LEONARDO: A Physics-Informed Generative Model for Stochastic Nanoparticle Dynamics in Liquid-Phase TEM

Liquid-phase transmission electron microscopy (LPTEM) enables direct visualization of nanoparticle motion in the native liquid environment with nanometer and millisecond resolution. These combined capabilities open new opportunities for studying nanoscale dynamics, but also create a broad space of experimental choices where automation can play a critical role. Developing such automation requires realistic simulators of particle motion in LPTEM, yet quantitative interpretation and simulation of the resulting complex stochastic motion remain challenging due to the lack of tractable, physics-aware models. To address this, we introduce LEONARDO, a transformer-based variational autoencoder (VAE) with a physics-informed loss, trained on $\sim$38,000 experimental gold nanoparticle trajectories from LPTEM. The model encodes temporal dependencies of nanoparticle motion via self-attention and reconstructs trajectories by matching key statistical descriptors linked to physical phenomena, resulting in latent variables that capture experimental properties in an unsupervised way. To evaluate generative fidelity, we introduce Fréchet Motion Distance (FMD), an analogue of the Fréchet Inception Distance designed for stochastic time-series data. FMD measures the Fréchet distance between feature embeddings from MoNet, a domain-specific CNN trained for anomalous diffusion classification. LEONARDO achieves an FMD of 7.8 with experimental trajectories, compared to 22.6-39.9 achieved by classical stochastic models, and >95\% of its generated trajectories are labeled "LPTEM'' by a domain classifier. By functioning as a black-box simulator, LEONARDO generates realistic and diverse trajectories, providing a foundation for autonomous electron microscopy, where physically faithful synthetic data enable the development of data-driven control and analysis methods.