Resolving energy transfer dynamics in Eu²⁺-activated multi-site phosphors via metaheuristic optimization and physics-informed neural networks

Multi-exponential fitting has long been the standard approach for luminescence decay analysis, not because it is physically meaningful but because it offers empirical convenience. Rigorous nonlinear rate-equation models have existed for decades, yet their application was hindered by computational costs. Recent advances in artificial intelligence and high-performance computing now make such models tractable, enabling physically grounded analyses of complex relaxation dynamics. Here we examine donor-acceptor interactions in a prototypical Eu²⁺-activated multi-site phosphor (La_2.544Ca_1.456Si₁₂O_4.456N_16.544:Eu²⁺) that exhibits wavelength quenching. Metaheuristic-driven Runge-Kutta simulations enabled the extraction of quantitative radiative and non-radiative rate constants, while physics-informed neural networks provided a complementary framework that independently reproduced the experimental decay dynamics. Both approaches converged to consistent rate constants, establishing donor-acceptor transfer as the dominant relaxation pathway over radiative and same-species interactions, offering quantitative, physics-based insight into complex dynamical behaviors beyond phosphors.