FLUXtrapolation: A benchmark on extrapolating ecosystem fluxes

Many biological systems evolve through continuous local dynamics while switching between latent regimes defined by learning, stimulus context, internal state, or developmental stage. These processes are often observed only as unpaired longitudinal snapshots: the same cells, neurons, or animals are not tracked as matched trajectories, even though population states are sampled across successive stages. This creates two coupled challenges. First, trajectories must respect curved low-dimensional manifolds embedded in high-dimensional biological measurements. Second, the model must identify when the transport mechanism itself changes. We introduce FLUX (FLow matching for Unpaired longitudinal data with miXture-of-experts), a geometry-aware longitudinal flow-matching framework for joint transport modeling and unsupervised regime discovery. FLUX learns a data-dependent metric from pooled labeled and unlabeled observations, uses that metric to construct geometry-aware conditional paths between adjacent marginals, and decomposes the resulting velocity field into sparse expert vector fields selected by a Straight-Through Gumbel-Softmax router. Across manifold controls, a regime-switching Lorenz system, widefield cortical calcium imaging during associative learning, and embryoid body single-cell differentiation, FLUX reconstructs longitudinal transport while recovering interpretable regime structure. Ablations show that mixture-of-experts routing alone is insufficient: FLUX without geometric learning can fit local transport but fails or weakens regime discovery when regimes are encoded in local dynamics. These results suggest that geometry-aware velocity decomposition provides a general strategy for discovering latent biological state transitions from unpaired longitudinal snapshots.

High-resolution regional climate simulations provide critical information for climate impacts assessments but remain computationally expensive, motivating the development of machine-learning downscalers and emulators. A key challenge is determining how limited high-resolution simulations should be distributed across a changing climate trajectory to capture both forced climate response and internal variability. Using the CESM2 Large Ensemble over the western United States, we compare three training-year selection strategies under fixed data budgets: a contiguous block of historical years, years drawn from both the beginning and end of the simulation period, and years distributed throughout the full climate trajectory. Including both historical and future years consistently outperforms training on historical years alone, demonstrating the importance of exposing downscaling models to climate states outside the historical record and highlighting limitations of stationarity assumptions common in statistical downscaling. Training on years distributed throughout the full climate trajectory performs best overall, indicating that broad sampling of internal variability provides additional information beyond exposure to the forced climate response alone. Models trained on temporally distributed subsets more successfully reproduce variability in unseen ensemble members while retaining strong performance across a wide range of climate diagnostics. Even when trained on only one-tenth of the available high-resolution years, temporally distributed models remain highly competitive with full-data training. These results suggest that, under fixed computational budgets, broad sampling of climate states is more valuable than temporal continuity when allocating scarce high-resolution simulations. The findings provide practical guidance for regional climate downscaling and large-ensemble projection workflows.

Climate emulation is an out-of-distribution (OOD) projection task. This is precisely the challenge where modern Machine Learning (ML) methods are most prone to failure. Consequently, while current ML emulators trained on present climate achieve high in-distribution performance, their future reliability under the inevitable distribution shifts of a changing climate remains a critical, poorly understood blind spot. Addressing this challenge requires a fundamental shift in how we understand, evaluate, and design climate emulators. In this work, we first confirm that climate change drives a statistically significant and progressively growing shift in atmospheric state distributions, rendering standard evaluation protocols insufficient. We empirically establish that seasonal variation serves as an effective proxy for these long-term climate shifts, providing access to $\textit{real-world}$ distribution shifts without recourse to heuristics like synthetic perturbations. Motivated by this link, we introduce a novel evaluation framework that leverages seasonal shifts as a rigorous, zero-overhead testbed for emulator robustness. Our systematic characterisation confirms that current state-of-the-art hybrid-ML emulators degrade significantly under these realistic shifts. Finally, we chart a path forward by identifying compositional generalisation, the ability to form novel combinations from observed elementary components, as a principled route towards robust climate emulation. We demonstrate that physically motivated decompositions substantially improve OOD performance with only modest trade-offs against in-distribution performance, providing an avenue towards ML-driven climate emulators robust to an unknown future.