We present a neural network approach for closed-loop deep brain stimulation (DBS). We cast the problem of finding an optimal neurostimulation strategy as a control problem. In this setting, control policies aim to optimize therapeutic outcomes by tailoring the parameters of a DBS system, typically via electrical stimulation, in real time based on the patient's ongoing neuronal activity. We approximate the value function offline using a neural network to enable generating controls (stimuli) in real time via the feedback form. The neuronal activity is characterized by a nonlinear, stiff system of differential equations as dictated by the Hodgkin-Huxley model. Our training process leverages the relationship between Pontryagin's maximum principle and Hamilton-Jacobi-Bellman equations to update the value function estimates simultaneously. Our numerical experiments illustrate the accuracy of our approach for out-of-distribution samples and the robustness to moderate shocks and disturbances in the system.

通过神经网络方法实现闭环深度脑刺激(DBS)。以找到最佳神经刺激策略为目标，将问题转化为控制问题。我们通过离线使用神经网络近似价值函数，结合Pontryagin的最大值原理和Hamilton-Jacobi-Bellman方程更新值函数估计，实时依据患者的神经活动调整DBS系统参数，从而优化治疗效果。

霍奇金-休克利神经元动力学的学习控制策略