Computer imaging techniques are crucial in fields like medicine and engineering,
where CT scans help diagnose patients, and non-destructive testing (NDT) ensures
the safety of structures such as airplane wings. In this thesis, we study the full
waveform inversion (FWI) problem from a deep learning point of view. FWI,
initially developed in seismology and applied recently in NDT, is explored using
various neural network architectures, namely convolutional and feed-forward neu-
ral networks. Our initial goal was to apply a feed-forward neural network (FNN),
along with the ”Sample Where It Matters” (SWIM) weight sampling algorithm,
to solve the FWI problem outlined in [20]. We wanted to propose a new method
for the research described in the cited article. The approach sought to reduce the
number of trainable parameters and hence inference time by fixing hidden layer
weights and only optimizing the output layer. However, our FNN failed to pre-
dict the objective material distribution, even after adjusting and testing out differ-
ent initializations designed to make the algorithm converge easier, using different
SWIM domain approximations. A supervised learning experiment confirmed the
network could not approximate the discontinuous ground truth gamma using gra-
dient descent, which explained the failure in solving the FWI problem. Seeking to
determine the capabilities of neural networks to solve the FWI problem, we tested
smoother ground truth functions: (i) a Gaussian and (ii) a sinusoidal function. In
addition, we have also studied the effect of simulating a larger domain. Convo-
lutional neural networks (CNNs) could solve both supervised learning and FWI
tasks, independent of the discretization and domain size, whereas FNNs failed.
With an extended domain and the same number of grid points as in the original
experiments, an FNN with four hidden layers and 500 neurons per layer success-
fully handled smooth functions in the supervised learning framework, successfully
solved the FWI problem for the sinusoidal-shaped function, however struggled
with the Gaussian function in FWI. Lastly, we compared two CNN initializations
for FWI on smooth functions: (i) Xavier-Glorot and (ii) weights trained on a void-
less domain. We found that the first worked better for the Gaussian function,
while the second was more effective for the sinusoidal function. In this thesis, we
also discuss improvements and future work that could help answer our study’s
unresolved questions.
«
Computer imaging techniques are crucial in fields like medicine and engineering,
where CT scans help diagnose patients, and non-destructive testing (NDT) ensures
the safety of structures such as airplane wings. In this thesis, we study the full
waveform inversion (FWI) problem from a deep learning point of view. FWI,
initially developed in seismology and applied recently in NDT, is explored using
various neural network architectures, namely convolutional and feed-forward neu-
ral networks....
»