COGENT: Continuous Graph Emulators with Neural Ordinary Differential Equations for Long-Term Physical Forecasting
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.
AI Impact Assessments
(1 models)Scientific Impact Assessment: COGENT
1. Core Contribution
COGENT introduces a continuous-time graph neural emulator that combines Neural Ordinary Differential Equations (Neural ODEs) with graph-based spatial representations for long-horizon physical forecasting on irregular meshes. The key innovation is replacing discrete autoregressive or multi-horizon prediction with a latent ODE that evolves continuously, conditioned on encoded historical context, interpolated future forcings, static embeddings, and relative rollout time. This allows predictions at arbitrary future times without recursive feeding of predictions back into the model.
The three main novelties are: (1) a continuous latent trajectory replacing discrete forecast heads, (2) a non-autonomous graph ODE conditioned on the full future forcing path during integration, and (3) history-context and relative-time conditioning injected at every solver evaluation. The paper also proposes effective rollout-horizon sampling with a long-horizon-biased distribution and a progressive rollout-horizon scheduling strategy for training stabilization.
2. Methodological Rigor
The methodology is technically coherent and well-structured. The architecture cleanly separates spatial encoding (GraphSAGE), temporal aggregation (Transformer), latent initialization, continuous ODE integration, and residual decoding. The formulation is clearly presented with consistent notation.
However, several aspects limit confidence in the rigor:
3. Potential Impact
The paper addresses a real need in scientific computing: accelerating long-horizon physical simulations while maintaining accuracy on irregular meshes. Ice-sheet modeling is an important application for climate science, and faster emulators could enable ensemble forecasting and uncertainty quantification for sea-level rise projections.
The continuous-time formulation is architecturally appealing for several reasons: it decouples the model from specific temporal discretizations, it avoids autoregressive error accumulation in the physical state space, and it can query predictions at arbitrary times. These properties could be valuable beyond glaciology—in weather prediction, fluid dynamics, or other mesh-based simulations.
However, the actual demonstrated impact is narrow. The improvements, while meaningful (26.3% reduction in aggregate whole-trajectory RMSE over the best baseline), are shown on a single dataset with a specific mesh configuration. The arbitrary-time querying capability, frequently highlighted as an advantage, is never actually evaluated quantitatively.
4. Timeliness & Relevance
The paper addresses a current trend at the intersection of scientific machine learning and climate science. Neural ODEs for physical emulation and graph-based surrogate models are active research areas. The specific focus on ice-sheet dynamics is timely given the urgency of understanding sea-level rise under climate change.
The progressive rollout-horizon scheduling is a practical contribution for training Neural ODEs on long sequences, addressing known instability issues. This technique could be independently useful.
5. Strengths & Limitations
Strengths:
Limitations:
Overall Assessment
COGENT presents a well-designed architecture that makes sensible choices for continuous-time physical emulation on graphs. The progressive training strategy and the combination of Neural ODEs with graph networks for this specific problem class are novel. However, the empirical evaluation is too narrow—both in application domain and baseline comparisons—to convincingly support the paper's broad claims. The absence of computational analysis, arbitrary-time evaluation, and multi-domain testing leaves significant gaps. The paper represents a reasonable incremental advance in graph-based scientific emulation, but the demonstrated impact does not yet match the ambition of the framing.
Generated Jun 10, 2026
Comparison History (21)
Paper 2 introduces a highly novel methodological framework combining Graph Neural Networks and Neural ODEs for continuous-time physical forecasting. This approach addresses critical challenges in long-term simulation stability and arbitrary time querying, offering broad applicability across climate modeling, fluid dynamics, and other physical sciences. While Paper 1 addresses an important clinical problem with rigorous methodology, it relies on more established ML techniques. Paper 2's fundamental innovation in geometric deep learning and dynamic systems suggests a wider theoretical and cross-disciplinary impact.
Paper 2 addresses a broader and more widely applicable problem—multimodal learning with missing modalities—relevant across many fields including bioscience, healthcare, and general machine learning. Its framework (LWR) offers a principled, generalizable solution applicable to diverse multi-omics and clinical settings. Paper 1, while methodologically rigorous, targets a narrower domain (ice-sheet simulation on irregular meshes). Paper 2's potential for cross-disciplinary impact in precision medicine and its relevance to the growing multimodal learning community give it higher estimated scientific impact.
Paper 1 is more methodologically novel and broadly impactful: it unifies graph neural operators with history-conditioned latent Neural ODE dynamics for continuous-time forecasting on irregular meshes, enabling arbitrary-time queries and stable long-horizon rollouts—capabilities directly relevant to scientific computing and earth-system modeling. Its application to ice-sheet simulation emulation targets high-stakes climate/sea-level prediction, increasing real-world relevance and timeliness. Paper 2 is practically valuable for tabular continual anomaly detection, but its components (shared embedding, augmentation, replay/distillation, outlier exposure) are more incremental and narrower in cross-field scientific impact than continuous-time mesh-based physical emulation.
Paper 2 addresses a fundamental limitation in neural relational inference—oversimplified graph priors—with a novel diffusion-based calibration framework that is architecture-agnostic and applicable across multiple NRI methods. Its broader applicability to structure discovery problems, methodological novelty in reframing prior learning as denoising calibration, and demonstrated generalizability across architectures give it wider potential impact. Paper 1, while solid, is more application-specific (ice-sheet simulations) and represents a more incremental combination of existing techniques (graph networks + Neural ODEs).
Paper 2 addresses a critical real-world problem—long-term physical forecasting and climate modeling (ice-sheet simulations)—which has profound implications for climate science and physics. Its synthesis of Graph Neural Networks and Neural ODEs for irregular meshes offers broad applicability across scientific domains. In contrast, Paper 1 focuses on chess, which serves as a valuable AI benchmark but has significantly lower potential for direct real-world scientific and societal impact.
Paper 2 has higher potential impact: it introduces a broadly applicable ML framework (continuous-time graph Neural ODE emulator) for long-term forecasting on irregular meshes, a need spanning climate/earth systems, CFD, and geoscience. The ability to query arbitrary future times and improved long-horizon stability are timely and practically valuable for surrogate modeling. Paper 1 is methodologically rigorous with strong regret guarantees and novelty in learning both sides’ choice models, but its impact is more specialized to two-sided platform assortment/revenue management. Paper 2’s cross-domain applicability and timeliness likely yield wider scientific uptake.
Paper 2 addresses a foundational issue in machine learning uncertainty quantification. By introducing a novel, strictly stronger calibration metric and theoretical proofs, its impact spans across all high-stakes ML applications (e.g., medicine, autonomous systems). Paper 1 is valuable for physical modeling, but has a narrower methodological and application scope.
Paper 2 (COGENT) has higher potential scientific impact due to stronger methodological novelty (continuous-time graph emulation via Neural ODEs for irregular meshes), broader applicability across scientific domains (climate/earth systems, CFD, geophysics, any PDE-like forecasting on meshes), and high real-world relevance (long-horizon physical forecasting and emulation for expensive simulators). Paper 1 (MURMUR) is a solid systems contribution with clear practical value for ASR latency/accuracy, but is more incremental and narrower in cross-field impact compared to a general modeling framework for scientific forecasting.
Paper 2 presents a highly novel methodological framework combining Graph Neural Networks and Neural ODEs for physical forecasting. Its ability to handle irregular meshes and generate continuous-time predictions offers broad applicability across the physical sciences, including critical climate modeling applications like ice-sheet simulation. In contrast, Paper 1 is an applied case study utilizing standard machine learning models for a highly specific operational aviation problem, limiting its broader scientific impact.
Paper 2 likely has higher impact: it targets a central, timely problem—preference alignment for large text-to-image flow models—at the frontier of generative AI deployment. Its surrogate-trajectory framework unifies and generalizes prior connector/direct-gradient methods, offers a clear design space, and directly addresses key scalability pathologies (memory and gradient explosion). It is evaluated on widely used, high-profile model families, increasing reproducibility and downstream adoption across ML, vision, and alignment research. Paper 1 is innovative but more domain-specific (ice-sheet/mesh forecasting), with narrower immediate cross-field reach.