Update README.md

README.md

@@ -10,6 +10,8 @@ Details: Each subdirectory is the base (parent) system. The files in each subdir
 
 NOTE: we are working on a larger and improved dataset, with improved filtering for chaotic behavior. Stay tuned!
 
+NOTE: the training_info.json files from our model training runs may mention "final_base40/train_z5_z10"; this was merged into "final_base40/train" which is uploaded here, containing the union of the files.
+
 Paper abstract:
 
 >Chaotic systems are intrinsically sensitive to small errors, challenging efforts to construct predictive data-driven models of real-world dynamical systems such as fluid flows or neuronal activity. Prior efforts comprise either specialized models trained separately on individual time series, or foundation models trained on vast time series databases with little underlying dynamical structure. Motivated by dynamical systems theory, we present Panda, Patched Attention for Nonlinear DynAmics. We train Panda on a novel synthetic, extensible dataset of 2 \times 10^4 chaotic dynamical systems that we discover using an evolutionary algorithm. Trained purely on simulated data, Panda exhibits emergent properties: zero-shot forecasting of unseen real world chaotic systems, and nonlinear resonance patterns in cross-channel attention heads. Despite having been trained only on low-dimensional ordinary differential equations, Panda spontaneously develops the ability to predict partial differential equations without retraining. We demonstrate a neural scaling law for differential equations, underscoring the potential of pretrained models for probing abstract mathematical domains like nonlinear dynamics.