Data-driven learning of physical systems has attracted significant attention, where many neural models have been developed. In particular, mesh-based graph neural networks (GNNs) have demonstrated considerable potential in modeling spatiotemporal dynamics across arbitrary geometric domains. However, the existing node-edge message-passing and aggregation mechanism in GNNs limits the representation learning capability. In this paper, we propose a dual-module framework, Cell-embedded and Feature-enhanced Graph Neural Network (CeFeGNN), for learning spatiotemporal dynamics. Specifically, we embed learnable cell attributions to the common node-edge message passing process, thereby better capturing the spatial dependency of regional features. Such a strategy essentially upgrades the local aggregation scheme from first order (e.g., from edge to node) to a higher order (e.g., from volume and edge to node), which takes advantage of volumetric information in message passing. Meanwhile, a novel feature-enhanced block is designed to further improve the model's performance and alleviate the over-smoothing problem. Extensive experiments on various PDE systems and a real-world dataset demonstrate that CeFeGNN achieves superior performance compared with other baselines.

Object-centric learning aims to break down complex visual scenes into more manageable object representations, enhancing the understanding and reasoning abilities of machine learning systems toward the physical world. Recently, slot-based video models have demonstrated remarkable proficiency in segmenting and tracking objects, but they overlook the importance of the effective reasoning module. In the real world, reasoning and predictive abilities play a crucial role in human perception and object tracking; in particular, these abilities are closely related to human intuitive physics. Inspired by this, we designed a novel reasoning module called the Slot-based Time-Space Transformer with Memory buffer (STATM) to enhance the model's perception ability in complex scenes. The memory buffer primarily serves as storage for slot information from upstream modules, the Slot-based Time-Space Transformer makes predictions through slot-based spatiotemporal attention computations and fusion. Our experimental results on various datasets indicate that the STATM module can significantly enhance the capabilities of multiple state-of-the-art object-centric learning models for video. Moreover, as a predictive model, the STATM module also performs well in downstream prediction and Visual Question Answering (VQA) tasks. We will release our codes and data at https://github.com/intell-sci-comput/STATM.

Understanding and reasoning about dynamics governed by physical laws through visual observation, akin to human capabilities in the real world, poses significant challenges. Currently, object-centric dynamic simulation methods, which emulate human behavior, have achieved notable progress but overlook two critical aspects: 1) the integration of physical knowledge into models. Humans gain physical insights by observing the world and apply this knowledge to accurately reason about various dynamic scenarios; 2) the validation of model adaptability across diverse scenarios. Real-world dynamics, especially those involving fluids and objects, demand models that not only capture object interactions but also simulate fluid flow characteristics. To address these gaps, we introduce SlotPi, a slot-based physics-informed object-centric reasoning model. SlotPi integrates a physical module based on Hamiltonian principles with a spatio-temporal prediction module for dynamic forecasting. Our experiments highlight the model's strengths in tasks such as prediction and Visual Question Answering (VQA) on benchmark and fluid datasets. Furthermore, we have created a real-world dataset encompassing object interactions, fluid dynamics, and fluid-object interactions, on which we validated our model's capabilities. The model's robust performance across all datasets underscores its strong adaptability, laying a foundation for developing more advanced world models.

Data-centric methods have shown great potential in understanding and predicting spatiotemporal dynamics, enabling better design and control of the object system. However, deep learning models often lack interpretability, fail to obey intrinsic physics, and struggle to cope with the various domains. While geometry-based methods, e.g., graph neural networks (GNNs), have been proposed to further tackle these challenges, they still need to find the implicit physical laws from large datasets and rely excessively on rich labeled data. In this paper, we herein introduce the conservation-informed GNN (CiGNN), an end-to-end explainable learning framework, to learn spatiotemporal dynamics based on limited training data. The network is designed to conform to the general conservation law via symmetry, where conservative and non-conservative information passes over a multiscale space enhanced by a latent temporal marching strategy. The efficacy of our model has been verified in various spatiotemporal systems based on synthetic and real-world datasets, showing superiority over baseline models. Results demonstrate that CiGNN exhibits remarkable accuracy and generalizability, and is readily applicable to learning for prediction of various spatiotemporal dynamics in a spatial domain with complex geometry.

Simulation of fluid flows is crucial for modeling physical phenomena like meteorology, aerodynamics, and biomedicine. Classical numerical solvers often require fine spatiotemporal grids to satisfy stability, consistency, and convergence conditions, leading to substantial computational costs. Although machine learning has demonstrated better efficiency, they typically suffer from issues of interpretability, generalizability, and data dependency. Hence, we propose a learnable and differentiable finite volume solver, called LDSolver, designed for efficient and accurate simulation of fluid flows on spatiotemporal coarse grids. LDSolver comprises two key components: (1) a differentiable finite volume solver, and (2) an learnable module providing equivalent approximation for fluxes (derivatives and interpolations), and temporal error correction on coarse grids. Even with limited training data (e.g., only a few trajectories), our model could accelerate the simulation while maintaining a high accuracy with superior generalizability. Experiments on different flow systems (e.g., Burgers, decaying, forced and shear flows) show that LDSolver achieves state-of-the-art performance, surpassing baseline models with notable margins.

Simulating high quality user behavior data has always been a fundamental yet challenging problem in human-centered applications such as recommendation systems, social networks, among many others. The major difficulty of user behavior simulation originates from the intricate mechanism of human cognitive and decision processes. Recently, substantial evidence has suggested that by learning huge amounts of web knowledge, large language models (LLMs) can achieve human-like intelligence and generalization capabilities. Inspired by such capabilities, in this article, we take an initial step to study the potential of using LLMs for user behavior simulation in the recommendation domain. To make LLMs act like humans, we design profile, memory and action modules to equip them, building LLM-based agents to simulate real users. To enable interactions between different agents and observe their behavior patterns, we design a sandbox environment, where each agent can interact with the recommendation system, and different agents can converse with their friends via one-to-one chatting or one-to-many social broadcasting. In the experiments, we first demonstrate the believability of the agent-generated behaviors based on both subjective and objective evaluations. Then, to show the potential applications of our method, we simulate and study two social phenomena including (1) information cocoons and (2) user conformity behaviors. We find that controlling the personalization degree of recommendation algorithms and improving the heterogeneity of user social relations can be two effective strategies for alleviating the problem of information cocoon, and the conformity behaviors can be highly influenced by the amount of user social relations. To advance this direction, we have released our project at https://github.com/RUC-GSAI/YuLan-Rec .