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This work presents predictive hydrodynamic simulations empowered by artificial intelligence (AI) for laser driven implosion experiments, taking the double-cone ignition (DCI) scheme as an example. A Transformer-based deep learning model MULTI-Net is established to predict implosion features according to laser waveforms and target radius. A Physics-Informed Decoder (PID) is proposed for high-dimensional sampling, significantly reducing the prediction errors compared to Latin hypercube sampling. Applied to DCI experiments conducted on the SG-II Upgrade facility, the MULTI-Net model is able to predict the implosion dynamics measured by the x-ray streak camera. It is found that an effective laser absorption factor about 65\% is suitable for the one-dimensional simulations of the DCI-R10 experiments. For shot 33, the mean implosion velocity and collided plasma density reached 195 km/s and 117 g/cc, respectively. This study demonstrates a data-driven AI framework that enhances the prediction ability of simulations for complicated laser fusion experiments.