Three independent active learning cycles were run for 15 iterations, one based on identifying new structures using local uncertainties, one based on atomic uncertainties, and one based on sampling randomly. All start from a model trained on an 80:20 split of the 50 highest energy structures contained in the water dataset described above. At each iteration, a 20 ps molecular dynamics simulation of a system containing 128 water molecules at a fixed density of 0.86 g cm -3 was run with a timestep of 0.5 fs in the NVT ensemble at 350 K using a Nosé-Hoover thermostat. LAMMPS version 2023.3.28 was used with MACE as the engine for energy and force evaluations. The given density lies below the experimental density of water, as expected for the RPBE-D3 level of theory. The trajectories obtained from the MD simulations were used to generate new training data to improve the models: At each active learning step, the first 10 ps of the trajectory were divided into ten evenly sized segments to guarantee new structures were sampled at different intervals of the simulation. For the active learning cycle based on randomly selecting new data, a random snapshot was selected from each of the ten segments. For the local uncertainty-based runs, snapshots were selected from the subsets by calculating the locally aggregated uncertainties (as detailed in the Results section) for each atom based on a committee of five MACE models using an aggregation r cut = 4 Å and choosing the frames featuring the environments with the highest uncertainties. For the atomic uncertainties, frames and atoms were selected based on the highest atomic force uncertainty (as detailed in the Results section). Boxes containing 64 water molecules were subsequently cut out from the snapshots: A central oxygen atom and the 63 closest oxygen atoms to it were selected, and the water molecules determined by selecting the two hydrogen atoms closest to each oxygen respectively. The box length for the new, smaller configuration is given by l new = 1 2 V init 3 and the originally selected center oxygen atom was placed in the center of a cubic box with this length. For the active learning cycle based on local uncertainties, the central atom was given by the oxygen atom featuring the maximum local uncertainty in the snapshot. For the run based on random selection, the index of the central oxygen atom was randomly generated. To avoid introducing high energies and forces due to cutting a periodic box from a larger initial configuration, the atoms close to the border of the new box were relaxed using the MACE model at the current active learning iteration based on the following procedure: All atoms within a distance of 0.8 l new /2 of the central oxygen atoms were kept fixed. The box was then padded by 2 Å in each direction. Five BFGS iterations were performed to relax the positions of the free atoms and the box size decreased by 0.2 Å in each direction. This procedure was repeated until the original box size was recovered, to allow the border regions to relax to physically meaningful structures. Energies and forces for the configurations obtained by this procedure were then calculated using the DFT setup described above. A new active learning iteration was then started by adding the new configurations to the dataset from the previous iteration and retraining MACE models from randomly initialized model parameters based on the new dataset.