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Terrestrial ecosystems constitute a major component of the global carbon sink and play a critical role in regulating the global carbon cycle. Although process-based models such as the Ecosystem Demography (ED) model are widely used to simulate these dynamics and widely adopted in research and applications, they remain computationally intensive and are not well suited for large-scale (e.g., global) projections at high spatial and temporal resolution, or under wide-range of future scenarios. AI-based emulators of process-based physical models have emerged as promising ways to accelerate the computation. However, there are several challenges in developing emulators for ecosystem processes, including error accumulation over long sequences, single-step initial conditions, and high-dimensional environmental conditions. Existing works often rely on time-series patterns in look-back windows, which are not well-suited for the problem with single-step initial conditions. Moreover, they often do not consider uncertainty, making it hard to know when the approximations are highly confident and when the results may need to be updated, e.g., by the process-based models. To address these limitations, we introduce EcoDiffusion, a conditional diffusion framework tailored for ecosystem dynamics emulation. We evaluated EcoDiffusion at locations distributed worldwide under different scenarios and showed that it demonstrated significant improvements over existing models. 

Environmental modeling faces critical challenges in predicting ecosystem dynamics across unmonitored regions due to limited and geographically imbalanced observation data. This challenge is compounded by spatial heterogeneity, causing models to learn spurious patterns that fit only local data. Unlike conventional domain generalization, environmental modeling must preserve invariant physical relationships and temporal coherence during augmentation. In this paper, we introduce Generalizable Representation Enhancement via Auxiliary Transformations (GREAT), a framework that effectively augments available datasets to improve predictions in completely unseen regions. GREAT guides the augmentation process to ensure that the original governing processes can be recovered from the augmented data, and the inclusion of the augmented data leads to improved model generalization. Specifically, GREAT learns transformation functions at multiple layers of neural networks to augment both raw environmental features and temporal influence. They are refined through a novel bi-level training process that constrains augmented data to preserve key patterns of the original source data. We demonstrate GREAT's effectiveness on stream temperature prediction across six ecologically diverse watersheds in the eastern U.S., each containing multiple stream segments. Experimental results show that GREAT significantly outperforms existing methods in zero-shot scenarios. This work provides a practical solution for environmental applications where comprehensive monitoring is infeasible. 

A dynamical low-rank approximation is developed for reduced-order modelling (ROM) of the filtered density function (FDF) transport equation, which is utilised for large eddy simulation (LES) of turbulent reacting flows. In this methodology, the evolution of the composition matrix describing the FDF transport via a set of Langevin equations is con- strained to a low-rank matrix manifold. The composition matrix is approximated using a low-rank factorisation, which consists of two thin, time-dependent matrices repre- senting spatial and composition bases, along with a small time-dependent coefficient matrix. The evolution equations for spatial and composition subspaces are derived by projecting the composition transport equation onto the tangent space of the low-rank matrix manifold. Unlike conventional ROMs, such as those based on principal com- ponent analysis, both subspaces are time-dependent and the ROM does not require any prior data to extract the low-dimensional subspaces. As a result, the constructed ROM adapts on the fly to changes in the dynamics. For demonstration, LES via the time-dependent bases (TDB) is conducted of the canonical configuration of a tempo- rally developing planar CO/H2 jet flame. The flame is rich with strong flame-turbulence interactions resulting in local extinction followed by re-ignition. The combustion chem- istry is modelled via the skeletal kinetics, containing 11 species with 21 reaction steps. It is shown that the FDF-TDB yields excellent predictions of various sta