diffusion convolution recurrent neural network for … · •non-euclidean spatial geometry...
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DIFFUSION CONVOLUTION RECURRENT NEURAL NETWORK FOR TRAFFIC FORECASTING
SCIENCE USE CASE 2
AUGUST 9, 2019
Tanwi Mallick and Prasanna BalaprakashATPESC 2019
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Traffic forecasting• Given• Historic traffic metrics {speed, flow, etc}• Road network distance and connectivity
• Predict • Future traffic metrics
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Large-scale machine (supervised) learning problem!
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Traffic data from Caltrans Performance Measurement System (PeMS)
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The data includes:• Timestamp• Loop IDs• District• Freeway name • Freeway direction• Total flow • Average speed
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Location data of Loop IDs
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Available data set for CaltransDistrict Total Stations
District 3 1247
District 4 3880
District 5 382
District 6 624
District 7 4856
District 8 2115
District 10 1189
District 11 1502
District 12 2539
Total 18334
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http://pems.dot.ca.gov/
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Available data set for Caltrans
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Total : 11, 160 detector stationsDuration: 1st Jan 2018 to 31st Dec 2018
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Network distance computation• OSRM local server (unlimited query)• Find the driving distance between two nearest loop IDs by querying
in OSRM server– Nearest neighbor using Euclidean distance (to speedup)
• OSRM gives shortest driving distance between two latitude and longitude
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Problem statement: Traffic prediction
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h(.)
X t - T’ + 1 X t X t + 1 X t + T
… …
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Challenges
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• Complex spatial dependency
• Non-stationary temporal dynamics
• Non-Euclidean spatial geometry
• Model each sensor independently fail to capture spatial correlation
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Forecasting for multiple loop detector
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• Transportation network as graph• V = Vertices (sensors)• E = Edges (roads)• A = Weighted adjacency matrix
(A function of the road network distance)
Capturing the road network in terms of graphs
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Diffusion convolution
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Out-degree In-degree
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Recurrent Neural Network
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Encoder decoder Framework of DCRNN
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Current time
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GRU cell
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𝑢𝑡 = 𝜎(𝑤'[ℎ*+,, 𝑥*])
𝑟𝑡 = 𝜎(𝑤2[ℎ*+,, 𝑥*])
𝑐* = 𝑡𝑎𝑛ℎ(𝑤6[𝑟*∗ ℎ*+,, 𝑥*])
ℎ* = 1 − 𝑢* ∗ ℎ*+, +𝑢𝑡 ∗ 𝑐*
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DCRNN cell
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𝑢𝑡 = 𝜎(𝑤'∗;[ℎ*+,, 𝑥*])
𝑟𝑡 = 𝜎(𝑤2∗;[ℎ*+,, 𝑥*])
𝑐* = 𝑡𝑎𝑛ℎ(𝑤6∗;[𝑟*∗ ℎ*+,, 𝑥*])
ℎ* = 1 − 𝑢* ∗ ℎ*+, +𝑢𝑡 ∗ 𝑐*
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Traffic forecasting using DCRNN
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Scaling DCRNN on HPC systems• Domain decomposition for large networks– Partition large graph into sub-graph– Run DCRNN for each sub-graph on a compute
node – Combine the results and forecast traffic
• Simultaneous execution of DCRNN
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Graph partitioning using Metis• 3 major phases– coarsening– initial partitioning– refinement
• Key advantage– millions of vertices in
few seconds
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Partitions on the map
Partition 1 Partition 2
Partition 4
Partition 8
Partition 3
Partition 7
Partition 5
Partition 6
Partition
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Simultaneous execution of DCRNN
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Data set
• Total stations: 11160• Divide the whole data
set in different number of partitions
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Number of partitions
Stations per partition (aprox)
2 5580
4 2790
8 1395
16 697
32 348
64 174
128 87
256 43
512 21
1024 11
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Forecasting accuracy
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Execution time
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DCRNN results
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Group: 1 Node: 247
Group: 2 Node: 247
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DCRNN results
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Group: 3 Node: 256
Group: 7 Node: 260
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Speed prediction
26Group: 5
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Speed prediction
27Group: 2
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Speed prediction
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Speed prediction
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Summary• DCRNN captures the spatial as well as
temporal dynamics well• DCRNN is scalable for large network without
performance degradation
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