Field dynamics inference for local and causal interactions
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Complex systems with many constituents are often approximated in terms of a stochastic differential equation (SDE). Although implemented as an effective description, these models often inherit several fundamental aspects such as the principles of locality and causality. In this work we show that these two concepts are sufficient to infer non-degenerate solutions for linear autonomous SDEs, from observational data of the system alone without measurements of the exciting forces. Furthermore we construct a prior structure encoding these concepts and solve the resulting inference problem via a variational approximation of the posterior. We demonstrate that a dynamical field, the dynamical law governing the field, as well as the stochastic excitations can be inferred from noisy and incomplete data of the field only.
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