Schmidt and Lipson use genetic programming that starts with random guesses at a solution and then employs an evolution-inspired algorithm to shuffle and change pieces of the equations until it finds a solution that works. They demonstrate their approach:
...by automatically searching motion-tracking data captured from various physical systems, ranging from simple harmonic oscillators to chaotic double-pendula. Without any prior knowledge about physics, kinematics, or geometry, the algorithm discovered Hamiltonians, Lagrangians, and other laws of geometric and momentum conservation. The discovery rate accelerated as laws found for simpler systems were used to bootstrap explanations for more complex systems, gradually uncovering the "alphabet" used to describe those systems.King et al. constructed a robot scientist named Adam that used artificial intelligence to come up with a hypothesis about genes in baker’s yeast and the enzymes produced by the genes. It then designed and ran experiments to test its hypothesis. Using the results, it revised its hypothesis and ran more experiments before arriving at its conclusions. From their abstract:
Adam has autonomously generated functional genomics hypotheses about the yeast Saccharomyces cerevisiae and experimentally tested these hypotheses by using laboratory automation. We have confirmed Adam's conclusions through manual experiments. To describe Adam's research, we have developed an ontology and logical language. The resulting formalization involves over 10,000 different research units in a nested treelike structure, 10 levels deep, that relates the 6.6 million biomass measurements to their logical description. This formalization describes how a machine contributed to scientific knowledge.