Density Functional Theory (DFT) is currently the standard reference method for modeling Quantum Dots (QDs) and Nanocrystals (NCs). However, the high computational cost of Ab Initio Molecular Dynamics (AIMD) prohibits the study of long-timescale evolution in these systems. To bridge this gap, classical force fields and Machine Learning Interatomic Potentials (MLIPs) are often trained to reproduce DFT potential energy surfaces.

While MLIPs have achieved near-DFT accuracy, they present significant drawbacks. They act as uninterpretable “black boxes” that obscure physical insights, require vast amounts of training data, and often fail catastrophically in out-of-distribution (OOD) scenarios. Furthermore, MLIPs remain significantly more computationally expensive than classical potentials during production runs. Classical potentials offer a lighter alternative but face their own parameterization challenges. Current programs, particularly for QDs, rely on gradient-free stochastic search techniques, such as Genetic Algorithms or Monte Carlo methods, to fit parameters. These methods require expensive iterative simulations and frequently fail to converge on optimal parameters, especially within high-dimensional spaces or complex loss landscapes. Additionally, these programs are often biased toward bulk properties, neglecting the unique surface physics of finite nanostructures.

In this work, we present a differentiable parameterization framework designed to overcome these limitations. By reformulating the fitting process as a gradient-based optimization problem rather than a stochastic search, we eliminate the need for iterative simulations during training. Our approach utilizes automatic differentiation to match energies and forces against DFT data directly, enabling the rapid parameterization of finite nanostructures. This method reduces computational time from days to minutes while maintaining the physical rigor of classical potentials through physics-aware constraints.