Towards stable and accurate electron dynamics via neural network based time-dependent variational Monte Carlo

Abstract: Real-time dynamics of interacting electrons lies at the interface between quantum mechanics and non-equilibrium physics, governing the microscopic origin of ultrafast phenomena of molecules and nano-materials. Though neural network variational Monte Carlo has achieved unprecedented accuracy for stationary state calculations, its extension to real-time evolution remains challenging. In this work, we introduce the neural basis time-dependent variational Monte Carlo framework, which achieves stable and highly accurate simulations of electron dynamics. By constraining the time evolution to a compact, customized manifold spanned by the neural basis, we effectively bypass instability issues and achieve long-term stable evolution. Moreover, we demonstrate that this framework yields benchmark-quality accuracy in simulating the laser-driven dipole responses of the hydrogen atom and a stretched hydrogen molecule, and accurately extracts the dynamic polarizabilities of helium and beryllium atoms. Our work reveals the vast potential of neural network wavefunctions for accurately describing real-time electron dynamics and establishes a promising new route for first-principles simulations of complex, time-dependent electronic phenomena.