=Paper=
{{Paper
|id=Vol-2587/article_17
|storemode=property
|title=Surfzone Topography-informed Deep Learning Techniques to Nearshore Bathymetry with
Sparse Measurements
|pdfUrl=https://ceur-ws.org/Vol-2587/article_17.pdf
|volume=Vol-2587
|authors=Yizhou Qian,Hojat Ghorbanidehno,Matthew Farthing,Ty Hesser,Peter K. Kitanidis,Eric F. Darve
|dblpUrl=https://dblp.org/rec/conf/aaaiss/QianGFHKD20
}}
==Surfzone Topography-informed Deep Learning Techniques to Nearshore Bathymetry with
Sparse Measurements==
https://ceur-ws.org/Vol-2587/article_17.pdf
Surfzone Topography-informed Deep Learning Techniques to Nearshore
Bathymetry with Sparse Measurements
Yizhou Qian,1 Hojat Ghorbanidehno,2 Matthew Farthing,3
Ty Hesser,3 Peter K. Kitanidis,4 Eric F. Darve2
1
Institute for Computational and Mathematical Engineering, Stanford University, CA
2
Department of Mechanical Engineering, Stanford University, CA
3
US Army Engineer Research and Development Center, Vicksburg, MS
4
Department of Civil and Environmental Engineering, Stanford University, CA
1
yzqian@stanford.edu,2 {hojjatgh, darve}@stanford.edu, 3 jonghyun.harry.lee@hawaii.edu,
4
{mwfarthing, thesser1}@gmail.com,5 peterk@stanford.edu
Abstract forcing as well as long-term climate and sea level changes.
In this work, we focus primarily on the comparisons of spa-
Nearshore bathymetry, the knowledge of water depth in
coastal zones, has played a vital role in a wide variety of tial interpolation methods (SIMs) for nearshore bathymetry.
applications including shipping operations, coastal manage- In particular, Kriging, which is one of the most widely used
ment, and risk assessment. However, direct high resolution stochastic techniques for environmental data, will be com-
surveys of nearshore bathymetry are relatively difficult to per- pared with our deep learning methods.
form due to budget constraints and logistical restrictions. One
possible approach to nearshore bathymetry without such lim-
itations is the use of spatial interpolation with sparse mea-
Generative Adversarial Networks
surements of water depth by using, for example, geostatis- Generative Adversarial Networks are a class of deep gener-
tics. However, it is often difficult for traditional methods ative models that consists of two types of neural networks
to recognize patterns with a sharp gradient often shown on (Goodfellow et al. 2014): a generator G and a discrimina-
coastal sand bars, especially in the case of sparse measure- tor D. The generator G takes some noise vector z, which
ments. In this work, we use a conditional Generative Adver-
sarial Neural Network (cGAN) to generate abruptly changing
is usually from some normal distribution p1 (z), as input to
bathymetry samples while being consistent with our sparse, generate fake images, and the discriminator takes images as
multi-scale measurements. We train our neural network based input and tries to classify them as real or fake. The networks
on synthetic data generated from nearshore surveys provided are trained in an adversarial manner: the generator G tries to
by the U.S. Army Corps of Engineer Field Research Facil- generate as realistic images as possible to fool the discrim-
ity (FRF) in Duck, North Carolina. We compare our method inator D, while D tries to accurately distinguish between
with Kriging on real surveys as well as ones with artificially real images and fake images generated by G. Formally, let x
added patterns of sharp gradient. Results show that our con- represent the bathymetric images with some prior distribu-
ditional Generative Adversarial Network provides estimates tion p2 (x), then the objective function of GAN will be:
with lower root mean squared errors than Kriging in both
cases. min max Ex∼p2 (x) (log D(x))+Ez∼p1 (z) (1−log D(G(z)))
G D
Introduction Conditional Generative Adversarial Networks (cGANs)
Nearshore bathymetry, or the topography of ocean floor in are an extension of GANs (Mirza and Osindero 2014), in
coastal zones, has been one of the most critical variables in which an extra label y, which represents indirect observa-
many areas including geomorphology (Finkl, Benedet, and tions, is passed as input to both the generator G and the
Andrews 2005), harbor managements (Grifoll et al. 2011) discriminator D. The two networks are trained alternatively
and flood risk assessment (Casas et al. 2006). Hence, ac- using the output of each other, and the generator will suppos-
curate estimations of nearshore bathymetry with relatively edly generate sample images consistent with observations at
low cost in area of interest, have become increasingly im- the end of several training cycles. In this work, two differ-
portant in recent years due to the expansion of coastal activ- ent scale data types of 1) point-wise sparse measurements
ities and the improvement of sensor technologies. Nearshore and 2) averages over each grid are used with labels y for
bathymetry typically exhibits time-varying multi-scale fea- our cGAN. The overall scheme is shown in Figure 1. The
tures such as sand bars due to short-term wave and storm objective function of cGAN then becomes:
Copyright c 2020, for this paper by its authors. Use permitted un- min max Ex∼p2 (x) (log D(x|y))+Ez∼p1 (z) (1−log D(G(z|y)))
der Creative Commons License Attribution 4.0 International (CC G D
BY 4.0).
Comparison of OK and cGAN on Real Surveys
Label Generator 0.7
cGAN
0.6 OK
Root Mean Squared Error
0.5
Label
Noise
0.4
0.3
Discriminator
0.2
0.1
0.0
Real Fake 0 2 4 6 8 10 12 14
FRF Surveys
Figure 1: Conditional Generative Adversarial Network Figure 2: Comparison of Kriging and cGAN on FRF Sur-
veys
Numerical Experiments
Artificially Added Sharp Gradient
240 surveys are used to generate synthetic training data for In the second case, one FRF survey taken on June 21th,
cGAN by adding Gaussian noises with the following covari- 2017 is chosen for comparisons on performance of cGAN
ance matrix: and Kriging while random rectangular jumps are added (uni-
kxi − xj k2
formly random location and sizes). Similarly, 100 samples
Cij = αexp − are generated by cGAN to compute the average as its fi-
r2
nal prediction. The result is shown in Figure 3 and Fig-
where α is chosen in (1, 2) and r is chosen in (80, 100). ure 4. Figure 3 shows predictions of nearshore bathymetry
9600 training samples in total are generated to be training by cGAN and Kriging with the corresponding mean abso-
data. We also introduce random sand bar structures as our lute error (MAE), as well as the variance of samples gen-
topographical understanding in the surf zone and investigate erated by cGAN. Figure 4 shows the corresponding cross
cGAN’s potential ability to recognize patterns with sharp section plots near the location of discontinuity. We ob-
gradient. For this, rectangular jumps with random locations serve that cGAN gives estimates with almost vertical jumps,
(uniformly in the computational domain) and random sizes as well as a lower mean absolute error. This is because
are added to real bathymetry surveys (9600 samples) as well deep neural networks can express highly complex func-
as profiles with constant values uniformly chosen from 0 to tions in an efficient manner (Poole et al. 2016) while Krig-
10 (9600 samples) with Gaussian variations. We also add ing requires a carefully chosen nonlinear kernel function
Gaussian white noise with a variance of 0.2 to all training to achieve the same performance (Williams 1996). Further-
input. In our comparisons below, we consider using only 35 more, GAN tends to produce sharper samples than other
evenly distributed grid points with a grid size of 136 meters available methods (Goodfellow 2017), thus is suitable for
along-shore and 76 meters across-shore for our sparse mea- general nearshore bathymetry interpolation applications.
surements. For Kriging, we used the method of CoKriging
to incorporate grid cell averages as auxiliary measurements. Conclusion
In this work, we compare cGAN with Kriging on real
Performance on Real Data nearshore bathymetry surveys. Results show that cGAN pro-
vides estimates with lower root mean squared errors than
In the first case, we compare cGAN with Kriging based on Kriging on real FRF surveys not included in the training set.
15 real FRF surveys not included in the training set. For We also compared cGAN with Kriging on synthetic surveys
each prediction, 100 samples are generated by cGAN and with rectangular jumps. It is shown that cGAN produces
we use the point-wise average over those samples as our samples with lower mean absolute errors as well as sharper
final estimate. Figure 2 shows the root mean squared er- boundaries.
rors of cGAN and Kriging on those 15 surveys. Our results
show that cGAN produces estimates of bathymetry profiles Acknowledgement
with consistently lower root mean squared errors than Krig- This research was supported in part by an appointment to
ing. This is because when training data are sampled from the Research Participation Program at the U.S. Army En-
a carefully chosen prior distribution, deep neural networks gineer Research and Development Center, Coastal and Hy-
are known to provide posterior estimates that minimize the draulics Laboratory (ERDC-CHL) administered by the Oak
mean squared error (Adler and Öktem 2018). Ridge Institute for Science and Education through an in-
teragency agreement between the U.S. Department of En-
Performance on Data with ergy and ERDC. The research is also supported in part by
2014. Generative adversarial nets. In Advances in neural
information processing systems, 2672–2680.
Goodfellow, I. J. 2017. NIPS 2016 tutorial: Generative ad-
versarial networks. CoRR abs/1701.00160.
Grifoll, M.; Jordà, G.; Espino, M.; Romo, J.; and Garcı́a-
Sotillo, M. 2011. A management system for accidental
water pollution risk in a harbour: The barcelona case study.
Journal of Marine Systems 88(1):60–73.
Mirza, M., and Osindero, S. 2014. Conditional generative
adversarial nets. arXiv preprint arXiv:1411.1784.
Poole, B.; Lahiri, S.; Raghu, M.; Sohl-Dickstein, J.; and
Ganguli, S. 2016. Exponential expressivity in deep neural
networks through transient chaos. In Lee, D. D.; Sugiyama,
M.; Luxburg, U. V.; Guyon, I.; and Garnett, R., eds., Ad-
vances in Neural Information Processing Systems 29. Cur-
ran Associates, Inc. 3360–3368.
Williams, C. K. I. 1996. Computing with infinite net-
Figure 3: Performance with rectangular discontinuities.
works. In Proceedings of the 9th International Conference
cGAN denotes conditional Generative Adversarial Network,
on Neural Information Processing Systems, NIPS96, 295–
OK denotes Kriging
301. Cambridge, MA, USA: MIT Press.
Figure 4: Cross section comparisons. cGAN denotes condi-
tional Generative Adversarial Network, OK denotes Kriging
funding from the Army High Performance Computing Re-
search Center (AHPCRC), sponsored by the U.S. Army Re-
search Laboratory under contract No. W911NF-07-2-0027,
at Stanford. Jonghyun Lee was supported in part by Hawai’i
Experimental Program to Stimulate Competitive Research
(EPSCoR) provided by the National Science Foundation Re-
search Infrastructure Improvement (RII) Track-1: ’Ike Wai:
Securing Hawai’i’s Water Future Award #OIA-1557349.
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