Physics-informed learning for end-to-end acoustic scattering of wavelength-order axisymmetric objects: From geometric profiles to acoustic radiation forces

Theoretical computations of scattering fields and radiation forces for axisymmetric objects typically rely on coordinate mapping techniques to parameterize geometric features and coordinate transformations to enforce boundary conditions within a closed-form governing framework. However, these approaches often suffer from computational inefficiency. Here, we propose a two-stage physics-informed neural network framework that decomposes the cross-scale mapping task into two specialized sub-networks. The first stage, the physics-informed geometric mapping network, integrates conformal transformation theory to efficiently encode raw spatial coordinate distributions into a compact set of mapping coefficients. The second stage, the physics-informed partial-wave network, expands the input dimensions to include these geometric descriptors alongside incident field parameters, encompassing the complete state-space of the scattering problem. By embedding the Helmholtz equation and corresponding boundary conditions as explicit physical constraints within the partial-wave expansion framework, the network is guided toward physically consistent solutions: Near-instantaneous and accurate prediction of scalar scattering coefficients for given object–wave configurations, with inference times of approximately 5–4 s for physics-informed geometric mapping network and 6.5–4 s for physics-informed partial-wave network. The well-trained model is further employed to reconstruct the scattered fields and evaluate the radiation forces in real-world wavelength-order objects. The predicted results basically agree with those obtained from numerical simulations, while achieving significantly improved in computational efficiency.