COGENT: Continuous Graph Emulators with Neural Ordinary Differential Equations for Long-Term Physical Forecasting
2026-06-09 • Machine Learning
Machine Learning
AI summaryⓘ
The authors developed COGENT, a tool that predicts how physical systems change over time using a special kind of math model called Neural Ordinary Differential Equations combined with graph-based data. This approach lets them forecast future states continuously at any time point, rather than fixed steps, and handles irregular map-like data well. They tested it on ice-sheet simulations and found it gave more stable and accurate long-term predictions than previous methods. Their training method also helps the model learn better for longer time forecasts.
Neural Ordinary Differential EquationsGraph Neural NetworksPhysical forecastingIrregular geospatial meshesLong-term predictionLatent dynamical systemIce-sheet simulationRollout horizonResidual decoder
Authors
Zesheng Liu, Maryam Rahnemoonfar
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.