AI with Super-computed Data for Monte Carlo Earthquake Hazard Classification
Tsuyoshi Ichimura1,2, Kohei Fujita1,2, Takuma Yamaguchi1, Muneo Hori1,2, Maddegedara Lalith1,2 and Naonori Ueda3
1. Earthquake Research Institute & Department of Civil Engineering, The University of Tokyo 2. Advanced Institute for Computational Science, RIKENIntroduction & Objective

3. Center for Advanced Intelligence Project, RIKEN

Development of Supercomputing Method

Evaluation of earthquake damage scenarios (i.e., estimation of damage to citiesand buildings) required to mitigate from earthquakes
Knowledge of the distribution of shaking (i.e., earthquake hazard) at the groundlevel in cities with an area of 100km2 is required to improve damage scenarios• Soil at a depth of 100 m from the surface has a complex geometry that changes
every 10 m
• The ground shaking due to earthquakes becomes highly nonlinear• Local ground shaking varies significantly with local position [1]Target problem

Proposed solver (nominated as SC15 Gordon Bell Prize finalist [2])Solving preconditioning matrix• Implicit nonlinear wave simulation with low-ordered unstructured
finite elements• Much difficult than explicit time integration due to convergence of
iterative solver and global communication

CG loop

Discretized wave equation (solve for each of 6,000 time-steps)

Second ordered
tetrahedron

Matrix (components
Unknown vector
changes every time step) (0.1 trillion DOF order)

Groundshaking
Soft soil layers

<100m
<100m
1920m

Input wave

Distribution of earthquake
shaking at ground surface

1696m

Improvement of hazard maps in higher resolution considering uncertainty• Observing ground shaking is difficult at high spatial resolution (less than 50 m)• Simulations using 3D ground information useful for generating hazard map;
however, this requires a very large-scale analysis• Subsurface ground data cannot be measured and its uncertainty must be
quantified in the hazard maps
• Monte Carlo simulations suitable for considering uncertainty of data; however,this is impractical because it requires 102-3 repetitions of large-scale analyses
10,250 m × 9,250 m area ofCentral Tokyo provided byNational Digital Soil Map

3D ground information iscurrently being accumulated
for whole urban areas
O(10m)

Known vector

10,250 m

Super-computed ground motion data is classified into 20 levelsof severity for 50-m grid points inside an 8,350 m × 7,200 m
area of Central Tokyo (24,360 points).

Input:
elevation data(vector)

NeuralNetwork

Output: estimatedearthquake hazard
classification(1 scalar)

Softmax
Cross
Entropy

Case A
Environment for training• Pietra (SGI, Tesla P100 × 4, Intel E5-2690v4 × 2)
• Chainer (batch size=8000, optimizer=Adam)…construct complex neural networkby the combination of simple components# of iterations

Elevation at ground surfacemElevation of interface
between 1st and 2nd layermElevation of interface
between 2nd and 3rd layer

In this study, we develop a practical approach to enable uncertainty analysisof large-scale ground motion analysis
1. Enable super-large scale analysis by heroic computing using fullsupercomputer system
2. Use super-computed data to construct an AI methodology
3. Apply AI methodology to conduct Monte Carlo simulations
Combination of AI and HPC enables us to step towards high-quality computing(HQC) of Earthquakes• Verified HPC results itself not sufficient for HQC without considering uncertainty• Importance of HPC that enables heroic computing is strengthened by
combination with AI that makes uncertainty analysis possible

Surface

Training data

Test data

Check data Total# ofsamples

22360

1000

1000

24360

Case A

19929(89.1%)

880(88.0%)

891(89.1%)

21700(89.1%)

22219(99.4%)

992(99.2%)

994(99.4%)

24205(99.4%)

Case BThe number of correct answers and correct ratios. Judged correct if|target value - estimated value| < 21000 points are picked up from 23,460 points as test data and check data.

By Supercomputing

Comparison ofearthquake
hazardclassification
Distribution by AI match
adequately tosupercomputing results
for whole domain

Solve system roughly using CG solver(single precision)
Second orderedtetrahedron

AI-based Monte Carlo
Earthquake Hazard Classification• Change elevation2(x, y) and elevation3(x, y) by a normal distribution with amean of 0 m and a standard deviation of 5 m on a 1,000 m grid
• Conduct a Monte Carlo simulation with 1,000 samples on this stochastic
model using the constructed AI
ResultMean
3 x Standard deviationzy

elevation1(x,y)

Layer 1elevation2(x,y)

Layer 2elevation3(x,y)

Layer 3x
Bottom of model (elevation = 0 m)

Selection and normalization of input data
Case B

Outer loop

Use as initial solution

Characteristic value in target problem

Schematic view of AI

Result in learning
Elevation of subsurface is not
5 miles (8.04km)
highly accurate

mComputations ofouter loop

Inner fine loop

Linear tetrahedron

Structuring unstructured mesh:
Omit costly geometry computation part of unstructured elements

Implicit nonlinear wave simulation in soft soil ofTokyo is conducted by proposed supercomputing
method on full K computer (663,552 CPU cores)
with max available time (8 hours)• Minimum element size: 1m (2nd ordered
unstructured tetrahedral elements)• Problem size: 0.133 trillion DOF & 6,600 time-steps• Analyzed data size: 0.133 trillion DOF×double
precision× 6600 time-steps = 6,600 TB

9,250 mAccuracy in test data

Sedimentation: very soft

Solve system roughly using CG solver(single precision)

Use for preconditioner of outer loop

Development of AI with Super-computed Data for
Earthquake Hazard Classification
3 soil layers

Soil structure data in TokyoSolvingpreconditioning
matrixEquation to be solved(double precision)

Soft layers

Inner coarse loop

Case A: selection and normalization based on seismic design• Elevation1(x, y), elevation2(x, y), elevation3(x, y) are usedas predominant parameters for ground motion at point(x,y)
in earthquake resistant designs. These three values areused as input data.
Case B: selection & normalization based on physics• In the nonlinear wave propagation, the ground motion atpoint(x, y) is sensitive to the structure within one
wavelength of the observation point. Thus 75 points, i.e.,elevation1(x+50 i, y+50 j), elevation2(x+50 i, y+ 50 j),elevation3(x+50 i, y+50 j) (i=-2, 2, j=-2, 2) (50m grid) areused as input data.
• To enhance sensitivity, we convert elevation into thethickness of layers and normalized by subtracting averagevalue and divided by standard deviation
Summary：Case B shows better accuracy. We use the AI in
Case B in following parts. Case A has lower sensitivity and its
accuracy was saturated after 50 iterations. This accuracy wasfound to be improved to some extent by subtracting a constantand enhancing the sensitivity.
By AI with Super-computed data

• Both mean and standard deviation differ largely from location to location• This information is first been evaluated via uncertainty analysis using AI

Concluding Remarks• Highly nonlinear problem with complex resulting distribution and uncertain
data targeted: important to consider uncertainty for this problem• Conducting 1,000 cases of heroic computing is impractical; instead we takea practical approach• Performed one case of heroic computing using our proposed method anddeveloped an AI methodology based on the obtained super-computed data
• Conducted Monte Carlo Simulation with constructed AI methodology• High accuracy obtained by selecting and normalizing the training data withconsideration of the underlying physical problem• AI that can confirm permissible level of accuracy can enhance HPC via an
uncertainty analysis: large step towards achieving HQC for Earthquakes• We plan to improve both the AI methodology and the settings for theproblem to further improve performance

Acknowledgments
Our results were obtained using the K computer at the RIKEN Advanced Institute for Computational Science(proposal numbers: hp160221, hp160160, hp160157, and hp170249). We acknowledge the support provided
by the Japan Society for the Promotion of Science (15K18110, 26249066, 25220908, and 17K14719). We
thank the Operations and Computer Technologies Division of RIKEN AICS and the High Performance
Computing Infrastructure helpdesk for their support in the use of the K computer.

References[1] T. Ichimura et al. American Society of Mechanical Engineers, 2014. [2] T. Ichimura et al. SC’15, 2015.