In many engineering domains such as fluid dynamics, heat transfer, and materials science, accurate predictive models rely heavily on expensive experimental data, with sample sizes typically ranging from hundreds to thousands of data points. Traditional empirical formulas, while physically interpretable, often exhibit limited accuracy due to their simplified assumptions. We present Physics-Guided Scientific Discovery Networks (PGSDN), a practical approach that combines domain-specific physical insights with neural networks to learn more accurate empirical relationships from small experimental datasets. Our method incorporates physical constraints and domain knowledge through a dual-pathway architecture that balances interpretability with predictive performance. Experiments across three engineering domains—wire-wrapped fuel assembly friction factor prediction in fast reactors, rod bundle heat transfer, and concrete strength estimation—demonstrate that PGSDN consistently outperforms classical empirical formulas and standard machine learning methods while maintaining physical interpretability. The learned relationships provide both improved accuracy and physically meaningful insights that can guide engineering design decisions.