Neural-network-based methods to solve Partial Differential Equations (PDEs) such as the Deep Ritz method rely on stochastic integration to approximate the loss functional and its gradient. Thus, the choice of sampling strategy critically affects accuracy and convergence. Standard Monte Carlo (MC) sampling, although unbiased, often requires a large number of samples to avoid high variance. Importance Sampling (IS) offers a remedy by replacing uniform sampling with a proposal distribution—a customized probability density function designed to concentrate samples in regions where the integrand is largest. By focusing on these influential regions, IS reduces estimator variance while maintaining unbiasedness. In this work, we propose Multi-Integral Importance Sampling (MIIS), a novel IS-based method that makes the proposal distribution depend on the trainable parameters. To construct a distribution for this framework, we utilize a first-degree Taylor expansion in the parameter domain. This approximation allows us to effectively capture the local variations of the integrand as the network parameters evolve. Numerical experiments with the Deep Ritz method demonstrate that MIIS achieves a variance reduction of up to three orders of magnitude, resulting in faster and more stable convergence to the PDE solution.