FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation

Data-driven modeling of fluid dynamics has advanced rapidly with neural PDE solvers, yet a fair and strong benchmark remains fragmented due to the absence of unified PDE datasets and standardized evaluation protocols. Although architectural innovations are abundant, fair assessment is further impeded by the lack of clear disentanglement between spatial, temporal and loss modules. In this paper, we introduce FD-Bench, the first fair, modular, comprehensive and reproducible benchmark for data-driven fluid simulation. FD-Bench systematically evaluates 85 baseline models across 10 representative flow scenarios under a unified experimental setup. It provides four key contributions: (1) a modular design enabling fair comparisons across spatial, temporal, and loss function modules; (2) the first systematic framework for direct comparison with traditional numerical solvers; (3) fine-grained generalization analysis across resolutions, initial conditions, and temporal windows; and (4) a user-friendly, extensible codebase to support future research. Through rigorous empirical studies, FD-Bench establishes the most comprehensive leaderboard to date, resolving long-standing issues in reproducibility and comparability, and laying a foundation for robust evaluation of future data-driven fluid models. The code is open-sourced at https://anonymous.4open.science/r/FD-Bench-15BC.

Deep Generative Models with Hard Linear Equality Constraints

While deep generative models~(DGMs) have demonstrated remarkable success in capturing complex data distributions, they consistently fail to learn constraints that encode domain knowledge and thus require constraint integration. Existing solutions to this challenge have primarily relied on heuristic methods and often ignore the underlying data distribution, harming the generative performance. In this work, we propose a probabilistically sound approach for enforcing the hard constraints into DGMs to generate constraint-compliant and realistic data. This is achieved by our proposed gradient estimators that allow the constrained distribution, the data distribution conditioned on constraints, to be differentiably learned. We carry out extensive experiments with various DGM model architectures over five image datasets and three scientific applications in which domain knowledge is governed by linear equality constraints. We validate that the standard DGMs almost surely generate data violating the constraints. Among all the constraint integration strategies, ours not only guarantees the satisfaction of constraints in generation but also archives superior generative performance than the other methods across every benchmark.

Inverse Attention Agent for Multi-Agent System

A major challenge for Multi-Agent Systems is enabling agents to adapt dynamically to diverse environments in which opponents and teammates may continually change. Agents trained using conventional methods tend to excel only within the confines of their training cohorts; their performance drops significantly when confronting unfamiliar agents. To address this shortcoming, we introduce Inverse Attention Agents that adopt concepts from the Theory of Mind, implemented algorithmically using an attention mechanism and trained in an end-to-end manner. Crucial to determining the final actions of these agents, the weights in their attention model explicitly represent attention to different goals. We furthermore propose an inverse attention network that deduces the ToM of agents based on observations and prior actions. The network infers the attentional states of other agents, thereby refining the attention weights to adjust the agent's final action. We conduct experiments in a continuous environment, tackling demanding tasks encompassing cooperation, competition, and a blend of both. They demonstrate that the inverse attention network successfully infers the attention of other agents, and that this information improves agent performance. Additional human experiments show that, compared to baseline agent models, our inverse attention agents exhibit superior cooperation with humans and better emulate human behaviors.