Several branches of computing use a system's physical dynamics to do computation. We show that the dynamics of an underdamped harmonic oscillator can perform multifunctional computation, solving distinct problems at distinct times within a single dynamical trajectory. Oscillator computing usually focuses on the oscillator's phase as the information-carrying component. Here we focus on the time-resolved amplitude of an oscillator whose inputs influence its frequency, which has a natural parallel as the activity of a time-dependent neural unit. Because the activity of the unit at fixed time is a nonmonotonic function of the input, the unit can solve nonlinearly-separable problems such as XOR. Because the activity of the unit at fixed input is a nonmonotonic function of time, the unit is multifunctional in a temporal sense, able to carry out distinct nonlinear computations at distinct times within the same dynamical trajectory. Time-resolved computing of this nature can be done in or out of equilibrium, with the natural time evolution of the system giving us multiple computations for the price of one.

翻译：计算机科学的多个分支利用系统的物理动力学进行计算。我们证明了一个欠阻尼谐振子的动力学能够执行多功能计算，在单一动力学轨迹的不同时间点解决不同问题。谐振子计算通常将相位作为信息载波组件。本文重点关注受输入影响频率的谐振子时间分辨振幅，该振幅与时间依赖神经单元的活性存在天然的平行关系。由于固定时刻的单元活性是输入的非单调函数，该单元能够解决非线性可分问题（如异或）。由于固定输入下的单元活性是时间的非单调函数，该单元在时间维度上具有多功能性，能在同一动力学轨迹的不同时间点执行不同的非线性计算。这种时间分辨计算可在平衡态或非平衡态下进行，系统的自然时间演化使我们能以单一计算成本实现多重计算。