Lorenz System Time Series Across Multiple Parameter Regimes

Dataset Description The datasets consist of simulated trajectories of the Lorenz system generated using MATLAB. Data generation details: Numerical integration performed using the ODE45 solver with multistep integration Initial conditions sampled uniformly at random from the interval [0, 1] System parameter (ρ) range: 5 to 225 Simulation time span: 1 to 500 Time step: 0.05 Number of simulations: 10 independent runs for each ρ value Length per simulation: 19,810 data points Datasets: Training dataset: 891,450 data points Testing dataset: 891,450 data points Training and testing sets are generated independently Noise model: At each simulation step, additive Gaussian noise is injected into all state variables These datasets are intended for evaluating regime-dependent predictability and long-term forecasting performance of sequence models under parameter variations.