Abstract: Warm Dense Matter (WDM) represents a transitional state of matter situated between condensed matter and plasma, emerging as a cutting-edge research direction within the realms of planetary physics, laboratory astrophysics, and inertial confinement fusion in the field of high-energy density physics. WDM is characterized by significant quantum effects, partial ionization, strong coupling, electron degeneracy, and thermal effects, necessitating a description based on fundamental quantum mechanical theories. In recent years, simulations and calculations based on quantum mechanics’ first principles have rapidly advanced, increasingly becoming an effective tool for a deeper understanding of WDM properties. On one hand, applying First Principles widely used in condensed matter physics and materials science to WDM poses considerable challenges, especially under extreme conditions such as broad temperature ranges and high pressures, which require continuous improvements to existing first-principle algorithms and software. On the other hand, the rapid development of machine learning-based molecular dynamics methods offers new tools for simulating WDM. In this review, we initially revisit traditional first principles applicable to WDM simulations, including Kohn-Sham Density Functional Theory and Orbital-free Density Functional Theory. Subsequently, we introduce newly developed methods and software, such as Extended First Principles Molecular Dynamics and Stochastic Density Functional Theory, the latter of which has been implemented in the domestically developed open-source density functional theory software, Atomic-orbital Based Ab-initio Computation at UStc (ABACUS). These innovative approaches significantly boost the computational scale and efficiency of WDM studies, thereby elevating the precision of structural, dynamical, and transport coefficient calculations related to WDM

Key words: warm dense matter, first principle, molecular dynamic, machine learning, Atomicorbital Based Ab-initio Computation at UStc (ABA