Abstract
Simulating the temporal evolution of wavefield solutions through models with heterogeneous material properties is of practical interest for many scientific applications. The acoustic wave equation (AWE) is often used for studying wave propagation in both fluids and solids and is crucial for many applications including seismic imaging and inversion and non-destructive testing. Because analytical AWE solutions rarely exist for complex heterogeneous media, methods for generating numerical AWE solutions are very desirable. Traditional numerical solvers require discrete model representations with many restrictions placed on the shape and spacing of grid elements. This work uses a relatively new class of numerical solvers known as physics-informed neural networks (PINNs) that provide a mesh-free alternative for generating AWE solutions using a deep neural-network framework. We encapsulate a time-domain AWE formulation within a loss function that is used to train network parameters. The initial conditions are implemented by enforcing hard constraints on the neural network instead of including them as separate loss-function terms. We also use a Fourier neural network (FNN) to alleviate the spectral bias commonly observed when using fully connected neural network in the conventional PINN approach. Numerical tests on both 2D homogeneous and heterogeneous velocity models confirm the accuracy of our approach. We observe that using FNNs helps in the convergence of AWE solutions especially for heterogeneous models. We compare PINN-based solutions with those computed by the highly accurate conventional pseudo-spectral method, and observe that the normalized energy differences between the two sets of solutions were less than 4% for all numerical tests.
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Acknowledgements
The authors would like to acknowledge Oliver Hennigh, Sanjay Choudry, and NVIDIA Simnet team for technical help as well as the sponsors of the Center for Wave Phenomena research consortium at the Colorado School of Mines. We thank the two anonymous reviewers for helpful comments that improved quality of the manuscript. We also acknowledge the Mines HPC facility for compute time allocations on the Wendian cluster.
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This research was partially sponsored by Center for Wave Phenomena research consortium at the Colorado School of Mines.
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Sethi, H., Pan, D., Dimitrov, P. et al. Hard enforcement of physics-informed neural network solutions of acoustic wave propagation. Comput Geosci 27, 737–751 (2023). https://doi.org/10.1007/s10596-023-10232-3
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DOI: https://doi.org/10.1007/s10596-023-10232-3