Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 8 min ago
Peer-reviewedCC BY 4.0Mathematics

Variational Inference and Error Estimation for Inverse Heat Dissipation Models with Quasi-Reversibility Regularization

  • Zhiqi Tong1
  • Zheng Han1
  • Qinghua Hu2
  • Jing Zheng2
  1. 1School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
  2. 2Department of Statistics, Hangzhou Dianzi University, Hangzhou 310018, China
Open at sourceDOICite

Abstract

While the inverse heat dissipation model has shown success in image generation, it is intrinsically ill-posed. To address this issue, we introduce a quasi-reversibility regularization technique and propose a quasi-reversibility-regularized inverse heat dissipation model. We derive the variational formulation of the objective function for the proposed model and establish an upper bound on the error between the regularized solution obtained from noisy observations and the exact solution in the relevant function space. These findings provide a theoretical basis for improving inverse heat dissipation models. The experimental results demonstrate that compared with the original inverse heat dissipation model, the new model achieves an 34.6% reduction in Fréchet Inception Distance on the MNIST dataset.

Related

  1. From Variational Optimization to Flow-Based Transport: Posterior-Geometry Regularization for Ill-Conditioned Data Assimilation
    Siming Liang, Feng Bao, Hristo G. Chipilski +2
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  2. Asymptotically Compatible Variational Energy Dissipation Laws and Structure-Preserving Variable-Step Linear Relaxation Schemes for a Subdiffusive Tumor-Nutrient Model
    Hui Yu, Zhaoyang Wang, Ping Lin
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  3. Preserving Structure in Variational Data Assimilation of Hyperbolic Conservation Laws via Regularization
    Yao Xiao, Anne Gelb
    arXivPreprintarXiv licenceFull textNumerical analysis & scientific computingarXiv
  4. Iterated Lavrentiev regularization under random noise: variational source conditions and rates in expectation
    Ankit Singh, Hemant Sharma, Kiran Davuluri
    arXivPreprintarXiv licenceFull textAnalysis & PDEsNumerical analysis & scientific computingarXiv
  5. A Variational Principle for the Parabolic Response Function (Part II): Lyapunov Scale-Dissipation, Energy Curvature, and the Geometric Prohibition of O-Critical Zeros
    Aziz Arbai
    HALPreprintCC BY 4.0Full textAlgebra & number theoryAnalysis & PDEsHAL

Cite

BibTeXRIS
BibTeX
@article{tong2026variational,
  title = {{Variational Inference and Error Estimation for Inverse Heat Dissipation Models with Quasi-Reversibility Regularization}},
  author = {Zhiqi Tong and Zheng Han and Qinghua Hu and Jing Zheng},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14213965},
  url = {https://www.mdpi.com/2227-7390/14/21/3965},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Variational Inference and Error Estimation for Inverse Heat Dissipation Models with Quasi-Reversibility Regularization
AU  - Zhiqi Tong
AU  - Zheng Han
AU  - Qinghua Hu
AU  - Jing Zheng
PY  - 2026
DA  - 2026/10/30
JO  - Mathematics
DO  - 10.3390/math14213965
UR  - https://www.mdpi.com/2227-7390/14/21/3965
AB  - While the inverse heat dissipation model has shown success in image generation, it is intrinsically ill-posed. To address this issue, we introduce a quasi-reversibility regularization technique and propose a quasi-reversibility-regularized inverse heat dissipation model. We derive the variational formulation of the objective function for the proposed model and establish an upper bound on the error between the regularized solution obtained from noisy observations and the exact solution in the relevant function space. These findings provide a theoretical basis for improving inverse heat dissipation models. The experimental results demonstrate that compared with the original inverse heat dissipation model, the new model achieves an 34.6% reduction in Fréchet Inception Distance on the MNIST dataset.
SN  - 2227-7390
ER  -