AID enables a numerical solution to inverse problems based on or motivated by the seminal concept of algorithmic probability. AID studies computable discrete or discretized dynamical systems in software space where all possible computable models can be found or approximated under the assumption that discrete longitudinal data such as particle orbits in state and phase space can approximate continuous systems by Turing-computable means. AID combines counterfactual and perturbation analysis with algorithmic information theory to guide a search for sets of models compatible with observations and to precompute and exploit those models as testable generative mechanisms and causal first principles underlying data and systems. AID is an alternative or a complement to other approaches and methods of experimental inference, such as statistical machine learning and classical information theory. For more information go to http://www.scholarpedia.org/article/Algorithmic_Information_Dynamics