Inference Lab Sungkyunkwan University · School of Mechanical Engineering

We infer what cannot be observed in multiscale stochastic systems — the hidden state, the hidden function, the hidden model — and we work out when the answer can be trusted.

Led by Jun H. Park. The lab works at the meeting point of stochastic dynamics, inverse problems, and machine learning, on problems where the quantity you care about is never measured directly.

Three layers of one question

01

The hidden state

Given noisy, partial observations of a system with dynamics too fast to resolve, what is it doing now? Nonlinear filtering in multiscale and hybrid stochastic systems — where averaging and homogenization must happen before the filter, not after.

2004 – 2013
02

The hidden function

Now the unknown is not a trajectory but a function — a spectral density, an operator behind the data. Ill-posed inversion needs a prior, and a learned prior with an exact likelihood makes the posterior tractable.

2021 – 2024
03

The hidden model

The unknown becomes the equation itself: the closure standing in for physics a model cannot resolve. And a new question appears alongside it — not only what the closure is, but whether its statistics can be trusted.

2024 – present

Each layer is the one before it with the unknown moved up a level. The lab published particle filtering on the Lorenz '96 atmospheric model in 2011, and publishes learned closures on the same system today — the same testbed, fifteen years apart, with a different unknown each time.

What we are working on now

Machine-learned components are being placed inside climate and weather models faster than the tools to certify them are being built.

An emulator that forecasts well can still get the long-run statistics wrong, and the long-run statistics are exactly what climate questions depend on. Our current program is the mathematics of that gap: what a learned closure preserves, what it quietly destroys, and how you would know the difference. Read more →

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