Notes on scientific machine learning, JAX/XLA engineering, and operator-theoretic methods.https://minchanjeong.github.io/en-ushttps://minchanjeong.github.io/blog/data-driven-sciml-ceiling/https://minchanjeong.github.io/blog/data-driven-sciml-ceiling/The big-data scaling recipe applies unevenly across scientific machine learning: it works for equilibrium tasks like AlphaFold but hits a structural ceiling at per-trajectory prediction of chaotic systems.Tue, 19 May 2026 00:00:00 GMThttps://minchanjeong.github.io/blog/llm-inference-nondeterminism/https://minchanjeong.github.io/blog/llm-inference-nondeterminism/LLM inference nondeterminism is rarely a hardware artifact: dynamic batching switches kernels, the kernel switch reorders floating-point summations, and the resulting drift in logits silently turns RLVR training off-policy.Wed, 26 Nov 2025 00:00:00 GMThttps://minchanjeong.github.io/blog/koopman-adjoint-normality-svd/https://minchanjeong.github.io/blog/koopman-adjoint-normality-svd/What is the adjoint of the Koopman operator on a stochastic Markov process, when is the operator normal, and why does the singular value decomposition become the natural object the moment normality fails?Sat, 17 May 2025 00:00:00 GMThttps://minchanjeong.github.io/blog/adjoint-normality-spectral-theorem/https://minchanjeong.github.io/blog/adjoint-normality-spectral-theorem/Building the finite-dimensional spectral theorem from the basis-free adjoint, normality, and Gram–Schmidt induction on eigenvectors. Part I of a three-part series, with a separate Operator SVD capstone.Tue, 18 Feb 2025 00:00:00 GMThttps://minchanjeong.github.io/blog/compact-operator-spectral-theorem/https://minchanjeong.github.io/blog/compact-operator-spectral-theorem/The compact case between finite dimension and general bounded operators: the variational principle as the eigenvalue source, compactness itself as the discretizer that forces the eigenvalues to decay to zero. Part II of a three-part series, with a separate Operator SVD capstone.Tue, 18 Feb 2025 00:00:00 GMThttps://minchanjeong.github.io/blog/functional-analytic-spectral-theorem/https://minchanjeong.github.io/blog/functional-analytic-spectral-theorem/When a bounded self-adjoint operator has no eigenvectors at all, the eigenbasis is replaced by a projection-valued measure built from continuous functional calculus. Part III of a three-part series, with a separate Operator SVD capstone.Tue, 18 Feb 2025 00:00:00 GMThttps://minchanjeong.github.io/blog/operator-svd/https://minchanjeong.github.io/blog/operator-svd/The SVD as the spectral theorem applied to L*L via the polar form L = U|L|: why it is the optimal low-rank object, what shape it takes at each spectral-theorem rung, and where it stops existing.Tue, 18 Feb 2025 00:00:00 GMThttps://minchanjeong.github.io/blog/tisr-operational-graphcast/https://minchanjeong.github.io/blog/tisr-operational-graphcast/The library default for TOA solar radiation was a different physical quantity than GraphCast's training data. How I diagnosed and reconstructed the correct one.Fri, 15 Mar 2024 00:00:00 GMThttps://minchanjeong.github.io/blog/staged-single-node-etl/https://minchanjeong.github.io/blog/staged-single-node-etl/Materialized intermediates, fit-once transforms, executor per stage, quarantined dependencies: four design decisions in a single-node ETL for terabyte-scale weather data, with the alternatives I rejected.Fri, 01 Dec 2023 00:00:00 GMT