equations(PDEs)on unbounded domains to be solved.The classical approach to solving such problems involves truncating them to problems on bound...Wave propagation problems are typically formulated as partial differential equations(PDEs)on unbounded domains to be solved.The classical approach to solving such problems involves truncating them to problems on bounded domains by designing the artificial boundary conditions or perfectly matched layers,which typically require significant effort,and the presence of nonlinearity in the equation makes such designs even more challenging.Emerging deep learning-based methods for solving PDEs,with the physics-informed neural networks(PINNs)method as a representative,still face significant challenges when directly used to solve PDEs on unbounded domains.Calculations performed in a bounded domain of interest without imposing boundary constraints can lead to a lack of unique solutions thus causing the failure of PINNs.In light of this,this paper proposes a novel and effective data generationbased operator learning method for solving PDEs on unbounded domains.The key idea behind this method is to generate high-quality training data.Specifically,we construct a family of approximate analytical solutions to the target PDE based on its initial condition and source term.Then,using these constructed data comprising exact solutions,initial conditions,and source terms,we train an operator learning model called MIONet,which is capable of handling multiple inputs,to learn the mapping from the initial condition and source term to the PDE solution on a bounded domain of interest.Finally,we utilize the generalization ability of this model to predict the solution of the target PDE.The effectiveness of this method is exemplified by solving the wave equation and the Schr¨odinger equation defined on unbounded domains.More importantly,the proposed method can deal with nonlinear problems,which has been demonstrated by solving Burgers’equation and Korteweg-de Vries(KdV)equation.The code is available at https://github.com/ZJLAB-AMMI/DGOL.展开更多
The integration of physics-based modelling and data-driven artificial intelligence(AI)has emerged as a transformative paradigm in computational mechanics.This perspective reviews the development and current status of ...The integration of physics-based modelling and data-driven artificial intelligence(AI)has emerged as a transformative paradigm in computational mechanics.This perspective reviews the development and current status of AI-empowered frameworks,including data-driven methods,physics-informed neural networks,and neural operators.While these approaches have demonstrated significant promise,challenges remain in terms of robustness,generalisation,and computational efficiency.We delineate four promising research directions:(1)Modular neural architectures inspired by traditional computational mechanics,(2)physics informed neural operators for resolution-invariant operator learning,(3)intelligent frameworks for multiphysics and multiscale biomechanics problems,and(4)structural optimisation strategies based on physics constraints and reinforcement learning.These directions represent a shift toward foundational frameworks that combine the strengths of physics and data,opening new avenues for the modelling,simulation,and optimisation of complex physical systems.展开更多
Transformer has achieved remarkable results in various fields,including its application in modeling dynamic systems governed by partial differential equations.However,transformer still face challenges in achieving lon...Transformer has achieved remarkable results in various fields,including its application in modeling dynamic systems governed by partial differential equations.However,transformer still face challenges in achieving long-term stable predictions for three-dimensional turbulence.In this paper,we propose an implicit factorized transformer(IFactFormer)model,which enables stable training at greater depths through implicit iteration over factorized attention.IFactFormer is applied to large eddy simulation of three-dimensional homogeneous isotropic turbulence(HIT),and is shown to be more accurate than the FactFormer,Fourier neural operator,and dynamic Smagorinsky model(DSM)in the prediction of the velocity spectra,probability density functions of velocity increments and vorticity,temporal evolutions of velocity and vorticity root-mean-square value and isosurface of the normalized vorticity.IFactFormer can achieve long-term stable predictions of a series of turbulence statistics in HIT.Fur-thermore,IFactFormer showcases superior computational efficiency compared to the conventional DSM in large eddy simulation.展开更多
Digital twins of lithium-ion batteries are increasingly used to enable predictive monitoring,control,and design at system scale.Increasing their capabilities involves improving their physical fidelity while maintainin...Digital twins of lithium-ion batteries are increasingly used to enable predictive monitoring,control,and design at system scale.Increasing their capabilities involves improving their physical fidelity while maintaining sub-millisecond computational speed.In this work,we introduce machine learning surrogates that learn physical dynamics.Specifically,we benchmark three operator-learning surrogates for the Single Particle Model(SPM):Deep Operator Networks(DeepONets),Fourier Neural Operators(FNOs)and a newly proposed parameter-embedded Fourier Neural Operator(PE-FNO),which conditions each spectral layer on particle radius and solid-phase diffusivity.We extend the comparison to classical machine-learning baselines by including U-Nets.Models are trained on simulated trajectories spanning four current families(constant,triangular,pulse-train,and Gaussian-random-field)and a full range of State-of-Charge(SOC)(0%to 100%).DeepONet accurately replicates constant-current behaviour but struggles with more dynamic loads.The basic FNO maintains mesh invariance and keeps concentration errors below 1%,with voltage mean-absolute errors under 1.7mV across all load types.Introducing parameter embedding marginally increases error but enables generalisation to varying radii and diffusivities.PE-FNO executes approximately 200 times faster than a 16-thread SPM solver.Consequently,PE-FNO’s capabilities in inverse tasks are explored in a parameter estimation task with Bayesian optimisation,recovering anode and cathode diffusivities with 1.14%and 8.4%mean absolute percentage error,respectively,and 0.5918 percentage points higher error in comparison with classical methods.These results pave the way for neural operators to meet the accuracy,speed and parametric flexibility demands of real-time battery management,design-of-experiments and large-scale inference.PE-FNO outperforms conventional neural surrogates,offering a practical path towards high-speed and high-fidelity electrochemical digital twins.展开更多
Operant conditioning is one of the fundamental mechanisms of animal learning, which suggests that the behavior of all animals, from protists to humans, is guided by its consequences. We present a new stochastic learni...Operant conditioning is one of the fundamental mechanisms of animal learning, which suggests that the behavior of all animals, from protists to humans, is guided by its consequences. We present a new stochastic learning automaton called a Skinner au- tomaton that is a psychological model for formalizing the theory of operant conditioning. We identify animal operant learning with a thermodynamic process, and derive a so-called Skinner algorithm from Monte Carlo method as well as Metropolis algo- rithm and simulated annealing. Under certain conditions, we prove that the Skinner automaton is expedient, 6-optimal, optimal, and that the operant probabilities converge to the set of stable roots with probability of 1. The Skinner automaton enables ma- chines to autonomously learn in an animal-like way.展开更多
基金supported in part by the National Defense Basic Scientific Research Program of China(No.JCKY2021603B030)the Shenzhen Fundamental Research Program,China(No.JCYJ20220818102601004)the Science Center Program of National Natural Science Foundation of China(No.62188101)。
文摘Rapid and reliable onboard optimization of bank angle profiles is crucial for mitigating uncertainties during Mars atmospheric entry.This paper presents a neural-network-accelerated methodology for optimizing parametric bank angle profiles in Mars atmospheric entry missions.The methodology includes a universal approach to handling path constraints and a reliable solution method based on the Particle Swarm Optimization(PSO)algorithm.For illustrative purposes,a mission with the objective of maximizing terminal altitude is considered.The original entry optimization problem is converted into optimizing three coefficients for the bank angle profiles with terminal constraints by formulating a parametric Mars entry bank angle profile and constraint handling methods.The parameter optimization problem is addressed using the PSO algorithm,with reliability enhanced by increasing the PSO swarm size.To improve computational efficiency,an enhanced Deep Operator Network(Deep ONet)is used as a dynamics solver to predict terminal states under various bank angle profiles rapidly.Numerical simulations demonstrate that the proposed methodology ensures reliable convergence with a sufficiently large PSO swarm while maintaining high computational efficiency facilitated by the neural-network-based dynamics solver.Compared to the existing methodologies,this methodology offers a streamlined process,the reduced sensitivity to initial guesses,and the improved computational efficiency.
基金supported by the China Postdoctoral Science Foundation(No.2023M743266)Zhejiang Provincial Postdoctoral Research Project Merit-based Funding(No.ZJ2023067)+1 种基金Exploratory Research Project(No.2022RC0AN02)Research Initiation Project(No.K2022RC0PI01)of Zhejiang Lab.
文摘Wave propagation problems are typically formulated as partial differential equations(PDEs)on unbounded domains to be solved.The classical approach to solving such problems involves truncating them to problems on bounded domains by designing the artificial boundary conditions or perfectly matched layers,which typically require significant effort,and the presence of nonlinearity in the equation makes such designs even more challenging.Emerging deep learning-based methods for solving PDEs,with the physics-informed neural networks(PINNs)method as a representative,still face significant challenges when directly used to solve PDEs on unbounded domains.Calculations performed in a bounded domain of interest without imposing boundary constraints can lead to a lack of unique solutions thus causing the failure of PINNs.In light of this,this paper proposes a novel and effective data generationbased operator learning method for solving PDEs on unbounded domains.The key idea behind this method is to generate high-quality training data.Specifically,we construct a family of approximate analytical solutions to the target PDE based on its initial condition and source term.Then,using these constructed data comprising exact solutions,initial conditions,and source terms,we train an operator learning model called MIONet,which is capable of handling multiple inputs,to learn the mapping from the initial condition and source term to the PDE solution on a bounded domain of interest.Finally,we utilize the generalization ability of this model to predict the solution of the target PDE.The effectiveness of this method is exemplified by solving the wave equation and the Schr¨odinger equation defined on unbounded domains.More importantly,the proposed method can deal with nonlinear problems,which has been demonstrated by solving Burgers’equation and Korteweg-de Vries(KdV)equation.The code is available at https://github.com/ZJLAB-AMMI/DGOL.
基金supported by the Australian Research Council(Grant No.IC190100020)the Australian Research Council Indus〓〓try Fellowship(Grant No.IE230100435)the National Natural Science Foundation of China(Grant Nos.12032014 and T2488101)。
文摘The integration of physics-based modelling and data-driven artificial intelligence(AI)has emerged as a transformative paradigm in computational mechanics.This perspective reviews the development and current status of AI-empowered frameworks,including data-driven methods,physics-informed neural networks,and neural operators.While these approaches have demonstrated significant promise,challenges remain in terms of robustness,generalisation,and computational efficiency.We delineate four promising research directions:(1)Modular neural architectures inspired by traditional computational mechanics,(2)physics informed neural operators for resolution-invariant operator learning,(3)intelligent frameworks for multiphysics and multiscale biomechanics problems,and(4)structural optimisation strategies based on physics constraints and reinforcement learning.These directions represent a shift toward foundational frameworks that combine the strengths of physics and data,opening new avenues for the modelling,simulation,and optimisation of complex physical systems.
基金supported by the National Natural Science Foundation of China(Grant No.12172161)the NSFC Basic Science Center Program(Grant No.11988102)+1 种基金the Shenzhen Science and Technology Program(Grant No.KQTD20180411143441009)supported by Center for Computational Science and Engineering of Southern University of Science and Technology.
文摘Transformer has achieved remarkable results in various fields,including its application in modeling dynamic systems governed by partial differential equations.However,transformer still face challenges in achieving long-term stable predictions for three-dimensional turbulence.In this paper,we propose an implicit factorized transformer(IFactFormer)model,which enables stable training at greater depths through implicit iteration over factorized attention.IFactFormer is applied to large eddy simulation of three-dimensional homogeneous isotropic turbulence(HIT),and is shown to be more accurate than the FactFormer,Fourier neural operator,and dynamic Smagorinsky model(DSM)in the prediction of the velocity spectra,probability density functions of velocity increments and vorticity,temporal evolutions of velocity and vorticity root-mean-square value and isosurface of the normalized vorticity.IFactFormer can achieve long-term stable predictions of a series of turbulence statistics in HIT.Fur-thermore,IFactFormer showcases superior computational efficiency compared to the conventional DSM in large eddy simulation.
基金funding from the project“SPEED”(03XP0585)funded by the German Federal Ministry of ResearchTech-nology and Space(BMFTR)and the project“ADMirABLE”(03ETE053E)funded by the German Federal Ministry for Economic Affairs and Energy(BMWE)support of Shell Research UK Ltd.for the Ph.D.studentship of Amir Ali Panahi and the EPSRC Faraday Institution Multi-Scale Modelling Project(FIRG084).
文摘Digital twins of lithium-ion batteries are increasingly used to enable predictive monitoring,control,and design at system scale.Increasing their capabilities involves improving their physical fidelity while maintaining sub-millisecond computational speed.In this work,we introduce machine learning surrogates that learn physical dynamics.Specifically,we benchmark three operator-learning surrogates for the Single Particle Model(SPM):Deep Operator Networks(DeepONets),Fourier Neural Operators(FNOs)and a newly proposed parameter-embedded Fourier Neural Operator(PE-FNO),which conditions each spectral layer on particle radius and solid-phase diffusivity.We extend the comparison to classical machine-learning baselines by including U-Nets.Models are trained on simulated trajectories spanning four current families(constant,triangular,pulse-train,and Gaussian-random-field)and a full range of State-of-Charge(SOC)(0%to 100%).DeepONet accurately replicates constant-current behaviour but struggles with more dynamic loads.The basic FNO maintains mesh invariance and keeps concentration errors below 1%,with voltage mean-absolute errors under 1.7mV across all load types.Introducing parameter embedding marginally increases error but enables generalisation to varying radii and diffusivities.PE-FNO executes approximately 200 times faster than a 16-thread SPM solver.Consequently,PE-FNO’s capabilities in inverse tasks are explored in a parameter estimation task with Bayesian optimisation,recovering anode and cathode diffusivities with 1.14%and 8.4%mean absolute percentage error,respectively,and 0.5918 percentage points higher error in comparison with classical methods.These results pave the way for neural operators to meet the accuracy,speed and parametric flexibility demands of real-time battery management,design-of-experiments and large-scale inference.PE-FNO outperforms conventional neural surrogates,offering a practical path towards high-speed and high-fidelity electrochemical digital twins.
基金supported by the National Natural Science Foundation of China(Grant Nos.61075110,60774077,61375086)the National Basic Research Program of China("973" Project)(Grant No.2012CB720000)+3 种基金the National High-Tech Research and Development Program of China("863" Project)(Grant No.2007AA04Z226)the Beijing Natural Science Foundation(Grant No.4102011)the Key Project of S&T Plan of Beijing Municipal Commission of Education(Grant Nos.KM2008-10005016,KZ201210005001)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20101103110007)
文摘Operant conditioning is one of the fundamental mechanisms of animal learning, which suggests that the behavior of all animals, from protists to humans, is guided by its consequences. We present a new stochastic learning automaton called a Skinner au- tomaton that is a psychological model for formalizing the theory of operant conditioning. We identify animal operant learning with a thermodynamic process, and derive a so-called Skinner algorithm from Monte Carlo method as well as Metropolis algo- rithm and simulated annealing. Under certain conditions, we prove that the Skinner automaton is expedient, 6-optimal, optimal, and that the operant probabilities converge to the set of stable roots with probability of 1. The Skinner automaton enables ma- chines to autonomously learn in an animal-like way.
