Join the lab
Inference Lab is new. Its first cohort will be MS students and undergraduate researchers; PhD positions open once that cohort is running.
What you would actually be doing
Scientific models cannot resolve everything. A climate model cannot resolve individual clouds; a filter cannot track every fast oscillation. So we replace what we cannot resolve with something learned from data — and then we are stuck with a question that is easy to state and hard to answer: is the replacement good enough, and good enough for what?
A learned model can forecast beautifully for three days and still get the thirty-year statistics wrong. That failure is invisible to the metric people usually check, and it is fatal for the purpose the model is actually used for. Our work is the mathematics of that gap.
In practice this means: stochastic dynamics, Bayesian inference, and a careful, slightly suspicious relationship with machine learning. We use neural networks as measuring instruments more than as products.
Who we are looking for
- MS students
- Two years. You own one research problem from its first week, take it through to a thesis and a paper, and present it at a meeting. Applications go through the SKKU Graduate School; contact the PI before you apply.
- Undergraduate researchers
- A scoped piece of a real project, with a deliverable you can show — not busywork. This is the usual route into the lab. Projects begin in the vacation, when you can concentrate on them and we can meet properly; if it is going well, you carry on at a lighter pace during term.
- PhD applicants
- Not in this first round. If you are interested, write anyway and say so — the first PhD position will go to someone who already knows how the lab works.
Preparation
The lab sits between mathematics, physics and computing. Nobody arrives holding all three; you need a solid footing in one and the willingness to pick up the rest here.
Undergraduate researchers — expected:
- Ordinary differential equations
- Some numerical methods — you should know why a Runge–Kutta step is not a Euler step
MS students — expected, in addition:
- Probability and statistics, to the level of a good undergraduate course
- Partial differential equations, at least acquaintance
The trait that matters most here is not cleverness but care — the willingness to check your own result before you believe it, and to keep checking after it starts agreeing with you. Most of what this lab has found came from taking a number seriously that everyone else had accepted.
MS projects
These are real, currently open, and scoped so that a first-year student can own one from the beginning. Say in your email which one interests you and why — or propose something else; these are starting points, not fences.
M1 · Do our closures get the extremes right?
Our stochastic closures reproduce the bulk of the distribution to the accuracy of the reference data. We predict, on theoretical grounds, that they nevertheless fail in the tails — because the mechanism that repairs the bulk acts at zero frequency, and extremes do not live at zero frequency.
You would test that prediction on a simulation grid that already exists. If it holds, asking what would repair the tails is the natural next step — an optional stretch, not a thesis requirement. Why it is a good first project: the infrastructure is built, so you spend your time on the science; and because the prediction is falsifiable, the project cannot quietly fail. You would learn: extreme-value statistics, and what it is like to work where theory has stuck its neck out.
M2 · Can the closure be written down in symbols?
Instead of a neural network, fit a sparse symbolic model to the same data and find out how much of the behaviour survives being made readable. The interesting question is not whether a symbolic model is worse — it usually is — but which statistics it loses first, and whether those are the ones anyone needs.
You would not start from zero: this project inherits a complete, audited pipeline — eight fitted closure families, evaluation with honest floors, and a written plan with named open questions. One of them is a small gem: a numerical error we proved has a closed form, which a sparse regressor should be able to rediscover from data alone.
You would learn: sparse regression, model selection, and the real trade-off between interpretability and fidelity — which is rarely the one people assume.
M3 · Learning for systems that hit things
Mechanical systems with impacts, friction and clearances are nonsmooth, and learned models of them fail in characteristic ways at the contact. This project asks the lab's usual question — is the learned replacement good enough, and for what statistic? — about a noisy impact oscillator.
Why it is here: beneath the mechanics sits the same question as the projects above — how a fast, noisy motion becomes a slow equation — in a setting where classical theory gives exact answers to check a learned model against. This one starts from a clean slate: you inherit an analysis whose theory provides those answers, and you write the simulator's first line yourself. Everything you build is yours. You would learn: nonsmooth dynamics, event-driven simulation, system identification, and how a method built for climate transfers to a bench-scale problem.
Undergraduate projects
Each of these is a bounded piece of a larger study, with a deliverable you can show at the end. The work starts in the vacation — an intensive block when your courses are not competing for your attention, and when there is time to teach you properly — and continues more lightly during term if you want it to.
U1 · One emulator, one statistic
Several groups have released machine-learned models that simulate the atmosphere far faster than a physics-based model. Whether they reproduce the long-run statistics — the climate, rather than the forecast — is much less clear. You would take one publicly released model and one statistic, compute it honestly with an uncertainty floor, and compare it to the reference. You would learn: time-series analysis, working with large public datasets, and how to build an evaluation you can defend.
U2 · Tail statistics on an existing grid
The data half of project M1: compute extreme-value statistics across a simulation grid that already exists, with proper uncertainty, and assemble them into one figure we can all read. You would learn: extreme-value statistics in practice, and what "with proper uncertainty" actually costs.
How to get in touch
Email jun.park@skku.edu. Please include:
- Your CV and transcript
- Which project interests you, and why — a couple of sentences is plenty
- One paragraph about something you once tried to understand and how far you got. It does not have to be a success story, and it does not have to be mathematics.
That last item is the one worth spending time on. It tells me far more than a transcript does.