Mechanism Learning through Prototype-Anchored Dynamics

We study mechanism learning for scientific forecasting: constructing an explicit description of local evolution and learning to use it in prediction. Prototype anchoring builds this dynamics descriptor from a finite bank of reusable support patterns. We instantiate this approach using local predictor coefficients in Burgers, observed increment patterns in WeatherBench 2 (WB2), and learned support vectors in Lorenz96. Three sets of experiments assess predictive utility, the contribution of anchoring, and the descriptor's dynamical meaning. First, across 20 shared seeds on a two-variable WB2 task at $+72$ h, the full model reduces temperature RMSE by $0.010$ K and Z500 RMSE by $45.6$ m${}^2$ s${}^{-2}$ relative to an approximately parameter-matched direct predictor (paired 95% CIs $[0.007,0.013]$ and $[42.1,49.1]$). Both contrasts remain significant after Holm correction. Second, finite support improves temperature forecasts over a learned descriptor generator with 20% and 50% of the training data; its effect varies with target and sample size. Third, Burgers descriptors align with independently computed PDE quantities after history matching and viscosity-pair/time controls (within-stratum partial rank correlation $0.210$), and shuffling them increases one-step RMSE by $0.0094$ (95% CI $[0.0057,0.0142]$). Matched swaps provide no clear evidence that descriptor changes reproduce the direction of dynamical change. These findings support an empirical form of mechanism learning: descriptors can organize local dynamics and contribute to prediction, while the value of prototype anchoring depends on the forecasting regime.