Simulating and modeling the long-term dynamics of multi-object physical
systems is an essential and challenging task. Current studies model the
physical systems utilizing Graph Neural Networks (GNNs) with equivariant
properties. Specifically, they model the dynamics as a sequence of discrete
states with a fixed time interval and learn a direct mapping for all the two
adjacent states. However, this direct mapping overlooks the continuous nature
between the two states. Namely, we have verified that there are countless
possible trajectories between two discrete dynamic states in current GNN-based
direct mapping models. This issue greatly hinders the model generalization
ability, leading to poor performance of the long-term simulation. In this
paper, to better model the latent trajectory through discrete supervision
signals, we propose a Physics-Inspired Neural Graph ODE (PINGO) algorithm. In
PINGO, to ensure the uniqueness of the trajectory, we construct a
Physics-Inspired Neural ODE framework to update the latent trajectory.
Meanwhile, to effectively capture intricate interactions among objects, we use
a GNN-based model to parameterize Neural ODE in a plug-and-play manner.
Furthermore, we prove that the discrepancy between the learned trajectory of
PIGNO and the true trajectory can be theoretically bounded. Extensive
experiments verify our theoretical findings and demonstrate that our model
yields an order-of-magnitude improvement over the state-of-the-art baselines,
especially on long-term predictions and roll-out errors.

通过使用物理启发的神经图常微分方程算法（Physics-Inspired Neural Graph ODE），我们提出了一种更好地建模离散监督信号下潜在轨迹的方法，同时利用基于 GNN 的模型以插拔的方式对神经图常微分方程进行参数化，实验证明我们的模型在长期预测和演化误差方面相较于现有方法有数量级的提升。

受物理启发的神经图 ODE 用于长期动态仿真

Physics-Inspired Neural Graph ODE for Long-term Dynamical Simulation

We present a video generation model that accurately reproduces object motion,
changes in camera viewpoint, and new content that arises over time. Existing
video generation methods often fail to produce new content as a function of
time while maintaining consistencies expected in real environments, such as
plausible dynamics and object persistence. A common failure case is for content
to never change due to over-reliance on inductive biases to provide temporal
consistency, such as a single latent code that dictates content for the entire
video. On the other extreme, without long-term consistency, generated videos
may morph unrealistically between different scenes. To address these
limitations, we prioritize the time axis by redesigning the temporal latent
representation and learning long-term consistency from data by training on
longer videos. To this end, we leverage a two-phase training strategy, where we
separately train using longer videos at a low resolution and shorter videos at
a high resolution. To evaluate the capabilities of our model, we introduce two
new benchmark datasets with explicit focus on long-term temporal dynamics.

本研究提出了一种视频生成模型，通过重新设计时域隐变量表示和学习长期一致性并进行长时间分辨率分别为低和高的两阶段训练策略来优化生成视频的时序一致性，所得的模型经过新的基准数据集的测试，取得了良好的效果。

生成动态场景的长视频

Generating Long Videos of Dynamic Scenes

Learning long-term dynamics models is the key to understanding physical
common sense. Most existing approaches on learning dynamics from visual input
sidestep long-term predictions by resorting to rapid re-planning with
short-term models. This not only requires such models to be super accurate but
also limits them only to tasks where an agent can continuously obtain feedback
and take action at each step until completion. In this paper, we aim to
leverage the ideas from success stories in visual recognition tasks to build
object representations that can capture inter-object and object-environment
interactions over a long-range. To this end, we propose Region Proposal
Interaction Networks (RPIN), which reason about each object's trajectory in a
latent region-proposal feature space. Thanks to the simple yet effective object
representation, our approach outperforms prior methods by a significant margin
both in terms of prediction quality and their ability to plan for downstream
tasks, and also generalize well to novel environments. Code, pre-trained
models, and more visualization results are available at this https URL

本论文通过 Region Proposal Interaction Networks 的方法在潜在区域建立对象表示来捕捉对象间和对象环境交互，并在长期预测中尤为有效，提高了预测质量和规划下游任务的能力，同时在新环境中具有良好的泛化性能。