AI 中文总结
该研究针对纳米机电致动器的卡西米尔-静电吸合问题，训练物理信息神经网络获取可微分设计灵敏度，明确了阻尼相关的坍缩边界特性，实现了高精度的器件间隙反推。
AI 中文摘要
间隙小于100纳米的纳米机电致动器会因静电与卡西米尔力的竞争引发吸合不稳定性而发生坍缩。三十年来，人们已明确界定了其安全工作范围的准静态折点，以及静态平衡无法维持的卡西米尔上限，该上限确定了给定刚度和面积的结构能抵抗量子真空保持开放的最小间隙。但该折点未给出从静止状态启动的阈值、其对阻尼的依赖性，也未涉及两者的设计灵敏度。我们在速坐标中训练了一个物理信息神经网络，该坐标可将可移动的吸合极点映射至无穷远，从而在固定步长Runge-Kutta积分会陷入非物理状态的坍缩阈值处保持残差有界。对训练后的代理模型求导可得到吸合电压灵敏度，其与闭式折点的相对误差达3×10^-6，并将器件规格反推至目标驱动电压下97.036纳米的间隙。将其应用于阻尼有限时无闭式解的从静止状态边界，该模型可提供无解析根存在时的相同灵敏度。我们证明该边界由两条闭式曲线夹在中间，其随阻尼比非递减，且当阻尼比超过2^(-1/4)时会与折点合并，间隙以(τ_*-τ)^(2/5)的形式闭合。数值上，合并已在0.396处发生，坍缩时间的增长在此处从对数型转变为反比平方根型。热Lifshitz降额的经典极限边界处于百分位水平，而这些间隙处的物理偏移比其低几个数量级。
英文摘要
Nanoelectromechanical actuators operating at sub-100-nm gaps collapse through a pull-in instability set by competing electrostatic and Casimir forces. The quasi-static fold that bounds their safe operating range has been known in closed form for three decades, together with the Casimir ceiling above which no static equilibrium survives, which fixes the smallest gap a given stiffness and area can hold open against the quantum vacuum. That fold does not give the threshold reached from rest, its dependence on damping, or the design sensitivities of either. We train a physics-informed neural network in a rapidity coordinate that maps the movable pull-in pole to infinity, which keeps the residual bounded across the collapse threshold where fixed-step Runge-Kutta integration steps into unphysical states. Differentiating the trained surrogate returns pull-in-voltage sensitivities that match the closed-form fold to a relative error of $3\times10^{-6}$ and inverts a device specification to a gap of 97.036 nm at a target actuation voltage. Applied to the from-rest boundary, which carries no closed form once the damping is finite, it supplies the same sensitivities where no analytic root exists. We prove that this boundary is bracketed by two closed-form curves, that it is nondecreasing in the damping ratio, that it merges with the fold once the damping ratio exceeds $2^{-1/4}$, and that the gap closes as $(τ_*-τ)^{2/5}$. Numerically the merger already occurs at $0.396$, and the growth of the collapse time changes there from logarithmic to inverse square root. The classical-limit bound on the thermal Lifshitz derating is at the percent level, and the physical shift at these gaps lies orders of magnitude below it.
Comments25 pages, 6 figures, 12 tables, 2 appendices. Includes supplemental material. REVTeX 4.2. Submitted to Physical Review Applied. Code, trained weights, training logs and data: https://doi.org/10.5281/zenodo.22142711
