3 papers
math.AP2026
Reduced Order Modeling of One-Dimensional Conservative PDEs via the Cumulative Distribution Transform
Harbir Antil, RocÃo DÃaz MartÃn, Ivan V. Medri +4
We propose a reduced order modeling (ROM) framework for 1D conservative PDEs based on the cumulative distribution transform (CDT). The CDT maps nonnegative, equal-mass states into…
math.ST2026
A Discrete Cumulative Distribution Transform via Optimal Transport
Harbir Antil, Gustavo Rohde, Aryan Saxena
This paper develops a fully discrete cumulative distribution transform (CDT) for atomic probability measures on the real line. The transform is defined through monotone quantile ma…
eess.SP2026
Additive Noise, Shift Recovery, and Signed Signals in the Cumulative Distribution Transform
Harbir Antil, Ratna Khatri, Aryan Saxena
The cumulative distribution transform (CDT) is a quantile-based transport representation that exactly linearizes one-dimensional translations of positive densities. We study how th…