Physics-informed polynomial chaos expansions: recent developments and comparisons

This work presents recent developments in a constrained polynomial chaos expansion as a physics-informed machine learning technique.Specifically, an optimized numerical solver for straightforward updating of Lagrange multipliers and an improved statistical sampling method are compared to the original algorithm for estimating deterministic coefficients.Both techniques are applied to solve a heat equation with Neumann boundary conditions.A second study presents a preliminary numerical comparison of the constrained polynomial chaos expansion and physics-informed deep operator networks with respect to computational cost and achieved accuracy.