3 papers
math.NA2026
An adaptive Galerkin neural-network method for minimum-norm control of wave equations
Nguyen Gia Hien
We develop an adaptive Galerkin neural-network method for computing minimum--norm interior controls for wave equations with spatially varying coefficients. Within the Hilbert…
math-ph2026
Global time-analytic strong solutions for a class of 3-wave kinetic equations
Nguyen Gia Hien, Gigliola Staffilani, Minh-Binh Tran
We study a class of 3-wave kinetic equations arising in wave turbulence theory, with regularized kernels. For radial, nonnegative initial data, we construct an exact global-in-time…
math.NA2026
A Microlocal Open-Boundary Method for Residual-Based Wave Solvers on Unbounded Domains
Avy Soffer, Nguyen Gia Hien, Minh-Binh Tran
We introduce a microlocal phase-space-filtered physics-informed neural network (PINN--TDPSF or Microlocal PINNFilter) framework for wave propagation on unbounded domains. The metho…