The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensiona...The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.展开更多
This paper proposes a novel approach to use artificial intelligence(Al),particularly large language models(LLMs)and other foundation models(FMs)in an educational environment.It emphasizes the integration of teams of t...This paper proposes a novel approach to use artificial intelligence(Al),particularly large language models(LLMs)and other foundation models(FMs)in an educational environment.It emphasizes the integration of teams of teachable and self-learning LLMs agents that use neuro-symbolic cognitive architecture(NSCA)to provide dynamic personalized support to learners and educators within self-improving adaptive instructional systems(SIAIS).These systems host these agents and support dynamic sessions of engagement workflow.We have developed the never ending open learning adaptive framework(NEOLAF),an LLM-based neuro-symbolic architecture for self-learning AI agents,and the open learning adaptive framework(OLAF),the underlying platform to host the agents,manage agent sessions,and support agent workflows and integration.The NEOLAF and OLAF serve as concrete examples to illustrate the advanced AI implementation approach.We also discuss our proof of concept testing of the NEOLAF agent to develop math problem-solving capabilities and the evaluation test for deployed interactive agent in the learning environment.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.62303289)Tianyuan Fund for Mathematics of the National Natural Science Foundation of China(Grant No.12426105)+3 种基金the Scientific and Technological Innovation Programs(STIP)of Higher Education Institutions in Shanxi(Grant No.2024L022)Fundamental Research Program of Shanxi Province(Grant Nos.202403021222001 and 202203021222003)the“Wen Ying Young Scholars”Talent Project of Shanxi University(Grant Nos.138541088,138541090,and 138541127)Funded by Open Foundation of Hubei Key Laboratory of Applied Mathematics(Hubei University)(Grant No.HBAM202401).
文摘The(3+1)-dimensional Boiti-Leon-Manna-Pempinelli(BLMP)equation serves as a crucial nonlinear evolution equation in mathematical physics,capable of characterizing complex nonlinear dynamic phenomena in three-dimensional space and one-dimensional time.With broad applications spanning fluid dynamics,shallow water waves,plasma physics,and condensed matter physics,the investigation of its solutions holds significant importance.Traditional analytical methods face limitations due to their dependence on bilinear forms.To overcome this constraint,this letter proposes a novel multi-modal neurosymbolic reasoning intelligent algorithm(MMNRIA)that achieves 100%accurate solutions for nonlinear partial differential equations without requiring bilinear transformations.By synergistically integrating neural networks with symbolic computation,this approach establishes a new paradigm for universal analytical solutions of nonlinear partial differential equations.As a practical demonstration,we successfully derive several exact analytical solutions for the(3+1)-dimensional BLMP equation using MMNRIA.These solutions provide a powerful theoretical framework for studying intricate wave phenomena governed by nonlinearity and dispersion effects in three-dimensional physical space.
文摘This paper proposes a novel approach to use artificial intelligence(Al),particularly large language models(LLMs)and other foundation models(FMs)in an educational environment.It emphasizes the integration of teams of teachable and self-learning LLMs agents that use neuro-symbolic cognitive architecture(NSCA)to provide dynamic personalized support to learners and educators within self-improving adaptive instructional systems(SIAIS).These systems host these agents and support dynamic sessions of engagement workflow.We have developed the never ending open learning adaptive framework(NEOLAF),an LLM-based neuro-symbolic architecture for self-learning AI agents,and the open learning adaptive framework(OLAF),the underlying platform to host the agents,manage agent sessions,and support agent workflows and integration.The NEOLAF and OLAF serve as concrete examples to illustrate the advanced AI implementation approach.We also discuss our proof of concept testing of the NEOLAF agent to develop math problem-solving capabilities and the evaluation test for deployed interactive agent in the learning environment.
