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We propose theadaptive hybrid particle-grid flow mapmethod, a novel flow-map approach that leverages Lagrangian particles to simultaneously transport impulse and guide grid adaptation, introducing a fully adaptive flow map-based fluid simulation framework. The core idea of our method is to maintain flow-map trajectories separately on grid nodes and particles: the grid-based representation tracks long-range flow maps at a coarse spatial resolution, while the particle-based representation tracks both long and short-range flow maps, enhanced by their gradients, at a fine resolution. This hybrid Eulerian-Lagrangian flow-map representation naturally enables adaptivity for both advection and projection steps. We implement this method inCirrus, a GPU-based fluid simulation framework designed for octree-like adaptive grids enhanced with particle trackers. The efficacy of our system is demonstrated through numerical tests and various simulation examples, achieving up to 512 × 512 × 2048 effective resolution on an RTX 4090 GPU. We achieve a 1.5 to 2× speedup with our GPU optimization over the Particle Flow Map method on the same hardware, while the adaptive grid implementation offers efficiency gains of one to two orders of magnitude by reducing computational resource requirements. The source code has been made publicly available at: https://wang-mengdi.github.io/proj/25-cirrus/. 

Deep learning models have achieved remarkable accuracy for structural response modeling. However, these models heavily depend on having a sufficient amount of training data, which can be challenging and time-consuming to collect. Moreover, data-driven models sometimes struggle to adhere to physics constraints. Therefore, in this study, a physics-informed long short-term memory (PI-LSTM) network was applied to structural response modeling by incorporating physics constraints into deep learning. The physics constraints were modified to accommodate the characteristics of both linear and nonlinear cases. The PI-LSTM network, inspired by and compared with existing physics-informed deep learning models (PhyCNN and PhyLSTM), was validated using the numerical simulation results of the single-degree-of-freedom (SDOF) system and the experimental results of the six-story building. Additionally, the PI-LSTM network underwent thorough investigation and validation across the four cases of the SDOF system and numerical simulation results of the six-story building with the comparison of the regular LSTM. The results indicate that the PI-LSTM network outperformed the regular LSTM models in terms of accuracy. Furthermore, the PI-LSTM network exhibited a more concentrated and higher accuracy range when analyzing the results of both the SDOF system and the six-story building. These findings demonstrate that the PI-LSTM network presents a reliable and efficient approach for structural response modeling.