This paper presents a highly efficient implicit unified gas-kinetic particle(IUGKP)method for obtaining steady-state solutions of multi-scale phonon transport.The method adapts and reinterprets the integral solution o...This paper presents a highly efficient implicit unified gas-kinetic particle(IUGKP)method for obtaining steady-state solutions of multi-scale phonon transport.The method adapts and reinterprets the integral solution of the Bhatnagar-Gross-Krook(BGK)equation for time-independent solutions.The distribution function at a given point is determined solely by the surrounding equilibrium states,where the corresponding macroscopic quantities are computed through a weighted sum of equilibrium distribution functions from neighboring spatial positions.From a particle perspective,changes in macroscopic quantities within a cell result from particle transport across cell interfaces.These particles are sampled according to the equilibrium state of their original cells,accounting for their mean free path as the traveling distance.The IUGKP method evolves the solution according to the physical relaxation time scale,achieving high efficiency in large Knudsen number regimes.To accelerate convergence for small Knudsen numbers,an inexact Newton iteration method is implemented,incorporating macroscopic equations for convergence acceleration in the near-diffusive limit.The method also addresses spatial-temporal inconsistency caused by relaxation time variations in physical space through the null-collision concept.Numerical tests demonstrate the method’s excellent performance in accelerating multi-scale phonon transport solutions,achieving speedups of one to two orders of magnitude.The IUGKP method proves to be an efficient and accurate computational tool for simulating multiscale non-equilibrium heat transfer,offering significant advantages over traditional methods in both numerical performance and physical applicability.展开更多
当我们回顾计算机发展的早期阶段时,一些熟悉的名字会浮现出来,其中包括冯·诺依曼(John von Neumann)、梅特罗波利斯(Nicholas Metropolis)和费曼(Richard Feynman)。但他们并非孤独的先驱者——他们是一个更庞大群体的一部分。这...当我们回顾计算机发展的早期阶段时,一些熟悉的名字会浮现出来,其中包括冯·诺依曼(John von Neumann)、梅特罗波利斯(Nicholas Metropolis)和费曼(Richard Feynman)。但他们并非孤独的先驱者——他们是一个更庞大群体的一部分。这个群体先使用机械计算机,随后使用电子计算机,完成了此前从未实现的计算。这些人(其中包括许多女性)是最早的科学程序员和计算科学家。她们精通早期计算设备复杂而繁琐的操作,往往拥有数学或科学领域的学位,是科研工作中不可或缺的一部分。然而,她们所做出的基础性贡献,却大多被遗忘了。展开更多
The precise modeling of strong nonlinear transient evolution in nonlinear dynamical systems,including soliton evolution,remains a long-term challenge.Deep learning models with powerful nonlinear fitting capabilities h...The precise modeling of strong nonlinear transient evolution in nonlinear dynamical systems,including soliton evolution,remains a long-term challenge.Deep learning models with powerful nonlinear fitting capabilities have become efficient tools for physical system modeling.However,existing initialization methods rely on statistical distribution assumptions and lack constraints from physical mechanisms,which easily lead to suboptimal solutions and severely limit model prediction accuracy and generalization.Based on the energy minimization principle of physical systems,this work proposes energy-based initialization(EBI).This method requires only prior structural knowledge of the physical system as input,without experimental data or architecture customization,to guide initial weights to align with the intrinsic dynamical structure of physical systems.The work further derives an upper bound on the distance between EBI initial weights and optimal weights for downstream tasks,and proves that its performance advantage increases monotonically with the expansion of model parameter scale.Validation across four typical physical scenarios shows that EBI outperforms classical initialization schemes across all metrics,while initialization for a model with 4.7 million parameters takes less than 5 minutes.This work fills the gap of specialized initialization methods in AI for physics,provides efficient support for tasks such as transient prediction of optical fiber laser and inverse sensing of laser structures,and is expected to open new directions for interdisciplinary research between artificial intelligence and physics.展开更多
This study presents a unified framework for analyzing electric circuits and Josephson junctions using a fractional action integral that incorporates memory effects and nonlocal behavior.Unlike classical integer-order ...This study presents a unified framework for analyzing electric circuits and Josephson junctions using a fractional action integral that incorporates memory effects and nonlocal behavior.Unlike classical integer-order models,the method extends the action principle to fractional orders,leading to fractional Euler-Lagrange equations that better describe currents,voltages,and phase evolution.It is particularly effective for Josephson junctions,where tunneling currents and phase dynamics show long-term correlations and dissipation.By including fractional-order elements,the framework captures anomalous damping,power-law relaxation,and persistent memory effects in complex circuits.Using a dissipative fractional standard map,the study investigates chaos and the influence of memory on system stability.Numerical results reveal strong sensitivity to fractional parameters,including bifurcations and chaotic attractors.These findings link the classical circuit theory with fractional dynamics,offering new insights for superconducting electronics and the design of nonlinear systems.展开更多
The year 2025 marked the passing of two towering figures of twentieth-century mathematical physics,Rodney Baxter and Chen-Ning Yang.Yang reshaped modern physics through the introduction of non-abelian gauge theory and...The year 2025 marked the passing of two towering figures of twentieth-century mathematical physics,Rodney Baxter and Chen-Ning Yang.Yang reshaped modern physics through the introduction of non-abelian gauge theory and,independently,through the consistency conditions that later became known as the Yang-Baxter equation.Baxter transformed those conditions into a systematic theory of exact solvability in statistical mechanics and quantum integrable systems.This article is written in memory of Baxter and Yang,whose work revealed how local consistency principles generate global mathematical structure.We review the Yang-Mills formulation of gauge theory,its mass obstruction and resolution via symmetry breaking,and the geometric framework it engendered,including instantons,Donaldson-Floer theory,magnetic monopoles,and Hitchin systems.In parallel,we trace the emergence of the Yang-Baxter equation from factorised scattering to solvable lattice models,quantum groups,and Chern-Simons theory.Rather than presenting two separate narratives,gauge theory and integrability are presented as complementary manifestations of a shared coherence principle-an ongoing journey from gauge symmetry toward mathematical unity.展开更多
Physics informed neural networks(PINNs)are a deep learning approach designed to solve partial differential equations(PDEs).Accurately learning the initial conditions is crucial when employing PINNs to solve PDEs.Howev...Physics informed neural networks(PINNs)are a deep learning approach designed to solve partial differential equations(PDEs).Accurately learning the initial conditions is crucial when employing PINNs to solve PDEs.However,simply adjusting weights and imposing hard constraints may not always lead to better learning of the initial conditions;sometimes it even makes it difficult for the neural networks to converge.To enhance the accuracy of PINNs in learning the initial conditions,this paper proposes a novel strategy named causally enhanced initial conditions(CEICs).This strategy works by embedding a new loss in the loss function:the loss is constructed by the derivative of the initial condition and the derivative of the neural network at the initial condition.Furthermore,to respect the causality in learning the derivative,a novel causality coefficient is introduced for the training when selecting multiple derivatives.Additionally,because CEICs can provide more accurate pseudo-labels in the first subdomain,they are compatible with the temporal-marching strategy.Experimental results demonstrate that CEICs outperform hard constraints and improve the overall accuracy of pre-training PINNs.For the 1D-Korteweg–de Vries,reaction and convection equations,the CEIC method proposed in this paper reduces the relative error by at least 60%compared to the previous methods.展开更多
基金supported by the National Key R&D Program of China(Grant No.2022YFA1004500)the National Science Foundation of China(Grant Nos.12172316,92371107,12302378,92371201,and 52506078)+1 种基金Hong Kong research grant council(Grant Nos.16301222 and 16208324)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2025SYS-SYSZD-070)。
摘要This paper presents a highly efficient implicit unified gas-kinetic particle(IUGKP)method for obtaining steady-state solutions of multi-scale phonon transport.The method adapts and reinterprets the integral solution of the Bhatnagar-Gross-Krook(BGK)equation for time-independent solutions.The distribution function at a given point is determined solely by the surrounding equilibrium states,where the corresponding macroscopic quantities are computed through a weighted sum of equilibrium distribution functions from neighboring spatial positions.From a particle perspective,changes in macroscopic quantities within a cell result from particle transport across cell interfaces.These particles are sampled according to the equilibrium state of their original cells,accounting for their mean free path as the traveling distance.The IUGKP method evolves the solution according to the physical relaxation time scale,achieving high efficiency in large Knudsen number regimes.To accelerate convergence for small Knudsen numbers,an inexact Newton iteration method is implemented,incorporating macroscopic equations for convergence acceleration in the near-diffusive limit.The method also addresses spatial-temporal inconsistency caused by relaxation time variations in physical space through the null-collision concept.Numerical tests demonstrate the method’s excellent performance in accelerating multi-scale phonon transport solutions,achieving speedups of one to two orders of magnitude.The IUGKP method proves to be an efficient and accurate computational tool for simulating multiscale non-equilibrium heat transfer,offering significant advantages over traditional methods in both numerical performance and physical applicability.
摘要当我们回顾计算机发展的早期阶段时,一些熟悉的名字会浮现出来,其中包括冯·诺依曼(John von Neumann)、梅特罗波利斯(Nicholas Metropolis)和费曼(Richard Feynman)。但他们并非孤独的先驱者——他们是一个更庞大群体的一部分。这个群体先使用机械计算机,随后使用电子计算机,完成了此前从未实现的计算。这些人(其中包括许多女性)是最早的科学程序员和计算科学家。她们精通早期计算设备复杂而繁琐的操作,往往拥有数学或科学领域的学位,是科研工作中不可或缺的一部分。然而,她们所做出的基础性贡献,却大多被遗忘了。
基金supported by the Fundamental Research Funds for the Beijing University of Posts and Telecommunications(Grant No.2025JCTP01)the National Key Research and Development Program of China(Grant No.2022YFB4601101)the National Natural Science Foundation of China(Grant No.12261131495).
摘要The precise modeling of strong nonlinear transient evolution in nonlinear dynamical systems,including soliton evolution,remains a long-term challenge.Deep learning models with powerful nonlinear fitting capabilities have become efficient tools for physical system modeling.However,existing initialization methods rely on statistical distribution assumptions and lack constraints from physical mechanisms,which easily lead to suboptimal solutions and severely limit model prediction accuracy and generalization.Based on the energy minimization principle of physical systems,this work proposes energy-based initialization(EBI).This method requires only prior structural knowledge of the physical system as input,without experimental data or architecture customization,to guide initial weights to align with the intrinsic dynamical structure of physical systems.The work further derives an upper bound on the distance between EBI initial weights and optimal weights for downstream tasks,and proves that its performance advantage increases monotonically with the expansion of model parameter scale.Validation across four typical physical scenarios shows that EBI outperforms classical initialization schemes across all metrics,while initialization for a model with 4.7 million parameters takes less than 5 minutes.This work fills the gap of specialized initialization methods in AI for physics,provides efficient support for tasks such as transient prediction of optical fiber laser and inverse sensing of laser structures,and is expected to open new directions for interdisciplinary research between artificial intelligence and physics.
基金supported by the Ministry of Education,Youth and Sport of the Czech Republic as a part of the Quantum Engineering and Nanotechnology project QUEENTEC under Grant No.reg.nr.CZ.02.01.01/00/22008/0004649 from Chiang Mai University.
摘要This study presents a unified framework for analyzing electric circuits and Josephson junctions using a fractional action integral that incorporates memory effects and nonlocal behavior.Unlike classical integer-order models,the method extends the action principle to fractional orders,leading to fractional Euler-Lagrange equations that better describe currents,voltages,and phase evolution.It is particularly effective for Josephson junctions,where tunneling currents and phase dynamics show long-term correlations and dissipation.By including fractional-order elements,the framework captures anomalous damping,power-law relaxation,and persistent memory effects in complex circuits.Using a dissipative fractional standard map,the study investigates chaos and the influence of memory on system stability.Numerical results reveal strong sensitivity to fractional parameters,including bifurcations and chaotic attractors.These findings link the classical circuit theory with fractional dynamics,offering new insights for superconducting electronics and the design of nonlinear systems.
摘要The year 2025 marked the passing of two towering figures of twentieth-century mathematical physics,Rodney Baxter and Chen-Ning Yang.Yang reshaped modern physics through the introduction of non-abelian gauge theory and,independently,through the consistency conditions that later became known as the Yang-Baxter equation.Baxter transformed those conditions into a systematic theory of exact solvability in statistical mechanics and quantum integrable systems.This article is written in memory of Baxter and Yang,whose work revealed how local consistency principles generate global mathematical structure.We review the Yang-Mills formulation of gauge theory,its mass obstruction and resolution via symmetry breaking,and the geometric framework it engendered,including instantons,Donaldson-Floer theory,magnetic monopoles,and Hitchin systems.In parallel,we trace the emergence of the Yang-Baxter equation from factorised scattering to solvable lattice models,quantum groups,and Chern-Simons theory.Rather than presenting two separate narratives,gauge theory and integrability are presented as complementary manifestations of a shared coherence principle-an ongoing journey from gauge symmetry toward mathematical unity.
基金supported by the National Natural Science Foundation of China(Grant Nos.1217211 and 12372244).
摘要Physics informed neural networks(PINNs)are a deep learning approach designed to solve partial differential equations(PDEs).Accurately learning the initial conditions is crucial when employing PINNs to solve PDEs.However,simply adjusting weights and imposing hard constraints may not always lead to better learning of the initial conditions;sometimes it even makes it difficult for the neural networks to converge.To enhance the accuracy of PINNs in learning the initial conditions,this paper proposes a novel strategy named causally enhanced initial conditions(CEICs).This strategy works by embedding a new loss in the loss function:the loss is constructed by the derivative of the initial condition and the derivative of the neural network at the initial condition.Furthermore,to respect the causality in learning the derivative,a novel causality coefficient is introduced for the training when selecting multiple derivatives.Additionally,because CEICs can provide more accurate pseudo-labels in the first subdomain,they are compatible with the temporal-marching strategy.Experimental results demonstrate that CEICs outperform hard constraints and improve the overall accuracy of pre-training PINNs.For the 1D-Korteweg–de Vries,reaction and convection equations,the CEIC method proposed in this paper reduces the relative error by at least 60%compared to the previous methods.