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A list of all the posts and pages found on the site. For you robots out there, there is an XML version available for digesting as well.

Posts

An optimizer’s view of rare event analysis

7 minute read

Published: November 03, 2025

Risk analysis

Temporal Normalizing Flows

4 minute read

Published: November 01, 2025

Normalizing flows provide a practical way to learn a probability density and sample from it by pushing forward a simple base distribution (e.g., a standard Gaussian) through an invertible mapping. This post describes a temporal extension—conditioning the flow on time, to model time-dependent densities \(p(t,x)\), with a physics-informed regularization based on a Fokker–Planck equation (FPE).

Data-driven Mori–Zwanzig reduction for cascading failures

7 minute read

Published: November 01, 2025

In this note, I revisit an older research direction at the intersection of stochastic dynamical systems, reduced-order modeling, and power-system stability. The motivating question is how to construct effective low-dimensional models for rare but consequential events such as cascading line failures.

Reconstructing PDE solutions

13 minute read

Published: October 31, 2025

In this short note, we discuss a data-driven viewpoint for reconstructing solutions of reduced partial differential equations arising from stochastic dynamical systems. A representative setting is the evolution of probability densities associated with a dynamical system of the form

A survey of math behind normalizing flows

19 minute read

Published: October 29, 2025

In this short note, we present normalizing flow as an expressive and powerful generative model under which both sampling and density evaluations are efficiently able to be implemented. Possible applications of normalizing flow can be found in solving high-dimensional partial differential equations (PDE).