Mathematical foundations of multidimensional AI for dynamic chemical process networks

Abstract

Chemical process networks combine partially observed dynamics, reaction and phase behavior,

transport, material history, and decisions across unequal timescales. This paper develops a

mathematical specification for integrating these features with learned models and coordinated

optimization in the Astralithos framework, using Lithos as a development and verification platform.

The formulation distinguishes physical states, controls, uncertain parameters, modes,

measurements, and economic objectives. Established balances, differential-algebraic models,

exact-lumping conditions, inference methods, and optimization results are connected through

explicit conditions for dynamic closure, feasible lifting, error propagation, and decision consistency.

Self-contained derivations state the assumptions needed for these connections. Measurement

uncertainty, process variability, model discrepancy, and numerical error remain distinct.

Three reproducible synthetic studies examine the specification. A historical three-stage

optimization example is reproduced with a feasible sequential comparator. A constructed

sufficient representation is compared with raw coordinates on the same physical problem and

evaluation budget. A coupled reaction, filtration, and drying model illustrates state memory and

evolving conditional response surfaces. These studies establish case-specific numerical results;

they do not establish a general low-dimensional representation, real-time industrial performance, or

added value from a learned reasoning model. The resulting framework supplies explicit

mathematical and evidential conditions for testing those claims.

Mathematical Characterization of Dynamic Risk Spillovers in Carbon-Energy Financial Networks with Multi-Dimensional Uncertainty: A TVP-VAR-DY Connectedness Approach via Generalized Forecast-Error Variance Decomposition
Wenxin Zhang, Rufei Zhang, Qian Zhu
Mathematics18 Oct 2026Peer-reviewedCC BY 4.0General mathematicsCrossref
Foundations of a Novel Mathematical Framework
Bassel Aldarra
Zenodo23 Oct 2026PreprintCC BY 4.0Zenodo
Theoretical Foundations of Ordinal Spherical Multidimensional Scaling
Elizabeth Coda, Ery Arias-Castro
arXiv7 Sep 2026PreprintarXiv licenceFull textStatisticsarXiv
On the Mathematical Foundations of Gravitational Decoupling in General Relativity
Andrea Giusti
arXiv13 Oct 2026PreprintarXiv licenceFull textGravitation & general relativityarXiv
Metadevices that compute: mathematical foundations and experimental implementations for neuromorphic nanophotonics
Xian Hadia, Odysseas Tsilipakos, Dimitrios C. Tzarouchis +1
arXiv29 Oct 2026PreprintarXiv licenceFull textOptics & photonicsarXiv

Cite

BibTeX RIS

BibTeX

@misc{gangopadhyay2026mathematical,
  title = {{Mathematical foundations of multidimensional AI for dynamic chemical process networks}},
  author = {Palash Gangopadhyay},
  howpublished = {Zenodo},
  year = {2026},
  month = oct,
  doi = {10.5281/zenodo.23600060},
  url = {https://zenodo.org/records/23600060},
  note = {CC BY 4.0},
}

RIS

TY  - UNPB
TI  - Mathematical foundations of multidimensional AI for dynamic chemical process networks
AU  - Palash Gangopadhyay
PY  - 2026
DA  - 2026/10/23
PB  - Zenodo
DO  - 10.5281/zenodo.23600060
UR  - https://zenodo.org/records/23600060
AB  - Chemical process networks combine partially observed dynamics, reaction and phase behavior,  transport, material history, and decisions across unequal timescales. This paper develops a  mathematical specification for integrating these features with learned models and coordinated  optimization in the Astralithos framework, using Lithos as a development and verification platform.  The formulation distinguishes physical states, controls, uncertain parameters, modes,  measurements, and economic objectives. Established balances, differential-algebraic models,  exact-lumping conditions, inference methods, and optimization results are connected through  explicit conditions for dynamic closure, feasible lifting, error propagation, and decision consistency.  Self-contained derivations state the assumptions needed for these connections. Measurement  uncertainty, process variability, model discrepancy, and numerical error remain distinct.  Three reproducible synthetic studies examine the specification. A historical three-stage  optimization example is reproduced with a feasible sequential comparator. A constructed  sufficient representation is compared with raw coordinates on the same physical problem and  evaluation budget. A coupled reaction, filtration, and drying model illustrates state memory and  evolving conditional response surfaces. These studies establish case-specific numerical results;  they do not establish a general low-dimensional representation, real-time industrial performance, or  added value from a learned reasoning model. The resulting framework supplies explicit  mathematical and evidential conditions for testing those claims.
ER  -

Abstract

Related

Cite