In the field of scientific computing and computational physics, Neural Networks (NNs) have become a powerful tool for building surrogate models for complex physical systems that are difficult to describe using traditional empirical models or closed-form solutions. NNs excel at approximating highly non-linear systems, achieving high accuracy and computational efficiency when large and well-distributed datasets are available. However, in scenarios where data is limited, insufficient, or widely dispersed NNs face significant challenges. Under these conditions, they tend to overfit the available data, resulting in decreased prediction performance. To address these challenges, several methods have been proposed that introduce prior knowledge into the training process. This knowledge can take various forms, including differential equations that describe the system or simpler insights like the gradients of the target function at specific points. However, there exist many physical phenomena where the underlying physics is either unknown or too complex to be expressed via differential equations, and no precise gradient information is available. In these cases, the only reliable information comes from experimental data and general prior beliefs about the system’s behavior. This work stems from the need to incorporate any high-level prior understanding of systems typically found in industrial applications, reducing the experimental costs associated with modeling. We therefore developed a method that allows us to incorporate limited experimental data while constraining the function’s form to match a certain prior belief. GradINNs, gradient-informed neural networks, address these settings by coupling a primary network with an auxiliary network that is used to incorporate prior beliefs about the gradients of the underlying system. An additional loss term, evaluated at collocation points, connects the networks, ensuring the primary network's gradients align with prior beliefs while allowing the latter to be updated based on the training data. We validated GradINNs on synthetic and real-world datasets, testing various input/output dimensions and dataset sizes, comparing against standard NNs trained solely on data. The results show GradINNs effectively regularize gradient predictions, outperforming traditional NNs by better capturing system dynamics and reducing overfitting, particularly when data is limited.