九州大学教育改革シンポジウム2017 ポスターセッション

1. any
flow grad curl harmonic
ξ = u + ×v + h
curl harmonic
grad
-div=grad*
curl
curl*
any flow grad
on the Graph500 Ranking of Supercomputers with
38621.4 GE/ s on Scale 40
on the 13th Graph500 list published at the International
for High Performance Computing, Networking, Storage, and Analysis
(SC’16), November 15, 2016.
Congratulations from the Graph500 Executive Committee
No.1
RIKEN Advanced Institute for Computational
Science (AICS)’s K computer
is ranked
Tsunami Evacuation Planning via Network Flow
and Deep Learning Approaches
Hierarchical Data Analysis and Optimization System
• Three hierarchical analysis layers according to
both of the computation time that we need to
solve and the data size of the optimization
problem
Akira Tanaka1, Nozomi Hata1 and Katsuki Fujisawa2
1Graduate School of Mathematics, Kyushu University
2Institute of Mathematics for Industry, Kyushu University
Background
Universally
• Minimizes the evacuation time Θ
• Maximizes the cumulative number of
evacuees at an arbitrary time until Θ
• LQF is a practical extension of UQF
and has a polynomial-time algorithm
• We can utilize the LQF to apply
the maximum-flow algorithm to the
time-expanded network
Quickest
Previous Works sinks without capacity
(higher ground)
West-Yodogawa High School
capacity : 4273
A municipal housing
capacity : 77
sinks with capacity
(shelter)
Original Flow = Gradient Flow + Cyclic Flow
a roundabout path
to the shelter
the shortest path
to the shelter
Shelter
Hodge decomposition
EvacuationCompletion(%)
Time
• #nodes : 2933
• #edges : 8924
• #evacuees : 50000 ~ 80000
• the total amount of shelters : 36549
• #sinks : 86
• with capacity : 36
• without capacity : 50
Graph500 Benchmark (http://graph500.org)
• Graph500 are new graph search based
benchmarks for ranking supercomputers
• Our project team has been a winner of the
8th,10th,11th,12th,13th and 14th Graph500 benchmark
Input
Evacuation Completion Time
• We can generate exact training data for
Deep Learning(DL) by utilizing LQF.
• Almost all errors* are less than 3 minutes.
• We can finally predict the evacuation
completion time of many flows at once,
which leads to evaluate the danger level
of each population distribution.
Note:
error* = | LQF - DL | (seconds)
Output
Network
4 Convolutional followed by max
pooling, and 2 fully-connected [2]
Results
Graph data for Osaka City Lexicographical Quickest Flow(LQF)[1]
H(55)×W(75)×C(5) = 20,625
Training = 43,200 Test, Validation = 5,400
Direction
Time
Proposed Algorithms and Experimental Analyses
Deep Learning Approach for Predicting
Evacuation Completion Time
[1] N. Kamiyama . Studies on Quickest Flow Problems in Dynamic Networks and Arborescence Problems in Directed Graphs -A Theoretical Approach to Evacuation Planning in Urban Areas- , 2009
[2] Yi Sun, Xiaogang Wang, and Xiaoou Tang. Deep Convolutional Network Cascade for Facial Point Detection, In prop. CVPR, 2013.
[3] Xiaoye Jiang, Lek-Heng Lim, Yuan Yao, and Yinyu Ye. Statistical ranking and combinatorial Hodge theory, Math. Program., Ser. B (2011) 127:203-244
• An "optimal" solution of the evacuation
can be obtained by using LQF with
respect to the evacuation time
• Some people need to take a detour for
evacuation
• These congestions are caused by
• the capacities of the shelters
• the widths of roads
• An evacuation plan without congestion
is better for all evacuees
• We can decompose any flow to
gradient flow and cyclic flow
(curl + harmonic) and detect
roundabout movements by using
Hodge decomposition algorithm [3],
which is useful for improving the quality
of the evacuation