Knowledge Assisted Visualization: Steady visualization of the dynamics in fluids using ε-machines

The visualization of unsteady scientific data is still a challenging problem. Most techniques rely on the animation of individual time-steps. In this paper we propose a steady visualization of the dynamics in fluids using @e-machines. @e-machines are a concept from computational mechanics and can be thought of as finite state machines that can be visualized as directed graphs. The nodes are the causal states of the process. Given a local past of a position, causal states comprise all the information needed to predict the future of this position. As causal states stem from information theory, it can be shown that they are the most compressed representation of local dynamics that still allows for this prediction. Edges in the graph indicate transition probabilities between causal states in successive time-steps. Hence, the visualization of the @e-machine graph provides a concise and highly compressed steady visualization of the system's dynamics that still allows for an in-depth examination. In this paper we describe the construction and visualization of @e-machines and how interaction mechanisms with the physical domain allow for a detailed analysis of data sets describing fluid dynamics.

[1]  Robert S. Laramee,et al.  The State of the Art , 2015 .

[2]  Gerik Scheuermann,et al.  The State of the Art in Flow Visualization: Partition-Based Techniques , 2008, SimVis.

[3]  Gerik Scheuermann,et al.  Eyelet particle tracing - steady visualization of unsteady flow , 2005 .

[4]  K. M. L. Suxena,et al.  Introduction to Statistical Theory , 1976 .

[5]  Gerik Scheuermann,et al.  Topology-based Methods in Visualization , 2007, Topology-based Methods in Visualization.

[6]  Hans Hagen,et al.  Topology-Based Visualization of Time-Dependent 2D Vector Fields , 2001, VisSym.

[7]  Mie Sato,et al.  A case study in selective visualization of unsteady 3D flow , 2002, IEEE Visualization, 2002. VIS 2002..

[8]  Robert J. Moorhead,et al.  Accelerated unsteady flow line integral convolution , 2005, IEEE Transactions on Visualization and Computer Graphics.

[9]  Robert S. Laramee,et al.  The State of the Art in Flow Visualisation: Feature Extraction and Tracking , 2003, Comput. Graph. Forum.

[10]  Hans-Peter Seidel,et al.  Feature Flow Fields , 2003, VisSym.

[11]  C. Moore,et al.  Automatic filters for the detection of coherent structure in spatiotemporal systems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Robert van Liere,et al.  Divide and Conquer Spot Noise , 1997 .

[13]  Hans J. W. Spoelder,et al.  Attribute-Based Feature Tracking , 1999 .

[14]  Hans-Peter Seidel,et al.  Eurographics/ Ieee-vgtc Symposium on Visualization (2006) Path Line Oriented Topology for Periodic 2d Time-dependent Vector Fields , 2022 .

[15]  James P. Crutchfield,et al.  Computational mechanics of cellular automata: an example , 1997 .

[16]  C. Shalizi,et al.  Causal architecture, complexity and self-organization in time series and cellular automata , 2001 .

[17]  Xavier Tricoche,et al.  Tracking of vector field singularities in unstructured 3D time-dependent datasets , 2004, IEEE Visualization 2004.

[18]  Joerg Meyer,et al.  Pathline predicates and unsteady flow structures , 2008, The Visual Computer.

[19]  Luca Bonaventura,et al.  The atmospheric general circulation model ECHAM 5. PART I: Model description , 2003 .

[20]  Hans Hagen,et al.  Efficient Computation and Visualization of Coherent Structures in Fluid Flow Applications , 2007, IEEE Transactions on Visualization and Computer Graphics.

[21]  William Ribarsky,et al.  Data Visualization ’99 , 1999, Eurographics.

[22]  Edward M. Reingold,et al.  Graph drawing by force‐directed placement , 1991, Softw. Pract. Exp..

[23]  Frits H. Post,et al.  Visualization of turbulent flow with particles , 1993, Proceedings Visualization '93.

[24]  James P. Crutchfield,et al.  Computational Mechanics: Pattern and Prediction, Structure and Simplicity , 1999, ArXiv.

[25]  Charles Hansen,et al.  The Visualization Handbook , 2011 .

[26]  Filip Sadlo,et al.  Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction , 2007, IEEE Transactions on Visualization and Computer Graphics.

[27]  Xavier Tricoche,et al.  Generalized Streak Lines: Analysis and Visualization of Boundary Induced Vortices , 2007, IEEE Transactions on Visualization and Computer Graphics.

[28]  Gerik Scheuermann,et al.  Multifield visualization using local statistical complexity , 2007, IEEE Transactions on Visualization and Computer Graphics.

[29]  Robert S. Laramee,et al.  The State of the Art in Flow Visualization: Dense and Texture‐Based Techniques , 2004, Comput. Graph. Forum.

[30]  Ronald Peikert,et al.  Vortex Tracking in Scale-Space , 2002, VisSym.

[31]  Min Chen,et al.  Data, Information, and Knowledge in Visualization , 2009, IEEE Computer Graphics and Applications.

[32]  Young,et al.  Inferring statistical complexity. , 1989, Physical review letters.

[33]  Xavier Tricoche,et al.  Automatic Detection and Visualization of Distinctive Structures in 3D Unsteady Multi‐fields , 2008, Comput. Graph. Forum.

[34]  Xin Wang,et al.  Tracking scalar features in unstructured data sets , 1998 .

[35]  Han-Wei Shen,et al.  Volume tracking using higher dimensional isosurfacing , 2003, IEEE Visualization, 2003. VIS 2003..