This paper investigates the problem of learning mesh-based physical simulations, which is a crucial task with applications in fluid mechanics and aerodynamics. Recent works typically utilize graph neural networks (GNNs) to produce next-time states on irregular meshes by modeling interacting dynamics, and then adopt iterative rollouts for the whole trajectories. However, these methods cannot achieve satisfactory performance in long-term predictions due to the failure of capturing long-term dependency and potential error accumulations. To tackle this, we introduce a new future-to-present learning perspective, and further develop a simple yet effective approach named Foresight And Interpolation (FAIR) for long-term mesh-based simulations. The main idea of our FAIR is to first learn a graph ODE model for coarse long-term predictions and then refine short-term predictions via interpolation. Specifically, FAIR employs a continuous graph ODE model that incorporates past states into the evolution of interacting node representations, which is capable of learning coarse long-term trajectories under a multi-task learning framework. Then, we leverage a channel aggregation strategy to summarize the trajectories for refined short-term predictions, which can be illustrated using an interpolation process. Through pyramid-like alternative propagation between the foresight step and refinement step, our proposed framework FAIR can generate accurate long-term trajectories, achieving a significant error reduction compared with the best baseline on four benchmark datasets. Extensive ablation studies and visualization further validate the superiority of our proposed FAIR.

This paper studies the problem of modeling multi-agent dynamical systems, where agents could interact mutually to influence their behaviors. Recent research predominantly uses geometric graphs to depict these mutual interactions, which are then captured by powerful graph neural networks (GNNs). However, predicting interacting dynamics in challenging scenarios such as out-of-distribution shift and complicated underlying rules remains unsolved. In this paper, we propose a new approach named Prototypical Graph ODE (PGODE) to address the problem. The core of PGODE is to incorporate prototype decomposition from contextual knowledge into a continuous graph ODE framework. Specifically, PGODE employs representation disentanglement and system parameters to extract both object-level and system-level contexts from historical trajectories, which allows us to explicitly model their independent influence and thus enhances the generalization capability under system changes. Then, we integrate these disentangled latent representations into a graph ODE model, which determines a combination of various interacting prototypes for enhanced model expressivity. The entire model is optimized using an end-to-end variational inference framework to maximize the likelihood. Extensive experiments in both in-distribution and out-of-distribution settings validate the superiority of PGODE compared to various baselines.

Due to the excellent computing efficiency, learning to hash has acquired broad popularity for Big Data retrieval. Although supervised hashing methods have achieved promising performance recently, they presume that all training samples are appropriately annotated. Unfortunately, label noise is ubiquitous owing to erroneous annotations in real-world applications, which could seriously deteriorate the retrieval performance due to imprecise supervised guidance and severe memorization of noisy data. Here we propose a comprehensive method DIOR to handle the difficulties of learning to hash with label noise. DIOR performs partitions from two complementary levels, namely sample level and parameter level. On the one hand, DIOR divides the dataset into a labeled set with clean samples and an unlabeled set with noisy samples using an ensemble of perturbed views. Then we train the network in a contrastive semi-supervised manner by reconstructing label embeddings for both reliable supervision of clean data and sufficient exploration of noisy data. On the other hand, inspired by recent pruning techniques, DIOR divides the parameters in the hashing network into crucial parameters and non-crucial parameters, and then optimizes them separately to reduce the overfitting of noisy data. Extensive experiments on four popular benchmark datasets demonstrate the effectiveness of DIOR.

Leading graph ordinary differential equation (ODE) models have offered generalized strategies to model interacting multi-agent dynamical systems in a data-driven approach. They typically consist of a temporal graph encoder to get the initial states and a neural ODE-based generative model to model the evolution of dynamical systems. However, existing methods have severe deficiencies in capacity and efficiency due to the failure to model high-order correlations in long-term temporal trends. To tackle this, in this paper, we propose a novel model named High-order graph ODE (HOPE) for learning from dynamic interaction data, which can be naturally represented as a graph. It first adopts a twin graph encoder to initialize the latent state representations of nodes and edges, which consists of two branches to capture spatio-temporal correlations in complementary manners. More importantly, our HOPE utilizes a second-order graph ODE function which models the dynamics for both nodes and edges in the latent space respectively, which enables efficient learning of long-term dependencies from complex dynamical systems. Experiment results on a variety of datasets demonstrate both the effectiveness and efficiency of our proposed method.

Modeling interacting dynamical systems, such as fluid dynamics and intermolecular interactions, is a fundamental research problem for understanding and simulating complex real-world systems. Many of these systems can be naturally represented by dynamic graphs, and graph neural network-based approaches have been proposed and shown promising performance. However, most of these approaches assume the underlying dynamics does not change over time, which is unfortunately untrue. For example, a molecular dynamics can be affected by the environment temperature over the time. In this paper, we take an attempt to provide a probabilistic view for time-varying dynamics and propose a model Context-attended Graph ODE (CARE) for modeling time-varying interacting dynamical systems. In our CARE, we explicitly use a context variable to model time-varying environment and construct an encoder to initialize the context variable from historical trajectories. Furthermore, we employ a neural ODE model to depict the dynamic evolution of the context variable inferred from system states. This context variable is incorporated into a coupled ODE to simultaneously drive the evolution of systems. Comprehensive experiments on four datasets demonstrate the effectiveness of our proposed CARE compared with several state-of-the-art approaches.