Inverse design of NURBS metasurfaces via deep learning for angular thermal emission control

Tailoring the angular distribution of thermal emission is crucial for applications in space thermal management, infrared stealth, and energy systems. The inverse design of nonlocal metasurfaces remains challenging due to the high-dimensional parameter space and computationally expensive full wave simulations. This work presents and experimentally validates an efficient, deep learning driven inverse design platform for nonlocal thermal photonic metasurfaces with customized directional emissivity. First, by applying particle swarm optimization (PSO) to introduce perturbations to a bound state in the continuum (BIC) metasurface, we demonstrate precise control over the angular emissivity profile within a ±60° range. Fourier-transform infrared spectroscopy and long wave infrared thermal imaging confirm the intended asymmetric emission, showing excellent agreement between experiments and simulations. To overcome the limited design freedom of perturbation-based strategies, we further develop a global optimization framework. It employs Non-Uniform Rational B-Splines (NURBS) for high-degree-of-freedom meta-atom parameterization, accelerated by an end-to-end deep learning surrogate model linked to spatiotemporal coupled-mode theory (STCMT). This differentiable surrogate bypasses repetitive full-wave simulations and enables efficient gradient based optimization without adjoint methods. Metasurfaces fabricated using this workflow exhibit thermal emissivity profiles at 150 °C in excellent agreement with predictions, achieving a normalized root mean square error below 0.15. This work demonstrates a robust and scalable platform for the inverse design of high performance nonlocal thermal metasurfaces with complex spectral-angular responses.