LSTM and DeepONet Surrogate Models for Particle Trajectory and Bed Segregation Prediction in Magnetically Fluidized Beds

Particle-resolved prediction in magnetically fluidized beds (MFBs) is needed to link local particle motion with bed-scale segregation, yet repeated CFD-DEM simulations remain computationally expensive. This study develops and benchmarks two complementary deep-learning surrogates for Lagrangian trajectory prediction in a magnetic-last MFB: a particle-wise long short-term memory (LSTM) network and a deep operator network (DeepONet). Both models are trained on a common CFD-DEM data set of 9240 binary particles under a magnetic-field gradient increasing from 0 to 0.30 T m–1. The source code developed in this study is openly available to facilitate reproducibility and future research. In particle-wise forecasting, both architectures achieve R2 > 0.99 and recover the segregation-index evolution from predicted positions; DeepONet yields narrower ensemble error bounds, whereas LSTM incurs lower training cost. A shared DeepONet further generalizes across particle identities (R2 = 0.9991, 0.9984, and 0.9975 in X, Y, and Z) while preserving principal collective structures. Applied without retraining to an unseen inlet gas velocity, the DeepONet retains an R2 above 0.99 in all three directions (pooled R2 of 0.998) and the LSTM retains a pooled R2 of 0.991, and trained-surrogate inference reproduces the full 14 s trajectory of all particles roughly an order of magnitude faster in wall-clock time than the reference CFD-DEM simulation while using eight times fewer cores. The results establish complementary sequence- and operator-learning routes for accelerated analysis of MFB dynamics with demonstrated transfer to an unseen operating condition.