The classic Cox Proportional-Hazards Model assumes that a patient’s log-risk of failure is a linear combination of the patient’s covariates.
How the near networks can help solve the issue? Are there any other approaches to predict survival in high dimensional, non-linear data?
Neither the Cox model nor any other regression model makes such an assumption. For example, regression splines have been used with Cox models since 1984. I go into this in detail in RMS.
Non-additive effects are more tricky. When they don't exist, neural networks are at a disadvantage because they prioritize interactions on a equal footing with additive main effects. When interactions exist but are not easy to pre-specify in a regression model, neural networks can have an advantage.
In very high dimensions, statistical models have advantages. That is because penalized maximum likelihood estimation (ridge regression, lasso, elastic net, etc.) scales to higher dimensions better than machine learning methods. This is strictly because the way most people state high-dimensional regression models is using purely additive constructs (additive in log hazard, etc.).
