PHYSICS-INFORMED NEURAL NETWORKS FOR INVERSE TASKS OF ONE-DIMENSIONAL WAVE PROPAGATION

Igor Kolych, Roman Shuvar

Abstract


Background. Physics‑informed neural networks (PINNs) are a family of learning methods that guide neural networks with the laws of physics, rather than relying only on data. PINNs demonstrated strong capabilities in solving forward and inverse problems for partial differential equations. In this study, the application of PINNs to single‐pulse wave propagation in non‐uniform media is explored, focusing on reconstructing velocity profiles from wavefield data. Specifically, we focus on reconstructing velocity profiles from wavefield data using PINNs and their convolutional extension, Physics‐Informed Convolutional Neural Networks (PICNNs). The work is motivated by applications in seismology, acoustics, and biomedical imaging, where accurate velocity estimation is crucial.

Materials and Methods. We generate synthetic wave data using the finite element method (FEM) and use a Gaussian impulse so that the result of the neural models can be directly compared against the numerical benchmark. PINNs and PICNNs are applied to solve forward tasks (wavefield prediction) and inverse tasks (velocity reconstruction). Also, we use training data that contains varying levels of Gaussian noise.

Results and Discussion. For the forward task, both PINNs and PICNNs closely match the numerical simulations, with PICNNs reaching high accuracy faster. For inverse tasks, PICNNs demonstrated superior performance in reconstructing spatially varying velocity profiles, while PINNs struggled with convergence due to local maxima in the optimization landscape. The inclusion of a smoothness constraint in the loss function eliminated artifacts in the reconstructed velocities without increasing computational cost. The approach remains effective on testing cases and is robust to moderate noise levels in the input data.

Conclusion. PICNNs efficiently solve forward and inverse single‑pulse propagation in non‑uniform media, matching FEM in forward accuracy and outperforming standard PINNs in inverse recovery. These results indicate strong potential for practical sensing and imaging. Future work will explore the extension of these methods to multi‐pulse scenarios.

Keywords: Physics‐informed neural networks, PICNN, single‐pulse, inverse problem, velocity reconstruction, non‐uniform media


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DOI: http://dx.doi.org/10.30970/eli.31.9

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