Learning Implicit Equations from Data

Reduced order modeling and dimensionality reduction techniques have become very popular in nuclear physics in the last decade. The motivations for speeding up computations include the developing of uncertainty quantification frameworks, experimental design, real time control for experimental set ups, and the ability to keep up with the computational burden of implementing ever-increasingly more complex models, among others.

Various of these techniques follow two steps to construct the reduced order model. First, we identify a set of suitable reduced coordinates to describe our usually high-dimensional system. Second, we find (or construct) equations that relate how these coordinates evolve as either time (for dynamical systems), or the controlling parameters change. The second step can be a challenge for non-affine or non-linear operators, while it can become almost impossible for experimental set-ups where there is no access to the underlying true high-dimensional equations of the system.

In this talk we will discuss some approaches to get around these problems by constructing implicit equations from "observed" data (full order model evaluations). These approaches allow us to swiftly build general surrogate models for complex computations, and offer an alternative path for model discovery when the driving data is experimental observations.