Fig. 3: Schematic illustration of AI-Hilbert and its components.
From: Evolving scientific discovery by unifying data and background knowledge with AI Hilbert
Using background knowledge encoded as multivariate polynomials, experimental data, and hyperparameters (e.g., a sparsity constraint on the background theory) to control our model’s complexity, we formulate scientific discovery as a polynomial optimization problem, reformulate it as a semidefinite optimization problem, and solve it to obtain both a symbolic model and its formal derivation. Dashed boxes correspond to optional components. An example is introducing an incorrect candidate formula as a new axiom in the background theory.
