Constrained Probabilistic Numerics: Gaussian Process Solvers for Linear PDEs under Linear Inequality Constraints
The paper adds inequality constraints directly into Gaussian-process PDE posteriors, instead of treating admissibility as cleanup.
The authors prove that equality conditioning and finite-dimensional inequality conditioning can be applied sequentially on the solution-space measure. That makes the usual physics-informed posterior a valid prior for virtual-point inequality updates. The resulting law is non-Gaussian but computable with truncated-Gaussian moments. In their tests, monotonicity, no-arbitrage, and nonnegativity constraints improved selected error or constraint metrics, with effects varying by data regime. ArXiv · AI/CL/LG's note
The authors prove that equality conditioning and finite-dimensional inequality conditioning can be applied sequentially on the solution-space measure. That makes the usual physics-informed posterior a valid prior for virtual-point inequality updates. The resulting law is non-Gaussian but computable with truncated-Gaussian moments. In their tests, monotonicity, no-arbitrage, and nonnegativity constraints improved selected error or constraint metrics, with effects varying by data regime. ArXiv · AI/CL/LG's note
score 4