10:32-10:46 4/7/2024
2024 World Conference of Earthquake Engineering: MONITOR 27

1TNM1/4/6 - TSUNAMIS: PREPAREDNESS, ENGINEERING AND RISK | Convenors: F. Jalayer, K.
Goda, M. Del Zoppo, D. Istrati, M. Baiguera, C. Reis, R. Omira

EFFICIENT TSUNAMI INUNDATION
PREDICTION UTILIZINGDEEP NEURAL NETWORKS
Yo Fukutani1 and Motoki Makoto1
1 Kanto Gakuin University, Yokohama, Japan

Introduction

2◼ Accurate prediction of tsunami inundation depth is crucialfor effective disaster preparedness and mitigation efforts.

◼ Existing methods based on non-linear long wave theory arecomputationally expensive,
especially for probabilistic tsunami
hazard analysis (PTHA).

◼ This study explores a DNN-based

approach to reduce computation
costs for tsunami hazard assessment.

Introduction

3◼ Many studies have constructed surrogate models fortsunami propagation and inundation analysis.

◼ Recent study examples:✓ Principal Component Analysis (PCA) (Mulia et al., 2018)✓ Gaussian Process Regression (GPR) (Gopinathan et al., 2021; Salmanidouet al., 2021)✓ Multiple-Output GPR (Giles et al., 2021)✓ MLP/CNN (Fauzi and Mizutani, 2020)✓ DNN (Mulia et al., 2020, 2022)✓ 1D-CNN (e.g., Makinoshima et al., 2021; Rim et al., 2022),focusing onlearning and predicting time-series coastal wave heights and inundation
depths✓ Proper Orthogonal Decomposition (POD) and Singular Value
Decomposition (SVD) (e.g., Kotani et al., 2020; Fukutani et al., 2021, 2023)

Objective of this study◼

4

We employed DNNs to establish the connection between the 2D
water level distributions at each time obtained from linear longwave theory or the slip distributions of the earthquakes and the2D inundation depth distributions obtained from nonlinear longwave theory.

Random source model(Goda et al., 2016)

nNon-linear long wave equation

Linear long wave equation
Low calculation cost∂η ∂M ∂N++ =0∂t ∂x ∂y∂M∂η++gD =0∂t∂x∂N∂η+gD =0∂t∂yWave height distribution
at each timen = 600
Slip distribution

Deep Neural Network(DNN)High calculation cost∂η ∂M ∂N++=0∂t ∂x ∂y∂M ∂ M2∂ MN∂η gn2 M+++gD +M2 +N2 =07൘∂t ∂x D∂y D∂xD 3∂N ∂ MN∂ N2∂η gn2 N+++gD +M2 +N2 =07൘∂t ∂x D∂y D∂y3
DMax. inundation depthdistribution (10m mesh)Target earthquakes and tsunamis◼ Focus on tsunamis generated by theNankai Trough megathrust earthquakes

The Nankai Trough megathrust earthquakes◼ Generate 600 cases with six different

earthquake magnitudes (Mw9.0, Mw8.8,Mw8.6, Mw8.4, Mw8.2, Mw8.0), with 100
cases for each magnitude◼ Using Okada's equation for generating

ninitial tsunami heights◼ Numerical simulations for tsunami

propagation and inundation (Linearand non-linear long wave equation)◼ The 600 earthquakes data are divided

into Train: Validation: Test = 432: 108: 60

5n = 600
Random source
parameter model(Goda et al., 2016)

Calculation Domains (Six domains)
(a)

(b)

Islands of Japan

Domain 4 (30m)
228×498

Domain 3 (90m)
558×438
Domain 2 (270m)
789×840

NW

Domain 1 (810m)
990×1500(c)

ES

Domain 5 (10m)
489×729

Domain 3 (90m)

6Domains 1, 2 and 3→ linear shallow waterequations
Domains 4, 5 and 6→ non-linear shallow waterequations for the inundation
depth(d)Elevation (m)Fishery port
Target area
50×50
Domain 4 (30m)

Tomoura fishery port, Tokushima, Japan

Deep Neural Network (DNN) Overview◼

An example of the five hidden layers

Input: 2D water level distributionsof fault slip distributions (afterNormalization)

Input layer◼

Output: Inundation depth
distribution in the target area◼

Hidden layers: one hidden layer(100 nodes), three hidden layers Wave height(100, 500, 1500 nodes), and fivehidden layers (1500, 500, 100, 500, Domain 1300 300
1500 nodes)◼

Model training: Optimization
algorithms RAdam, Dropout◼

Activation functions: ReLU◼

The loss function: RMSE

7

Output Layer

Hidden Layers

Inundation
depth50

Domain 2
200 200

Domain 3
100 100

Domain 1: 90,000
Domain 2: 40,000
Domain 3: 10,000
Slip Dist. : 5,669

1,500500

1005001,500

2,50050

Results and discussions
Input data:
The water level distribution from linear
long wave theory（Time after theearthquake 0, 2, 5, 10, 20, 40 minutes)
for Domain 1, 2 and 3.

Domainof Input
dataDomain 1◼

The results from Domain 1, which
encompasses a broader range,
including the entire earthquake
fault region, generally exhibited
lower validation loss average.

◼

Within Domain 1, the use of initialwater levels immediately after theearthquake occurrence suggests
a higher degree of accuracy◼

Number of the hidden layers don'tchange the results not so much.

Domain 2Domain 3

8Time after the Number
earthquake of input(minutes)
nodes
02510204002510204002510204090,00040,000

10,000Train Loss
Average
(m)
1.292
1.356
1.430
1.559
1.527
1.617
1.868
1.588
1.638
1.777
1.565
1.610
1.915
1.762
1.692
1.497
1.326
1.598

Validation
Loss
Average
(m)
1.253
1.257
1.331
1.470
1.398
1.448
1.775
1.601
1.624
1.630
1.510
1.551
1.724
1.711
1.656
1.393
1.354
1.613

Results and discussions

9

Input data:
The slip distributions (Slip amount of
the fault) of the earthquake◼

drastically improved training loss averages

In all cases, the train loss averageimproved compared to thescenario where initial water levels
were used as input values.

Numb Number
Input er ofof
Data input hidden
nodes layers
1◼ having three and five hidden layers

yields higher accuracy than one
hidden layer in terms of thevalidation loss average.

◼

However, a significant difference
between train loss average andvalidation loss average suggests
the possibility of overfitting to thetraining data.

Slip
amou
nt

5,669

3
5

Number ofValidationTrainnodes inLoss
Loss (m)each layer(m)100100, 500,1500
1500, 500,100, 500,
1500

0.258

1.642

0.528

1.195

0.397

1.147

Due to the potential overfitting to the training
data, we introduced a dropout at thenetwork's entranceResults and discussions

10◼ We found that the validation loss average was minimized to 1.060
meters when using fault slip distribution as input values: a five hidden
layers configuration, and a dropout rate of 80%.
Input
Data

Slip
amountNumberNumber ofof
nodes in eachhiddenlayer
layers1100

3100, 500, 1500

51500, 500, 100,500, 1500

Dropout
rate

Train LossAverage
(m)

0.8
0.6
0.4
0.8
0.6
0.4
0.8
0.6
0.4

0.452
0.320
0.282
0.778
0.527
0.469
0.742
0.465
0.506

Validation
Loss
Average
(m)
1.192
1.232
1.322
1.123
1.123
1.146
1.060
1.110
1.109

Test Loss
Average
(m)
1.521
1.507
1.574
1.569
1.459
1.414
1.548
1.541
1.540

Comparison of numerical and neural network outputs

11(a)Numerical simulation
results (10 cases)
Compares the original data
Numerical
simulation
results (only 10 cases)
23
45
used for validation and the data 1land
predicted using the DNN modelwith the minimal validation losssea
coastal lineaverage.

◼

The DNN outputs provide
accurate evaluations of theresults obtained from non-linear
long wave theory◼

Some results (No. 1, No. 3, No. 4,No.5, No. 9, No. 10) are
underestimated, while deep
inundation depths (No. 6) andthe inundation depths for No. 2,No. 7, and No. 8 are predictedwith relatively good accuracy.

678910DNN(only 10 cases)(b)
DNNoutputs
outputs (10 cases)
12345678910Tsunami inundation depth (m)◼

Comparison between the numerical simulation results and the DNN results

12◼

Numerical simulation results:
600 cases simulated by nonlinear long wave theory◼

DNN results: 1800 cases derived
from the constructed DNN using
only slip distribution of 1800
faults as input values.

Frequency

DNN results(1800 cases)

A

B
Frequency

Tsunami inundation depth (m)The overestimation using a large
number of unknown datasuggests that the training data
may have been insufficient orthat the network structure may
not be appropriate.

BCCTsunami inundation depth (m)Frequency◼

The peaks of predicted
inundation depths by the DNN
are higher than those of thenumerical simulations.

Numerical simulation results(600 cases)

Target area
Target area6)(DomainA

Tsunami inundation depth (m)Elevation (m)◼

◼We compared the numerical simulation results
and the DNN results.

Conclusion13◼ We tried to construct a DNN-based surrogate model, which determined therelationship between the water level distribution from linear long wave theory,or the slip distribution, and their association with the inundation depthdistribution.
◼ When predicting inundation depths with DNN using the slip distribution ofearthquake fault as input, the RMSE was approximately 1 meter,demonstrating relatively good accuracy.
◼ Finally, when conducting probabilistic inundation prediction using numerous
unknown slip distributions as input, the DNN-based predictions exceeded
those based on nonlinear long wave theory.
◼ To address these challenges, future plans involve increasing the size of the
training dataset and exploring alternative neural network architectures
including CNN.

Thank you for your attention.

If you have questions, please contact fukutani@kanto-gakuin.ac.jp
Acknowledgement: This study was partially supported by JSPS Kakenhi No.23K04351