Neural Network Simulation of Time-variant Waves on Arbitrary Grids with Applications in Active Sonar

Wave behavior underlies useful technologies such as active sonar, passive sonar, and echolocation. For instance, wave behavior is used to determine the sonar signature of underwater vehicles for stealth designs. To obtain a sonar signature, the fastest method is to simulate a sonar testbed using physics software. However, these software rely on the finite element method or finite difference method, which are slow due to their dependence on explicit computations. To overcome this issue, researchers have begun developing physics-informed neural networks (PINNs) to learn wave behavior. As PINNs rely on soft computing and act as operators, they can learn from noisy data and make quick predictions. Our PINN differs from other PINNs that are trained on static simulation grids with open boundaries. The goal of our PINN is to predict the reflection of a pressure wave off of a dynamic obstruction in an arbitrary grid, mimicking in part, the behavior of active sonar. Given a random source location, static obstructions, and a dynamic obstruction, the PINN predicted the wave evolution for 500 timesteps in 1.54 seconds and was over 1200 times faster than the finite difference method. The PINN was trained for 180 epochs using supervised and unsupervised learning and reached a mean squared error of 3E-5. Results show that the PINN demonstrates visual and numerical accuracy and avoids learning unwanted artifacts like spurious waves, due to its ability to generalize. For future work, we will add more degrees of freedom to define complex dynamic obstruction shapes like submarines.