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PreprintCC BY 4.0arXiv

Physics-informed traditional and generative Mori-Zwanzig-reduced models for multiscale systems

  • Emily Williams
  • Saad Qadeer
  • Amanda Howard
  • Panos Stinis
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Abstract

Model reduction via the Mori-Zwanzig (MZ) formalism is well understood for coarse-grained representations constructed from standard basis functions such as Fourier functions. We show that the same formalism can be used to build reduced-order models in bases discovered by physics-informed machine learning. The fluctuation-dissipation theorem (FDT) is used to close the resulting non-Markovian evolution equations for the expansion coefficients of the learned basis. We further introduce a complementary, generative closure model. Relative to the Markovian dynamics alone, both the MZ and generative closures substantially improve predictions of the filtered states.

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Cite

BibTeXRIS
BibTeX
@misc{williams2026physicsinformed,
  title = {{Physics-informed traditional and generative Mori-Zwanzig-reduced models for multiscale systems}},
  author = {Emily Williams and Saad Qadeer and Amanda Howard and Panos Stinis},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05211},
  eprint = {2611.05211},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05211},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Physics-informed traditional and generative Mori-Zwanzig-reduced models for multiscale systems
AU  - Emily Williams
AU  - Saad Qadeer
AU  - Amanda Howard
AU  - Panos Stinis
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05211
UR  - https://arxiv.org/abs/2611.05211
AB  - Model reduction via the Mori-Zwanzig (MZ) formalism is well understood for coarse-grained representations constructed from standard basis functions such as Fourier functions. We show that the same formalism can be used to build reduced-order models in bases discovered by physics-informed machine learning. The fluctuation-dissipation theorem (FDT) is used to close the resulting non-Markovian evolution equations for the expansion coefficients of the learned basis. We further introduce a complementary, generative closure model. Relative to the Markovian dynamics alone, both the MZ and generative closures substantially improve predictions of the filtered states.
ER  -