Weiqiu Zhu | Searcharxiv

arXiv2025

Solving a class of stochastic optimal control problems by physics-informed neural networks

The aim of this work is to develop a deep learning method for solving high-dimensional stochastic control problems based on the Hamilton--Jacobi--Bellman (HJB) equation and physics-informed learning. Our approach is to parameterize the feedback control and the value function using a decoupled neural network with multiple outputs. We train this network by using a loss function with penalty terms that enforce the HJB equation along the sampled trajectories generated by the controlled system. More significantly, numerical results on various applications are carried out to demonstrate that the proposed approach is efficient and applicable.

math.OC↗

arXiv2019

Ultrasensitive charge detection utilizing coupled nonlinear micromechanical resonators

Since the discovery of electrons, an accurate detection of electrical charges has been the dream of scientific community. Due to some remarkable advantages, micro/nano-electromechanical systems (M/NEMS) based resonators have been used to design electrometers with exquisite sensitivity and resolution. Inevitably, some limits including requisite ultra-low environmental temperature, complicated resonator structure and measurement circuit, required linear dynamic response, will cause a gap with respect to practical application. Here, we demonstrate a novel ultra-sensitive charge detection based on the linear dependence of peak frequency drift on the coupling voltage variation of two coupled nonlinear micromechanical resonators. We achieved ultra-high resolution of 2.051E-3 fC (about 13 electrons) of charge detection at the room temperature. We also show an extra application of this device for weak and ultra-low-frequency (ULF) signal detection. Our findings provide a simple strategy for measuring electron charges in an extreme accuracy and developing electrometers in smaller sizes.

cond-mat.mes-hall↗