Viviana Acquaviva

Gabriele Accarino, Juan Nathaniel, Carla Roesch et al.

Accurate emulation of multi-scale physical systems governed by PDEs demands models that remain stable over long autoregressive rollouts while preserving fine-scale structures. Deterministic emulators produce overly-smoothed predictions, while generative approaches better capture details but are costly. Latent-space generative models have emerged as a compromise but with the additional cost of separately pre-trained autoencoders. We propose Wavelet Flow Matching (WFM), a novel generative emulator that overcomes current trade-offs between cost and skill by performing optimal-transport directly in the multi-scale wavelet space. Rather than learning a latent compression, WFM leverages the hierarchical structure of a U-Net to jointly predict transport velocities of a prescribed wavelet representation. On three challenging systems of chaotic fluid dynamics, WFM achieves superior long-horizon stability, accuracy and spectral coherence compared to state-of-the-art models. Our results clearly position the wavelet space as an effective training-free representation for generative emulation of complex physical dynamics.

Gabriele Accarino, Viviana Acquaviva, Sara Shamekh et al.

We introduce WaveSim, a multi-scale similarity metric for the evaluation of spatial fields in weather and climate applications. WaveSim exploits wavelet transforms to decompose input fields into scale-specific wavelet coefficients. The metric is built by multiplying three orthogonal components derived from these coefficients: Magnitude, which quantifies similarities in the energy distribution of the coefficients, i.e., the intensity of the field; Displacement, which captures spatial shift by comparing the centers of mass of normalized energy distributions; and Structure, which assesses pattern organization independent of location and amplitude. Each component yields a scale-specific similarity score ranging from 0 (no similarity) to 1 (perfect similarity), which are then combined across scales to produce an overall similarity measure. We first evaluate WaveSim using synthetic test cases, applying controlled spatial and temporal perturbations to systematically assess its sensitivity and expected behavior. We then demonstrate its applicability to physically relevant case studies of key modes of climate variability in Earth System Models. Traditional point-wise metrics lack a mechanism for attributing errors to physical scales or modes of dissimilarity. By operating in the wavelet domain and decomposing the signal along independent axes, WaveSim bypasses these limitations and provides an interpretable and diagnostically rich framework for assessing similarity in complex fields. Additionally, the WaveSim framework allows users to place emphasis on a specific scale or component, and lends itself to user-specific model intercomparison, model evaluation, and calibration and training of forecasting systems. We provide a PyTorch-ready implementation of WaveSim, along with all evaluation scripts, at: https://github.com/gabrieleaccarino/wavesim.