ICML 2025 论文列表

Graph Neural Networks (GNNs) often struggle in preserving high-frequency components of nodal signals when dealing with directed graphs. Such components are crucial for modeling flow dynamics, without which a traditional GNN tends to treat a graph with forward and reverse topologies equal. To make GNNs sensitive to those high-frequency components thereby being capable to capture detailed topological differences, this paper proposes a novel framework that combines 1) explicit difference matrices that model directional gradients and 2) implicit physical constraints that enforce messages passing within GNNs to be consistent with natural laws. Evaluations on two real-world directed graph data, namely, water flux network and urban traffic flow network, demonstrate the effectiveness of our proposal.

We address the problem of predicting the next states of a dynamical system governed by *unknown* temporal partial differential equations (PDEs) using only a short trajectory. While standard transformers provide a natural black-box solution to this task, the presence of a well-structured evolution operator in the data suggests a more tailored and efficient approach. Specifically, when the PDE is fully known, classical numerical solvers can evolve the state accurately with only a few parameters. Building on this observation, we introduce DISCO, a model that uses a large hypernetwork to process a short trajectory and generate the parameters of a much smaller operator network, which then predicts the next states through time integration. Our framework decouples dynamics estimation -- i.e., DISCovering an evolution Operator from a short trajectory -- from state prediction -- i.e., evolving this operator. Experiments show that pretraining our model on diverse physics datasets achieves state-of-the-art performance while requiring significantly fewer epochs. Moreover, it generalizes well to unseen initial conditions and remains competitive when fine-tuned on downstream tasks.

Physics-informed neural networks (PINNs) aim to constrain the outputs and gradients of deep learning models to satisfy specified governing physics equations, which have demonstrated significant potential for solving partial differential equations (PDEs). Although existing PINN methods have achieved pleasing performance, they always treat both easy and hard sample points indiscriminately, especially ones in the physical boundaries. This easily causes the PINN model to fall into undesirable local minima and unstable learning, thereby resulting in an Unbalanced Prediction Problem (UPP). To deal with this daunting problem, we propose a novel framework named Cognitive Physical Informed Neural Network (CoPINN) that imitates the human cognitive learning manner from easy to hard. Specifically, we first employ separable subnetworks to encode independent one-dimensional coordinates and apply an aggregation scheme to generate multi-dimensional predicted physical variables. Then, during the training phase, we dynamically evaluate the difficulty of each sample according to the gradient of the PDE residuals. Finally, we propose a cognitive training scheduler to progressively optimize the entire sampling regions from easy to hard, thereby embracing robustness and generalization against predicting physical boundary regions. Extensive experiments demonstrate that our CoPINN achieves state-of-the-art performance, particularly significantly reducing prediction errors in stubborn regions.

Implicit neural representation (INR) has now been thrust into the limelight with its flexibility in high-fidelity flow field reconstruction tasks. However, the lack of standard benchmarking datasets and the grid independence assumption for INR-based methods hinder progress and adoption in real-world simulation scenarios. Moreover, naive adoptions of existing INR frameworks suffer from limited accuracy in capturing fine-scale structures and spatiotemporal dynamics. Tacking these issues, we first introduce HFR-Beach, a 5.4 TB public large-scale CFD dataset with 33,600 unsteady 2D and 3D vector fields for reconstructing high-fidelity flow fields. We further present PEINR, a physics-enhanced INR framework, to enrich the flow fields by concurrently enhancing numerical-precision and grid-resolution. Specifically, PEINR is mainly composed of physical encoding and transformer-based spatiotemporal fuser (TransSTF). Physical encoding decouples temporal and spatial components, employing Gaussian coordinate encoding and localized encoding techniques to capture the nonlinear characteristics of spatiotemporal dynamics and the stencil discretization of spatial dimensions, respectively. TransSTF fuses both spatial and temporal information via transformer for capturing long-range temporal dependencies. Qualitative and quantitative experiments and demonstrate that PEINR outperforms state-of-the-art INR-based methods in reconstruction quality.