For centuries, scientists have attempted to identify and document analytical laws that underlie physical phenomena in nature. Despite the prevalence of computing power, the process of finding natural laws and their corresponding equations has resisted automation. A key challenge to finding analytic relations automatically is defining algorithmically what makes a correlation in observed data important and insightful. We will show that by seeking dynamical invariants, we can go from finding just predictive models to finding deeper conservation laws. Applications to modeling physical and biological systems will be shown, and both deterministic and stochastic models will be considered.