My thesis research is focused on compositional design of complex physical systems from domain models of basic components and processes. The key idea that I am exploring is how correct designs can be obtained by incrementally composing and augmenting partial causal specifications of how behaviors get achieved. Such specifications are described in terms of the causal relations between quantities imposed by models of physical components and processes. The partial specification can be viewed as an abstraction which has completions that subsume the desired device behaviors. Due to the overwhelming complexity of the space of partial specifications, the search problem becomes intractable. I am also investigating techniques that reduce the complexity of the search. The techniques are based on developing reasoning strategies based on least commitment principles, such as lifting abstractions and use of approximation abstractions of domain models.