Simulation plays a crucial role in various robotics applications, such as policy learning [1, 2, 3, 4, 5, 6, 7], safe and scalable robotic control evaluation [8, 9, 10, 11], and computational optimization of robot designs [12, 13, 14]. Recently, neural robotics simulators have emerged as a promising alternative to traditional analytical simulators, as neural simulators can efficiently predict robot dynamics and learn intricate physics from real-world data. For instance, neural simulators have been leveraged to capture complex interactions challenging for analytical modeling [15, 16, 17, 18], or have served as learned world models to facilitate sample-efficient policy learning [19, 20]. However, existing neural robotics simulators typically require application-specific training, often assuming fixed environments [20, 21] or simultaneous training alongside control policies [22, 23]. These limitations primarily stem from their end-to-end frameworks with inadequate representations of the global simulation state, i.e., neural models often substitute the entire classical simulator and directly map robot state and control actions ( e.g., target joint positions, target link orientations) to the robot's next state. Without encoding the environment in the state representation, the learned simulators have to implicitly memorize the task and environment details. Additionally, utilizing controller actions as input causes the simulators to overfit to particular low-level controllers used during training. Consequently, unlike classical simulators, these neural simulators often fail to generalize to novel state distributions (induced by new tasks), unseen environment setups, and customized controllers ( e.g., novel control laws or controller gains).

Variational ab-initio methods in quantum chemistry stand out among other methods in providing direct access to the wave function. This allows in principle straightforward extraction of any other observable of interest, besides the energy, but in practice this extraction is often technically difficult and computationally impractical. Here, we consider the electron density as a central observable in quantum chemistry and introduce a novel method to obtain accurate densities from real-space many-electron wave functions by representing the density with a neural network that captures known asymptotic properties and is trained from the wave function by score matching and noise-contrastive estimation. We use variational quantum Monte Carlo with deep-learning ans\"atze (deep QMC) to obtain highly accurate wave functions free of basis set errors, and from them, using our novel method, correspondingly accurate electron densities, which we demonstrate by calculating dipole moments, nuclear forces, contact densities, and other density-based properties.