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Microfluidic cell sorters have shown great potential to revolutionize the current technique of enriching rare cells. In the past decades, different microfluidic cell sorters have been developed by researchers for separating circulating tumor cells, T-cells, and other biological markers from blood samples. However, it typically takes months or even years to design these microfluidic cell sorters by hand. Thus, researchers tend to use computer simulation (usually finite element analysis) to verify their designs before fabrication and experimental testing. Despite this, conducting precision finite element analysis of microfluidic devices is computationally expensive and labor-intensive. To address this issue, we recently presented a microfluidic simulation method that can simulate the behavior of fluids and particles in some typical microfluidic chips instantaneously. Our method decomposes the chip into channels and intersections. The behavior of fluid in each channel is determined by leveraging analogies with electronic circuits, and the behavior of fluid and particles in each intersection is determined by querying a database containing 92,934 pre-simulated channel intersections. While this approach successfully predicts the behavior of complex microfluidic chips in a fraction of the time required by existing techniques, we nonetheless identified three major limitations with this method: (1) the library of pre-simulated channel intersections is unnecessarily large (only 2,072 of 92,934 were used); (2) the library contains only cross-shaped intersections (and no other intersection geometries); and (3) the range of fluid flow rates in the library is limited to 0 to 2 cm/s. To address these deficiencies, in this work we present an improved method for instantaneously simulating the trajectories of particles in microfluidic chips. Firstly, inspired by dynamic programming, our new method optimizes the generation of pre-simulated intersection units and avoids generating unnecessary simulations. Secondly, we constructed a cloud database (http://cloud.microfluidics.cc) to share our pre-simulated results and to let users become contributors and upload their simulation results into the cloud database as a benefit to the whole microfluidic simulation community. Lastly, we investigated the impact of different channel angles and different fluid flow rates on predicting the trajectories of particles. We found a wide range of device geometries and flow rates over which our existing simulation results can be extended without having to perform additional simulations. Our method should accelerate the simulation of particles in microfluidic chips and enable researchers to design new microfluidic cell sorter chips more efficiently.