Discovering Hidden Predictive States in Kinetic Transport
Abstract
How do autonomous macroscopic transport laws emerge from kinetic dynamics, and which hidden degrees of freedom must survive coarse-graining? We address these questions by formulating kinetic state reduction as a problem of predictive sufficiency rather than conventional moment truncation. Starting from Boltzmann transport dynamics, we establish a quantitative connection between unresolved microscopic information, irreducible prediction error, and finite-horizon observability. Microscopic preparations with identical macroscopic observables but distinct subsequent evolution provide direct witnesses of incomplete dynamical closure. We develop an entropy-constrained learned state-reduction framework, demonstrated here through linear projections, that identifies the additional predictive states without prescribing their physical identities and determines their necessity through independent response tests, state deletion, and dynamical consistency. An exactly solvable three-velocity model demonstrates that a hidden higher-order moment can influence future energy transport despite identical initial energy and heat flux. Numerical experiments recover this missing direction and reveal how the required state dimension depends on observation scale, prediction horizon, preparation ensemble, and accuracy. In a synthetic 32-channel Boltzmann system, the learned representation identifies predictive combinations spanning multiple kinetic branches and relaxation groups that are not captured by low-order global moments. We further distinguish observable prediction accuracy from autonomous state closure and quantify the information retained through unresolved memory. These results establish an operational framework for testing the emergence of effective transport laws and identifying the microscopic information required for their predictive validity.
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BibTeX
@misc{zhu2026discovering,
title = {{Discovering Hidden Predictive States in Kinetic Transport}},
author = {Pengfei Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28383},
eprint = {2610.28383},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28383},
}
RIS
TY - UNPB
TI - Discovering Hidden Predictive States in Kinetic Transport
AU - Pengfei Zhu
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28383
UR - https://arxiv.org/abs/2610.28383
AB - How do autonomous macroscopic transport laws emerge from kinetic dynamics, and which hidden degrees of freedom must survive coarse-graining? We address these questions by formulating kinetic state reduction as a problem of predictive sufficiency rather than conventional moment truncation. Starting from Boltzmann transport dynamics, we establish a quantitative connection between unresolved microscopic information, irreducible prediction error, and finite-horizon observability. Microscopic preparations with identical macroscopic observables but distinct subsequent evolution provide direct witnesses of incomplete dynamical closure. We develop an entropy-constrained learned state-reduction framework, demonstrated here through linear projections, that identifies the additional predictive states without prescribing their physical identities and determines their necessity through independent response tests, state deletion, and dynamical consistency. An exactly solvable three-velocity model demonstrates that a hidden higher-order moment can influence future energy transport despite identical initial energy and heat flux. Numerical experiments recover this missing direction and reveal how the required state dimension depends on observation scale, prediction horizon, preparation ensemble, and accuracy. In a synthetic 32-channel Boltzmann system, the learned representation identifies predictive combinations spanning multiple kinetic branches and relaxation groups that are not captured by low-order global moments. We further distinguish observable prediction accuracy from autonomous state closure and quantify the information retained through unresolved memory. These results establish an operational framework for testing the emergence of effective transport laws and identifying the microscopic information required for their predictive validity.
ER -