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

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.