Unraveling the Size Determination Mechanism of Nanocrystal Synthesis via Interpretable Neural Networks

Deep learning models of nanocrystal synthesis enable the prediction of size and shape by encoding precursors and reaction conditions. However, their black-box nature hinders gaining deep insights into the underlying synthetic mechanisms. Here, we develop the Nanocrystal Equation Learner (NanoEQL), a fully white-box neural network to unravel the size determination mechanisms of nanocrystal synthesis. Building on the EQL architecture, eight operators are introduced to replace standard activation functions to fit the mathematical equations in nanocrystal synthesis. Among these operators, three smoothed operators address the gradient explosion of singular operators at zero. To evaluate the weights of different precursors, we develop a temperature-gated attention pooling strategy that encodes concentration-driven and reactivity-driven chemical synthesis mechanisms into the temperature gate. The NanoEQL model illustrates that the final nanocrystal size can be described by a linear equation composed of three scalars representing nanocrystallization capability (-Zp), growth capability (Zrea), and external input potential (-Zops). These interpretable scalars not only advance the rational design of nanocrystal synthesis but also establish a generalizable paradigm for deciphering chemical reaction mechanisms through white-box machine learning.