An Algebraic Framework for Stock & Flow Diagrams and Dynamical Systems Using Category Theory

• URL: http://arxiv.org/abs/2211.01290v1
• Date: Tue, 1 Nov 2022 16:15:54 GMT
• Title: An Algebraic Framework for Stock & Flow Diagrams and Dynamical Systems Using Category Theory
• Authors: Xiaoyan Li, John Baez, Sophie Libkind, Eric Redekopp, Long Pham, Nathaniel D Osgood
• Abstract summary: In this chapter, rather than focusing on the underlying mathematics, we informally use communicable disease examples created by the implemented software of StockFlow.jl. We first characterize categorical stock & flow diagrams, and note the clear separation between the syntax of stock & flow diagrams and their semantics. Applying category theory, these frameworks can build large diagrams from smaller ones in a modular fashion.
• Score: 2.030738254233949
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Mathematical modeling of infectious disease at scale is important, but challenging. Some of these difficulties can be alleviated by an approach that takes diagrams seriously as mathematical formalisms in their own right. Stock & flow diagrams are widely used as broadly accessible building blocks for infectious disease modeling. In this chapter, rather than focusing on the underlying mathematics, we informally use communicable disease examples created by the implemented software of StockFlow.jl to explain the basics, characteristics, and benefits of the categorical framework. We first characterize categorical stock & flow diagrams, and note the clear separation between the syntax of stock & flow diagrams and their semantics, demonstrating three examples of semantics already implemented in the software: ODEs, causal loop diagrams, and system structure diagrams. We then establish composition and stratification frameworks and examples for stock & flow diagrams. Applying category theory, these frameworks can build large diagrams from smaller ones in a modular fashion. Finally, we introduce the open-source ModelCollab software for diagram-centric real-time collaborative modeling. Using the graphical user interface, this web-based software allows the user to undertake the types of categorically-rooted operations discussed above, but without any knowledge of their categorical foundations.

Related papers

• DiagrammaticLearning: A Graphical Language for Compositional Training Regimes [39.26058251942536]
  A learning diagram compiles to a unique loss function on which component models are trained. We show that a number of popular learning setups can be depicted as learning diagrams.
  arXiv  Detail & Related papers  (2025-01-02T19:44:36Z)
• Quantifying analogy of concepts via ologs and wiring diagrams [0.0]
  We build on the theory of logs (ologs) created by Spivak and Kent, and define a notion of wiring diagrams. In this article, a wiring diagram is a finite directed labelled graph. The labels correspond to types in an olog; they can also be interpreted as readings of sensors in an autonomous system.
  arXiv  Detail & Related papers  (2024-02-01T21:15:55Z)
• State of the Art and Potentialities of Graph-level Learning [54.68482109186052]
  Graph-level learning has been applied to many tasks including comparison, regression, classification, and more. Traditional approaches to learning a set of graphs rely on hand-crafted features, such as substructures. Deep learning has helped graph-level learning adapt to the growing scale of graphs by extracting features automatically and encoding graphs into low-dimensional representations.
  arXiv  Detail & Related papers  (2023-01-14T09:15:49Z)
• Explanation Graph Generation via Pre-trained Language Models: An Empirical Study with Contrastive Learning [84.35102534158621]
  We study pre-trained language models that generate explanation graphs in an end-to-end manner. We propose simple yet effective ways of graph perturbations via node and edge edit operations. Our methods lead to significant improvements in both structural and semantic accuracy of explanation graphs.
  arXiv  Detail & Related papers  (2022-04-11T00:58:27Z)
• Classic Graph Structural Features Outperform Factorization-Based Graph Embedding Methods on Community Labeling [8.931361895613646]
  Graph representation learning (also called graph embeddings) is a popular technique for incorporating network structure into machine learning models. We provide an empirical and theoretical analysis for the performance of a class of embeddings on the common task of pairwise community labeling. We prove that popular low-dimensional factorization methods either cannot produce community structure, or can only produce unstable" communities.
  arXiv  Detail & Related papers  (2022-01-20T22:43:37Z)
• Model-Agnostic Graph Regularization for Few-Shot Learning [60.64531995451357]
  We present a comprehensive study on graph embedded few-shot learning. We introduce a graph regularization approach that allows a deeper understanding of the impact of incorporating graph information between labels. Our approach improves the performance of strong base learners by up to 2% on Mini-ImageNet and 6.7% on ImageNet-FS.
  arXiv  Detail & Related papers  (2021-02-14T05:28:13Z)
• CommPOOL: An Interpretable Graph Pooling Framework for Hierarchical Graph Representation Learning [74.90535111881358]
  We propose a new interpretable graph pooling framework - CommPOOL. It can capture and preserve the hierarchical community structure of graphs in the graph representation learning process. CommPOOL is a general and flexible framework for hierarchical graph representation learning.
  arXiv  Detail & Related papers  (2020-12-10T21:14:18Z)
• Structural Landmarking and Interaction Modelling: on Resolution Dilemmas in Graph Classification [50.83222170524406]
  We study the intrinsic difficulty in graph classification under the unified concept of resolution dilemmas'' We propose SLIM'', an inductive neural network model for Structural Landmarking and Interaction Modelling.
  arXiv  Detail & Related papers  (2020-06-29T01:01:42Z)
• Non-Parametric Graph Learning for Bayesian Graph Neural Networks [35.88239188555398]
  We propose a novel non-parametric graph model for constructing the posterior distribution of graph adjacency matrices. We demonstrate the advantages of this model in three different problem settings: node classification, link prediction and recommendation.
  arXiv  Detail & Related papers  (2020-06-23T21:10:55Z)
• Automated Diagram Generation to Build Understanding and Usability [0.0]
  Causal loop and stock and flow diagrams are broadly used in System Dynamics because they help organize relationships and convey meaning. This paper demonstrates how that information can be clearly presented in an automatically generated causal loop diagram.
  arXiv  Detail & Related papers  (2020-05-27T22:32:16Z)
• LogicalFactChecker: Leveraging Logical Operations for Fact Checking with Graph Module Network [111.24773949467567]
  We propose LogicalFactChecker, a neural network approach capable of leveraging logical operations for fact checking. It achieves the state-of-the-art performance on TABFACT, a large-scale, benchmark dataset.
  arXiv  Detail & Related papers  (2020-04-28T17:04:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.