In this paper, we revisit the problem of in- ducing a process modelfrom time-series data. Weillustrate this task with a realistic ecosys- tem model, review an initial method for its induction, then identify three challenges that require extension of this method. These in- clude dealing with unobservable variables, finding numeric conditions on processes, and preventing the creation of models that over- fit the training data. Wedescribe responses to these challenges and present experimental evidence that they have the desired effects. After this, we show that this extended ap- proach to inductive process modeling can ex- plain and predict time-series data from bat- teries on the International Space Station. In closing, we discuss related work and consider directions for future research.