A Microlocal Open-Boundary Method for Residual-Based Wave Solvers on Unbounded Domains

Abstract

We introduce a microlocal phase-space-filtered physics-informed neural network (PINN--TDPSF or Microlocal PINNFilter) framework for wave propagation on unbounded domains. The method combines a slabwise neural residual approximation of the interior evolution with a time-dependent phase-space filter applied in a buffer surrounding the physical computational domain. The central idea is to replace local artificial-boundary penalties by a phase-space radiation mechanism: a component is removed only when it is localized near the artificial boundary and its group velocity points outward. The proposed method is not intended to replace FFT, spectral, or split-step solvers for known-coefficient forward problems where such methods are available and highly accurate. Instead, it embeds the time-dependent phase-space filter into a residual-based neural framework. This coupling is useful when open-domain wave propagation must be combined with nonlinear residuals, sparse or off-grid observations, unknown coefficients, variable interior media, or other non-FFT-diagonalizable physics. Numerical experiments for linear Schrödinger propagation, potential scattering, anisotropic Schrödinger dynamics, nonlinear Schrödinger wave packets, soliton stress tests, linearized Euler waves, and sparse-data recovery of a localized acoustic defect show that the method reduces artificial reflection and wraparound, uses group velocity correctly in anisotropic media, preserves physically incoming branch components, and provides diagnostics when the assumptions behind outgoing-packet filtering are violated.