Physics-Constrained Adaptive Flow Matching for Climate Downscaling

Regional climate information at kilometer scales is essential for assessing the impacts of climate change, but generating it with global climate models is too expensive due to their high computational costs. Machine learning models offer a fast alternative, yet they often violate basic physical laws and degrade when applied to climates outside of their training distribution. We present Physics-Constrained Adaptive Flow Matching (PC-AFM), a generative downscaling model that addresses both problems. Building on the Adaptive Flow Matching (AFM) model of Fotiadis et al. (2025) as our baseline, we add soft conservation constraints that keep the downscaled output consistent with the large-scale input for precipitation and humidity, and use gradient surgery via the ConFIG algorithm to prevent these constraints from interfering with the generative objective. We train the model on Central Europe climate data, evaluate it on a 10-time downscaling task (63km to 6.3km) over six variables (near-surface temperature, precipitation, specific humidity, surface pressure, and horizontal wind components) across a comprehensive set of metrics including bias, ensemble skill scores, power spectra, and conservation error, and test the generalization on two held-out climate regions. Within the training distribution, PC-AFM reduces conservation errors and improves ensemble calibration while matching the baseline on standard skill metrics. Outside the training distribution, where unconstrained models develop large systematic errors by extrapolating learned statistics, PC-AFM halves precipitation wet bias, reduces conservation error and improves extreme-quantile accuracy, all without any information about the target climate at inference time. These results indicate that physical consistency is a practical requirement for deploying generative downscaling models in real-world applications.

Bootstrap aggregation and confidence measures to improve time series causal discovery

Causal discovery methods have demonstrated the ability to identify the time series graphs representing the causal temporal dependency structure of dynamical systems. However, they do not include a measure of the confidence of the estimated links. Here, we introduce a novel bootstrap aggregation (bagging) and confidence measure method that is combined with time series causal discovery. This new method allows measuring confidence for the links of the time series graphs calculated by causal discovery methods. This is done by bootstrapping the original times series data set while preserving temporal dependencies. Next to confidence measures, aggregating the bootstrapped graphs by majority voting yields a final aggregated output graph. In this work, we combine our approach with the state-of-the-art conditional-independence-based algorithm PCMCI+. With extensive numerical experiments we empirically demonstrate that, in addition to providing confidence measures for links, Bagged-PCMCI+ improves the precision and recall of its base algorithm PCMCI+. Specifically, Bagged-PCMCI+ has a higher detection power regarding adjacencies and a higher precision in orienting contemporaneous edges while at the same time showing a lower rate of false positives. These performance improvements are especially pronounced in the more challenging settings (short time sample size, large number of variables, high autocorrelation). Our bootstrap approach can also be combined with other time series causal discovery algorithms and can be of considerable use in many real-world applications, especially when confidence measures for the links are desired.