In this work, we present COGENT, a continuous graph emulator with Neural Ordinary Differential Equations for long-term physical forecasting on irregular geospatial meshes. COGENT encodes a finite history of system states and associated forcing fields and external forcings with a graph-based history encoder, producing node-wise context vectors that capture both local spatial interactions and temporal evolution. These context vectors initialize and condition a latent Neural Ordinary Differential Equation whose dynamics are driven by interpolated future forcings and explicit relative rollout time. By modeling the forecast trajectory as a continuous latent dynamical system, COGENT can generate predictions at arbitrary future times rather than being restricted to a fixed temporal discretization. A residual decoder maps the resulting latent trajectories back to future physical states, enabling direct multi-step forecasting without repeatedly feeding predicted states back into the model. This formulation combines graph-based spatial representation, history-conditioned latent dynamics, and continuous-time rollout in a unified framework for mesh-based physical simulation emulation. In order to stabilize training with long-horizon supervision, we also propose effective rollout-horizon sampling and a progressive rollout-horizon scheduling strategy. We evaluate COGENT on transient ice-sheet simulations generated by the Ice-sheet and Sea-level System Model, demonstrating improved long-range stability over autoregressive graph baselines. These results suggest that continuous graph Neural ODEs provide a promising methodology for scalable physical forecasting on irregular geospatial meshes, particularly in applications that require stable long-horizon predictions and the ability to query system states at arbitrary times.

翻译：本文提出了COGENT，一种结合神经常微分方程的连续图模拟器，用于不规则地理空间网格上的长期物理预测。COGENT通过基于图的历时编码器编码有限历史系统状态及相关强迫场与外部驱动力，生成节点级上下文向量，捕捉局部空间交互和时间演化。这些上下文向量初始化并约束潜在神经常微分方程，其动力学由插值的未来强迫场和显式相对展开时间驱动。通过将预测轨迹建模为连续潜在动力系统，COGENT可在任意未来时间生成预测，而非局限于固定时间离散化。残差解码器将所得潜在轨迹映射回未来物理状态，实现直接多步预测，无需反复将预测状态反馈至模型。该公式将基于图的空间表示、历史条件化潜在动力学和连续时间展开统一于框架中，用于基于网格的物理仿真模拟。为稳定长时间跨度监督下的训练，我们还提出了有效展开跨度采样和渐进式展开跨度调度策略。在冰盖与海平面系统模型生成的瞬态冰盖仿真上评估COGENT，结果表明其相较于自回归图基线方法具有更优的长期稳定性。这些成果表明，连续图神经常微分方程为不规则地理空间网格上的可扩展物理预测提供了有前景的方法论，尤其适用于需要稳定长期预测及任意时间查询系统状态的应用场景。