The simulation of nanoparticle growth processes requires accurate descriptions of atomic interactions across multiple timescales. Traditional molecular dynamics (MD) simulations rely on empirical interatomic potentials, which often lack the precision of quantum mechanical methods like density functional theory (DFT). Machine learning interatomic potentials (MLIPs) bridge this gap by combining the accuracy of ab initio calculations with the computational efficiency of classical potentials. These potentials enable large-scale simulations of nanoparticle formation, alloying, and defect evolution while maintaining near-DFT fidelity.

Three primary MLIP frameworks have emerged for nanoparticle simulations: neural network potentials (NNPs), Gaussian process potentials (GPPs), and moment tensor potentials (MTPs). Neural network potentials employ deep learning architectures to map atomic environments to energies and forces. A typical NNP consists of several hidden layers that transform input descriptors, such as atomic positions and chemical species, into a predicted potential energy surface. Gaussian process potentials use kernel-based regression to predict energies based on similarity measures between atomic configurations. These are particularly useful for uncertainty quantification, as GPPs provide error estimates for each prediction. Moment tensor potentials rely on a polynomial expansion of atomic neighbor densities, offering a balance between accuracy and computational efficiency. MTPs achieve this by constructing invariant descriptors from interatomic distances and angles, enabling rapid evaluation during MD simulations.

Training MLIPs requires high-quality datasets derived from ab initio calculations. These datasets must encompass diverse atomic configurations, including bulk phases, surfaces, defects, and transition states relevant to nanoparticle growth. A common strategy involves running DFT-based MD simulations at various temperatures to sample different atomic arrangements. Active learning techniques further enhance dataset quality by iteratively identifying and incorporating configurations where the potential's uncertainty exceeds a threshold. For example, a query-by-committee approach trains multiple MLIPs and flags regions of disagreement for additional DFT calculations. This minimizes the computational cost of data generation while maximizing the potential's transferability.

Applications of MLIPs in nanoparticle growth simulations have yielded insights into alloy formation and defect dynamics. In bimetallic systems like Au-Ag or Pt-Pd, MLIPs accurately capture segregation tendencies and surface alloying during nanoparticle synthesis. Simulations reveal how temperature and composition influence core-shell versus mixed-alloy structures, with predictions matching experimental observations. Defect dynamics, such as vacancy migration or dislocation nucleation, are also accessible through MLIP-enhanced MD. For instance, studies on Ni nanoparticles show that MLIPs correctly predict the energy barriers for surface diffusion, a critical factor in shape evolution during growth. These capabilities enable the exploration of synthesis conditions that optimize catalytic activity or thermal stability.

Active learning strategies play a crucial role in refining MLIP accuracy for complex growth processes. One approach involves on-the-fly training during MD simulations, where the potential dynamically requests new DFT calculations for unexplored configurations. Another method uses genetic algorithms to evolve nanoparticle structures, ensuring the training set includes high-energy intermediates and transition states. By prioritizing configurations near phase boundaries or chemical reactions, active learning reduces errors in predicting nucleation rates or interfacial energies. Recent advances also incorporate reinforcement learning to guide sampling toward regions that maximize the potential's improvement per additional DFT calculation.

The computational efficiency of MLIPs allows simulations spanning microseconds, far beyond the reach of direct ab initio methods. For a 10-nm nanoparticle containing thousands of atoms, MLIP-based MD can achieve nanosecond-scale sampling with forces computed in milliseconds per atom. This performance enables studies of Ostwald ripening, coalescence, and other growth mechanisms at experimentally relevant scales. Comparisons with traditional potentials, such as embedded atom models, demonstrate that MLIPs better reproduce DFT-level details like charge transfer and bond polarization in oxides or semiconductors.

Despite their advantages, MLIPs face challenges in extrapolation to unseen chemistries or extreme conditions. Transferability requires careful construction of training sets, particularly for multicomponent systems where combinatorial complexity grows rapidly. Hybrid approaches, combining MLIPs with physics-based constraints, address this by enforcing known asymptotic behaviors or symmetry conditions. For example, incorporating Ziegler-Biersack-Littmark stopping powers improves accuracy in radiation damage simulations. Future developments may integrate MLIPs with coarse-graining techniques to access even longer timescales while preserving atomic-scale fidelity.

In summary, machine learning interatomic potentials represent a transformative tool for simulating nanoparticle growth with quantum-mechanical accuracy. By leveraging neural networks, Gaussian processes, or moment tensor formulations, these potentials bridge the gap between DFT and MD timescales. Active learning strategies ensure robust performance across diverse atomic configurations, enabling predictive studies of alloy formation, defect dynamics, and growth pathways. As computational resources and algorithms advance, MLIPs will play an increasingly central role in designing nanomaterials with tailored properties for catalysis, energy storage, and other applications.