COGENT: Continuous Graph Emulators with Neural Ordinary Differential Equations for Long-Term Physical Forecasting

2026-06-09

AI Summary

This work addresses the challenges of error accumulation and temporal discretization inherent in autoregressive models for long-term forecasting of physical systems on irregular geospatial grids. To overcome these limitations, the authors propose a unified framework that integrates graph neural networks with neural ordinary differential equations. The approach employs a history encoder to extract spatiotemporal context vectors, which drive a continuous latent dynamical system; a residual decoder then directly predicts physical states at arbitrary time points, circumventing recursive inference. A progressive rollout scheduling strategy is introduced to enhance training stability over extended horizons. Evaluated on ice sheet simulation tasks, the model significantly outperforms autoregressive graph-based baselines, demonstrating superior long-term prediction stability and the ability to query states at any desired time instant.

Abstract

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.

Problem

• long-term physical forecasting
• irregular geospatial meshes
• continuous-time prediction
• physical simulation emulation
• long-horizon stability

Innovation

• Neural Ordinary Differential Equations
• Graph Neural Networks
• Continuous-time Forecasting
• Irregular Meshes
• Long-term Physical Simulation