CODES Dataset: lv_parametric

Dataset for the CODES benchmark (https://github.com/robin-janssen/CODES-Benchmark). This dataset was designed to test variations of the architectures that can take additional ODE parameters as inputs. It is related to lv_parametric_no_params, which contains the same trajectories, but not the parameter alpha used to generate them. This enables comparison between providing the architecture with the additional information that is the value of the parameter, and leaving out this additional information. Lotka-Volterra predator-prey model with three predators (p1, p2, p3) and three prey (q1, q2, q3), as well as a parameter alpha, which modifies reproduction and predation coefficients. The system is defined by its gradients as follows: # --- reproduction rates (prey) --- # baseline: 0.5, 0.6, 0.4 rep_p1 = 0.5 * (1.0 - alpha) * p1 rep_p2 = 0.6 * (1.0 - alpha) * p2 rep_p3 = 0.4 * (1.0 - alpha) * p3 # --- predation terms --- # baseline coefficients: 0.02, 0.01, 0.03, 0.015, 0.01, 0.025 pred1 = (0.02 * (1.0 + alpha)) * p1 * q1 + (0.01 * (1.0 + alpha)) * p1 * q2 pred2 = (0.03 * (1.0 + alpha)) * p2 * q1 + (0.015 * (1.0 + alpha)) * p2 * q3 pred3 = (0.01 * (1.0 + alpha)) * p3 * q2 + (0.025 * (1.0 + alpha)) * p3 * q3 # --- predator death rates (unchanged) --- death_q1 = 0.1 * q1 death_q2 = 0.08 * q2 death_q3 = 0.12 * q3 # --- predator gains (unchanged) --- gain_q1 = 0.005 * p1 * q1 + 0.007 * p2 * q1 gain_q2 = 0.006 * p1 * q2 + 0.009 * p3 * q2 gain_q3 = 0.008 * p2 * q3 + 0.01 * p3 * q3 # --- derivatives --- dp1_dt = rep_p1 - pred1 dp2_dt = rep_p2 - pred2 dp3_dt = rep_p3 - pred3 dq1_dt = -death_q1 + gain_q1 dq2_dt = -death_q2 + gain_q2 dq3_dt = -death_q3 + gain_q3 return np.array([dp1_dt, dp2_dt, dp3_dt, dq1_dt, dq2_dt, dq3_dt]) 101 timesteps in the interval [0, 100], solved with scipy.integrate.solve_ivp with the DOP853 method (atol = rtol = 1e-8). Initial conditions for each species sampled in log-space between 1 and 10, while alpha was sampled linearly between 0 and 1. Initial conditions and the parameter were jointly Sobol-sampled. 350/50/100 train/test/val samples.