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Silicate melts have served as transport agents in the chemical and thermal evolution of Earth. Molecular dynamics simulations based on a deep neural network potential trained by ab initiodata show that the viscosity of MgSiO3melt decreases with increasing pressure at low pressures (up to ∼6 GPa) before it starts to increase with further compression. The melt electrical conductivity also behaves anomalously; first increasing and then decreasing with pressure. The melt accumulation implied by the viscosity turnover at ∼23 GPa along mantle liquidus offers an explanation for the low‐velocity zone at the 660‐km discontinuity. The increase in electrical conductivity up to ∼50 GPa may contribute to the steep rise of Earth's electrical conductivity profiles derived from magnetotelluric observations. Our results also suggest that small fraction of melts could give rise to detectable bulk conductivity in deeper parts of the mantle. Dynamical behavior of silicate melts at high temperature and pressure controls melt distribution in Earth's interior. However, experimental data on the viscosity and electrical conductivity of silicate melts are limited to relatively low pressure. Moreover, the pressure dependence of viscosity is in debate, especially for depolymerized silicate melts. Using a new deep learning‐based simulation approach, we find that both the viscosity and electrical conductivity of MgSiO3melt behave anomalously with pressure, which could have important implications for zones with seismic velocity anomalies and high electrical conductivity in Earth's interior. The viscosity of MgSiO3melt behaves anomalously at relatively low temperatures; first decreasing and then increasing with pressureThe electrical (ionic) conductivity shows anomalous pressure behavior at all temperaturesDeep potential molecular dynamics simulations offer us a reliable and complete data set to study transport properties of silicate melts The viscosity of MgSiO3melt behaves anomalously at relatively low temperatures; first decreasing and then increasing with pressure The electrical (ionic) conductivity shows anomalous pressure behavior at all temperatures Deep potential molecular dynamics simulations offer us a reliable and complete data set to study transport properties of silicate melts