This study presents a novel deep learning approach aimed at enhancing stochastic Gust Load Alleviation (GLA) specifically for compliant wings. The approach incorporates the concept of smooth wing camber variation, where the camber of the wing's chord is actively adjusted during flight using a control signal to achieve the desired aerodynamic loading. The proposed method employs a deep learning-based model predictive controller designed for probability density shaping. This controller effectively solves the probability density evolution equation through a custom Physics-Informed Neural Network (PINN) and utilizes Automatic Differentiation for Model Predictive Control (MPC) optimization. Comprehensive numerical simulations were conducted on a compliant wing (CW) model, evaluating performance of the proposed approach against stochastic gust profiles. The evaluation involved stochastic aerodynamic loads generated from Band-Limited White Noise (BLWN) and Dryden gust models. The evaluation were conducted for two distinct Compliant Chord Fractions (CCF). The results demonstrate the effectiveness of the proposed probability density shaping model predictive control in alleviating stochastic gust load and reducing wing tip deflection.