More sophisticated NN architectures have recently been developed for constructing MLPs by incorporating equivariance in the molecular representation. Indeed, building on PhysNet, the equivariant model SpookyNet incorporates physically inspired modules that describe local and non-local pairwise interactions such as nuclear repulsion, electrostatics, and dispersion. Besides achieving state-of-the-art accuracy on benchmarks such as QM7-X (40) and MD17 , the SpookyNet model, trained on QM data of bottom-up and top-down molecular fragments (GEMS datasets), can accurately predict the structural properties of large and complex biomolecules such as polyalanine peptides, crambin in aqueous solution, and gas-phase binding curves of ACE2 and the RBD of the SARS-CoV spike protein . Allegro is another equivariant NN model that combines message passing NNs (MPNNs) with strict locality, effectively capturing local atomic interactions while maintaining a global view of the system. This model has proven transferable to high-temperature MD simulations and is scalable through GPU parallelization, enabling simulations with tens of millions of atoms (e.g., VIH capsid) . Using the local descriptors defined by the Allegro model, the FENNIX model (Force-Field-Enhanced Neural Network InteraXions) was developed to predict short-range energy, atomic charges, and volume. Similar to SpookyNet, these atomic properties are integrated into physically motivated functional forms for calculating electrostatic and dispersion energy contributions, enabling the investigation of relevant simulations at QM accuracy, such as the torsional free energy profile of solvated alanine dipeptide and bond dissociation energy profiles. Unlike previous models that explicitly use two-body interactions, the MACE model is built on an equivariant MPNN, which leverages higher-order symmetric features for each atom. This property enables the MACE model to more effectively capture QM many-body effects in the PES of molecular systems. Indeed, the MACE-OFF23 model was recently developed using diverse QM datasets comprising small and large single molecules as well as molecular dimers. This flexible model can calculate torsion profiles of drug-like molecules, enthalpies of molecular crystals, folding dynamics of alanine, and the power spectrum of crambin in explicit solvent. Following a similar reasoning, the SO3LR model ( ) was developed using an updated version of the SO3krates equivariant NN architecture, which now incorporates both short-and long-range physical models in its design. The applicability of the SO3LR model was demonstrated through nanosecond-long simulations with QM Figure : Evolution of the largest (bio)molecular systems investigated using machine learning (ML) potentials with quantummechanical (QM) accuracy. We highlight the key QM datasets employed in training these potentials. A schematic representation of the ML methodologies employed in related works is provided in the graph. The color coding of the ML potentials on the y-axis corresponds to the different ML methodologies. Figures of (bio)molecular systems have been adapted from the references corresponding to each ML methodology, except for the STMV and HIV capsid systems, which were adapted from Refs. ( ) and ( ), respectively. accuracy across a broad chemical space, including small biomolecular units, polyalanine systems, bulk water, the crambin protein, an N-linked glycoprotein, and a lipid bilayer.