Replication Data for: Robustly optimal dynamics for active matter reservoir computing (Gaimann and Klopotek, 2025)

We also provide the raw chaotic time series used as benchmark driving protocols: Hénon-Heiles Rössler Chua Lorenz-96 Each dataset typically contains 400 parameter combinations. Each parameter combination contains four files: config.yaml: controlled variables simulation_output_train.h5: physical simulation observables in first (training) run simulation_output_test.h5: physical simulation observables in second (testing) run reservoir_computer_output.h5: observables related to reservoir computing and time series prediction The second run has a different chaotic driving protocol, using the same underlying dynamical system (chaotic attractor) but different initial conditions.

Only the first file is generated if the dataset contains a simulation without an external driving force (undriven). By default, for all driven simulations, physical observables are only recorded for the test run for a full reservoir computing train/test cycle. Each simulation typically consists of 1,000.00 time units (50,000 integration time steps of 0.02 time units by default).

A burn-in phase of 20.0 simulation time units (1,000 integration time steps of 0.02 time units by default) takes place at the beginning of each simulation, which is not recorded by default (only recorded in the "speed-controller, with initial transient" dataset). Controlled variables are stored as HDF5 attributes. At each step, we predict by default 25 integration time steps ahead (=0.45283 L63-Lyapunov times).

For Lyapunov times adjusted attractor predictions, we predict n integration time steps ahead that equal 0.45283 Lyapunov times of the corresponding attractor. The simulation output files contain: agent_observables: positions, velocities, total forces, velocity fluctuations for all agents; for the first 20.0 simulation time units frame_observables: driver position (external driving trajectory / input time series), center of mass (taking periodic boundary conditions into account), agent-averaged observables, scalar polarity, scalar rotation; for the full simulation histograms: binned agent observables and derived quantities; for the full simulation radially_binned: radial distribution function (agent count), connected velocity correlation, cumulative velocity correlation time_lags: auto-correlations of agent observables and derived quantities, two-time correlations of agent observables and derived quantities reference_frame_steps: reference frames (measured in integration steps) for the recording of delay-based quantities in time_lags The reservoir computer output files contain: linear_regression_model: the weights of the linear model (readout layer) observer_kernel_params: placement positions and widths of the Gaussian observation kernels predictions_train: n-steps-ahead prediction using the trained linear model, on training data predictions_test: n-steps-ahead prediction using the trained linear model, on testing data Aggregates of physical observables across all parameter combinations in a single dataset are stored as CSV files for convenience, the relevant observable is indicated by the file name.

Files that carry the "time_avg" tag are averaged over all simulation time steps, for the "ensemble_avg" averaged over all seeds (only one seed is used here), and for the "array_avg" averaged over all recorded entries (typically samples at different time steps). We provide the following aggregated observables that were processed to generate figures in our associated publication: lymburn_correlation_coefficient: Correlation coefficient, predictive performance agent_avg_msd_at_lyapunov_time_step=55: Agent-averaged mean squared displacement at the Lyapunov integration time step of the Lorenz-63 attractor (after 55 integration time steps of 0.02 each) first_local_min.array_avg.h5?connected_velocity_correlation: First local minimum of the connected velocity correlation function, averaged over all recorded samples mean_speed: Agent-averaged speed scalar_polarity: Scalar polarity scalar_rotation: Scalar rotation attanasi_susceptibility: Dynamical susceptibility The supplementary videos generated using this raw data are published as: Gaimann, M. U., & Klopotek, M. (2025).

Supplementary Videos for: Robustly optimal dynamics for active matter reservoir computing (Gaimann and Klopotek, 2025). DaRUS. doi:10.18419/DARUS-4619. Changelog V2 Added raw random uniform driver trajectory files confined to a circle with radius 4.0, with different change intervals (used to compute the short-term memory capacity) Added datasets for the computation of the short-term memory capacity for parameter combinations of the speed-controller parameter scan, with different driving protocols (Lorenz-63, random uniform with different change intervals).

These datasets provide the full recorded Gaussian kernel observations of the simulation runs; datasets labeled with "memory-capacity" contain observables related to the memory capacity. Added datasets of a simple Echo State Network (ESN) comparison, following the recipe in Hinaut and Trouvain (2021) (inria.hal.science/hal-03203318v2) Added a dataset for the undriven active matter simulation of the homing-speed-controller-strength dataset with parameter combination K_h=483 and K_sc=0.0207 (highly condensed droplet case) Updated datasets used for figures in the main text with aggregates of more performance metrics (NMSE, NRMSE, sMAPE, Pearson correlation coefficient of the y coordinate computed according to Lymburn et al. (2021))