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Knowledge Graph Representation Learning using Ordinary Differential Equations

Mojtaba Nayyeri, Chengjin Xu, Franca Hoffmann, Mirza Mohtashim Alam, Jens Lehmann, Sahar Vahdati
2021 Proceedings of the 2021 Conference on Empirical Methods in Natural Language Processing   unpublished
To address this problem, we propose a neuro differential KGE that embeds nodes of a KG on the trajectories of Ordinary Differential Equations (ODEs).  ...  Knowledge Graph Embeddings (KGEs) have shown promising performance on link prediction tasks by mapping the entities and relations from a knowledge graph into a geometric space.  ...  Conclusion We presented FieldE -the first representation learning model for knowledge graphs based on Ordinary Differential Equations.  ... 
doi:10.18653/v1/2021.emnlp-main.750 fatcat:i3trqzrt3fdltfimq4bqkxok2e

Temporal Knowledge Graph Forecasting with Neural ODE [article]

Zhen Han, Zifeng Ding, Yunpu Ma, Yujia Gu, Volker Tresp
2021 arXiv   pre-print
Inspired by Neural Ordinary Differential Equation (NODE), we extend the idea of continuum-depth models to time-evolving multi-relational graph data, and propose a novel Temporal Knowledge Graph Forecasting  ...  Learning node representation on dynamically-evolving, multi-relational graph data has gained great research interest.  ...  We propose a multi-relational graph convolutional layer to capture structural dependencies on tKGs and learn continuous dynamic representations using graph neural ordinary differential equations.  ... 
arXiv:2101.05151v2 fatcat:etoszk2h2rcljbbfkwb23whmv4

Informed Machine Learning - A Taxonomy and Survey of Integrating Prior Knowledge into Learning Systems

Laura Vonrueden, Sebastian Mayer, Katharina Beckh, Bogdan Georgiev, Sven Giesselbach, Raoul Heese, Birgit Kirsch, Michal Walczak, Julius Pfrommer, Annika Pick, Rajkumar Ramamurthy, Jochen Garcke (+2 others)
2021 IEEE Transactions on Knowledge and Data Engineering  
Based on this taxonomy, we survey related research and describe how different knowledge representations such as algebraic equations, logic rules, or simulation results can be used in learning systems.  ...  It considers the source of knowledge, its representation, and its integration into the machine learning pipeline.  ...  Center for Machine Learning Rhine Ruhr (ML2R) which is funded by the Federal Ministry of Education and Research of Germany (grant no. 01|S18038B).  ... 
doi:10.1109/tkde.2021.3079836 fatcat:jbuzbl6vlzagxcnr52vkuqsj5a

Informed Machine Learning – A Taxonomy and Survey of Integrating Knowledge into Learning Systems [article]

Laura von Rueden, Sebastian Mayer, Katharina Beckh, Bogdan Georgiev, Sven Giesselbach, Raoul Heese, Birgit Kirsch, Julius Pfrommer, Annika Pick, Rajkumar Ramamurthy, Michal Walczak, Jochen Garcke, Christian Bauckhage, Jannis Schuecker
2020 arXiv   pre-print
Third, we survey related research and describe how different knowledge representations such as algebraic equations, logic rules, or simulation results can be used in learning systems.  ...  It considers the source of knowledge, its representation, and its integration into the machine learning pipeline.  ...  Center for Machine Learning Rhine Ruhr (ML2R) which is funded by the Federal Ministry of Education and Research of Germany (grant no. 01|S18038A).  ... 
arXiv:1903.12394v2 fatcat:57nj46tgpfeyfok55yfyyojxze

Motif Learning in Knowledge Graphs Using Trajectories Of Differential Equations [article]

Mojtaba Nayyeri, Chengjin Xu, Jens Lehmann, Sahar Vahdati
2020 arXiv   pre-print
To address this problem, we propose a neuro differential KGE that embeds nodes of a KG on the trajectories of Ordinary Differential Equations (ODEs).  ...  Knowledge Graph Embeddings (KGEs) have shown promising performance on link prediction tasks by mapping the entities and relations from a knowledge graph into a geometric space (usually a vector space).  ...  For a given Ordinary Differential Equation (ODE) Figure 2 : 2 The Architecture of FieldE Model. The input to FieldE model is a knowledge graph which is shown in the upper part.  ... 
arXiv:2010.06684v2 fatcat:iz4e5xxm6zbglfr6nlet73luvm

LEARNING DIFFERENTIAL EQUATIONS: A METASYNTHESIS OF QUALITATIVE RESEARCH

Aidayatey Azman, Zaleha Ismail
2017 Indonesian Journal of Educational Review  
In the last chapter, the researchers proposed using online learning as a new method of teaching. Keywords: metasynthesis, Differential Equations, teaching methodology, online learning, technology.  ...  This research explores the development of Differential Equations teaching methods from the year 2000 onwards. The methodology used in this paper is metasynthesis research.  ...  The keywords used to find the related papers are learning differential equations, differential equations and inquiry oriented differential equations.  ... 
doi:10.21009/ijer:01.01.06 fatcat:h3j6l53r4rcwhe7f65zdyvw67q

Using of the Application Programs for the Decision of Tasks on Physics

A. K. Salkeeva, A. S. Kusenova, K. B. Kopbalina, G. B. Turebaeva, A. Y. Davydova
2020 Asian Journal of Research in Computer Science  
This article shows methods for solving ordinary differential equations in the Mathcad package based on numerical methods.  ...  equation, and a graph is obtained.  ...  NUMERICAL METHODS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS (ODES) As you know, any physical phenomena are described by differential equations, so the solution of ordinary differential equations for  ... 
doi:10.9734/ajrcos/2020/v6i330161 fatcat:o7jkalmafbhd3miusqsavlheyq

Innovative Strategies for Learning and Teaching of Large Differential Equations Classes

Kuppalapalle Vajravelu
2018 IEJME-Mathematics Education  
Differential Equations I classes.  ...  Ordinary Differential Equations I, is one of the core courses for science and engineering majors. Practical problem solving in science and engineering programs require proficiency in mathematics.  ...  Effectively teaching differential equations establishes a strong base of knowledge from which all future learning of these concepts is supported.  ... 
doi:10.12973/iejme/2699 fatcat:lyzxtn7gnjft3a5zbpcmeqclky

Teaching of Ordinary Differential Equations Using the Assumptions of the PBL Method

Leandro Brito Santos, Paulo Henrique Farias Xavier, José Vicente Cardoso Santos, Renelson Ribeiro Sampaio
2020 International Journal of Engineering Pedagogy (iJEP)  
The study analyzes the effectiveness of Ordinary differential equations instruction given through this program using the specified methodology.  ...  solutions; at the same time, students experience diffi-culties when learning Ordinary differential equations and about their applications to real physical scenarios.  ...  He has worked in Paper-Teaching of Ordinary Differential Equations Using the Assumptions of the PBL Method http://www.i-jep.org Paper-Teaching of Ordinary Differential Equations Using the Assumptions  ... 
doi:10.3991/ijep.v10i3.12015 fatcat:jhnwc7cvcnaddk5r6rl545nali

NODIS: Neural Ordinary Differential Scene Understanding [article]

Cong Yuren, Hanno Ackermann, Wentong Liao, Michael Ying Yang, Bodo Rosenhahn
2020 arXiv   pre-print
In this work, we interpret that formulation as Ordinary Differential Equation (ODE).  ...  The proposed architecture performs scene graph inference by solving a neural variant of an ODE by end-to-end learning.  ...  Using this link, we propose to solve the labeling problem by means of neural ordinary differential equations.  ... 
arXiv:2001.04735v3 fatcat:cry67soiangltptjk324ctyali

Classroom Methodologies for Teaching and Learning Ordinary Differential Equations: A Systemic Literature Review and Bibliometric Analysis

Esperanza Lozada, Carolina Guerrero-Ortiz, Aníbal Coronel, Rigoberto Medina
2021 Mathematics  
In this paper, we develop a review of the research focused on the teaching and learning of ordinary differential equations with the following three purposes: to get an overview of the existing literature  ...  ordinary differential equations, present some topics to be addressed in the next years and define a starting point for researchers who are interested in developing research in this field.  ...  The authors of [4, 11] are interested in analyzing the different representations developed by students when learned ordinary differential equations using a computer algebra system as mediator.  ... 
doi:10.3390/math9070745 fatcat:e7syhsj2qvfxlf2au4a7lk6iyi

Data-driven discovery of free-form governing differential equations [article]

Steven Atkinson and Waad Subber and Liping Wang and Genghis Khan and Philippe Hawi and Roger Ghanem
2019 arXiv   pre-print
The key to our method is to learn differentiable models of the data that subsequently serve as inputs to a genetic programming algorithm in which graphs specify computation over arbitrary compositions  ...  We also demonstrate an active learning process to identify and remedy deficiencies in the proposed governing equations.  ...  Table 2 :Figure 5 : 25 Figure 5: From left to right: A slice in time of the ultrasound data, its GP function representation used exploring differential equations, the term u tt (x) evaluated on the function  ... 
arXiv:1910.05117v2 fatcat:frsuozma6jfrhbt3kdfi3tvwzm

High School Students' Language Related Struggles with Contextualized Differential Equations

Zakaria Ndemo
2019 International Journal of Applied Mathematics and Theoretical Physics  
investigate the kinds of such challenges and their impact on students' learning of differential equations.  ...  of differential equations.  ...  Chinamasa for his encouragement, Ms G Sunzuma, a mathematics educator for revising the manuscript and making useful suggestions.  ... 
doi:10.11648/j.ijamtp.20190501.13 fatcat:nnrs35uir5cldnftwfofvl3s2u

Perceptual Learning Modules in Mathematics: Enhancing Students' Pattern Recognition, Structure Extraction, and Fluency

Philip J. Kellman, Christine M. Massey, Ji Y. Son
2010 Topics in Cognitive Science  
In the MultiRep PLM, practice in matching function information across multiple representations improved students' abilities to generate correct graphs and equations from word problems.  ...  Learning in educational settings emphasizes declarative and procedural knowledge.  ...  Department of Education, Institute for Education Sciences, Cognition and Student Learning Program, through grant R305H060070 and from National Science Foundation grant REC-0231826 to PK and CM.  ... 
doi:10.1111/j.1756-8765.2009.01053.x pmid:25163790 fatcat:fevanuotercsrnzil3vetuaxua

Model inference for Ordinary Differential Equations by parametric polynomial kernel regression [article]

David K. E. Green, Filip Rindler
2019 arXiv   pre-print
Using numerical integration techniques, parametric representations of Ordinary Differential Equations can be learnt using Backpropagation and Stochastic Gradient Descent.  ...  This work introduces a parametric polynomial kernel method that can be used for inferring the future behaviour of Ordinary Differential Equation models, including chaotic dynamical systems, from observations  ...  Using numerical integration techniques, parametric representations of Ordinary Differential Equations can be learnt using Backpropagation and Stochastic Gradient Descent.  ... 
arXiv:1908.02105v1 fatcat:slereoipxfgipao4mfnve6emwe
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