Toy dataset for the CODES benchmark (https://github.com/robin-janssen/CODES-Benchmark). Five-species coupled ODE system. The system features some soft non-linear effects and does not conserve abundances. The following system of equations describes the dynamics: # Rate constants k1, k2, k3, k4 = 0.7, 0.3, 0.4, 0.2 k5, k6 = 0.25, 0.15 influx = 0.1 # Interaction terms rate1 = k1 * s1 * (1 - s1) # Logistic-like self-regulation rate2 = k2 * s2 * s3 # Simple interaction between s2 and s3 rate3 = k3 * s4 * (1 - 0.1 * s4) # Mild quadratic feedback for saturation rate4 = k4 * s5 * s2 # Interaction between s5 and s2 rate5 = k3 * s4 # Loss terms decay1 = k5 * s1 decay2 = k6 * s3 # Derivatives ds1_dt = influx + rate1 - decay1 # s1 has an external source and self-regulation ds2_dt = rate2 - 0.5 * s2 # s2 grows via interaction with s3 and has linear damping ds3_dt = -rate2 + rate5 - decay2 # s3 is consumed by s2 but replenished by s4 ds4_dt = rate3 - 0.1 * s4 # Simple growth and decay for stability ds5_dt = rate4 - 0.2 * s5 # Simple linear decay 101 timesteps in the interval [0, 10], solved with scipy.integrate.solve_ivp with the DOP853 method (atol = rtol = 1e-8). Initial conditions for each species sobol-sampled in the interval (0.1, 10). 700/100/200 train/test/val samples.