Ali Mohammad-Djafari

Inverse problems arise across scientific and engineering domains, where the goal is to infer hidden parameters or physical fields from indirect and noisy observations. Classical approaches, such as variational regularization and Bayesian inference, provide well established theoretical foundations for handling ill posedness. However, these methods often become computationally restrictive in high dimensional settings or when the forward model is governed by complex physics. Physics Informed Neural Networks (PINNs) have recently emerged as a promising framework for solving inverse problems by embedding physical laws directly into the training process of neural networks. In this paper, we introduce a new perspective on the Bayesian Physics Informed Neural Network (BPINN) framework, extending classical PINNs by explicitly incorporating training data generation, modeling and measurement uncertainties through Bayesian prior modeling and doing inference with the posterior laws. Also, as we focus on the inverse problems, we call this method BPINN-IP, and we show that the standard PINN formulation naturally appears as its special case corresponding to the Maximum A Posteriori (MAP) estimate. This unified formulation allows simultaneous exploitation of physical constraints, prior knowledge, and data-driven inference, while enabling uncertainty quantification through posterior distributions. To demonstrate the effectiveness of the proposed framework, we consider inverse problems arising in infrared image processing, including deconvolution and super-resolution, and present results on both simulated and real industrial data.

Neural Networks (NNs) have been used in many areas with great success. When an NN’s structure (model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm (training). Then, the trained model can be used for the prediction or inference step (testing). As there are also many hyperparameters related to optimization criteria and optimization algorithms, a validation step is necessary before the NN’s final use. One of the great difficulties is the choice of NN structure. Even if there are many “on the shelf” networks, selecting or proposing a new appropriate network for a given data signal or image processing task, is still an open problem. In this work, we consider this problem using model-based signal and image processing and inverse problems methods. We classify the methods into five classes: (i) explicit analytical solutions, (ii) transform domain decomposition, (iii) operator decomposition, (iv) unfolding optimization algorithms, (v) physics-informed NN methods (PINNs). A few examples in each category are explained.

Infrared thermography is widely used in intelligent industrial anomaly detection and automated monitoring systems for its noncontact temperature measurement capabilities, while visible images often serve as complementary information sources. However, infrared propagation and external environmental disturbances introduce measurement uncertainties—among which surface emissivity remains particularly difficult to quantify. To address this challenge, we present an efficient temperature calibration method that integrates Bayesian inference-based semantic segmentation with uncertainty quantification, enabling accurate calibration across equipment with diverse material surfaces. Specifically, a variational Bayesian approach (VBA) is developed for semantic segmentation of infrared thermography, incorporating aligned visible images as a helper for better segmentation, thanks to their richer textures and structural geometry information. Using the segmentation results along with their quantified uncertainties, we introduce a prior emissivity model and construct a hierarchical temperature calibration framework that accounts for physical fluctuations and segmentation-induced errors. Final temperature estimates are derived using a maximum a posteriori (MAP) inference algorithm. Experimental results on blackbody and blower datasets validate the effectiveness of the proposed method in calibrating temperatures across materials with varying emissivities.

A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: How can models utilize physics or mathematical principles to enhance predictions when dealing with sparse, noisy, or incomplete data? Physics-Informed Neural Networks (PINNs) put this idea into practice by incorporating a forward model, such as Partial Differential Equations (PDEs), as soft constraints. This guidance helps the networks find solutions that align with established laws. Recently, researchers have expanded this framework to include Bayesian NNs (BNNs) which allow for uncertainty quantification. However, what happens when the governing equations of a system are not completely known? In this work, we introduce methods to automatically select PDEs from historical data in a parametric family. We then integrate these learned equations into three different modeling approaches: PINNs, Bayesian-PINNs (B-PINNs), and Physical-Informed Bayesian Linear Regression (PI-BLR). To assess these frameworks, we evaluate them on a real-world Multivariate Time Series (MTS) dataset related to electrical power energy management. We compare their effectiveness in forecasting future states under different scenarios: with and without PDE constraints and accuracy considerations. This research aims to bridge the gap between data-driven discovery and physics-guided learning, providing valuable insights for practical applications.

Infrared thermography faces persistent challenges in temperature accuracy due to material emissivity variations, where existing methods often neglect the joint optimization of radiometric calibration and image degradation. This study introduces a physically guided neural framework that unifies temperature correction and image enhancement through a symmetric skip-CNN architecture and an emissivity-aware attention module. The pre-processing stage segments the ROIs of the image and and initially corrected the firing rate. A novel dual-constrained loss function strengthens the statistical consistency between the target and reference regions through mean-variance alignment and histogram matching based on Kullback-Leibler dispersion. The method works by dynamically fusing thermal radiation features and spatial context, and the model suppresses emissivity artifacts while recovering structural details. After validating the industrial blower system under different conditions, the improved network realizes the dynamic fusion of thermal radiation characteristics and spatial background, with accurate calibration results in various industrial conditions.

A thermal fault detection method for High-speed direct-driven blower components is proposed, utilizing thermal and visible image fusion along with semantic segmentation. The proposed method follows three steps: multimodal image fusion, component semantic segmentation of the fused image, and temperature level segmentation. Firstly, an end-to-end image fusion network based on an improved denoising diffusion model is used, a perceptually prioritized weighted loss is introduced for training, and an alternate training strategy is used to improve the quality of the fused images. In the second step, a lightweight segmentation network is proposed to reduce the model size and inference time while improving the segmentation accuracy. At last, thermal images are processed by clustering methods. Experiments on real industrial objects show that the proposed method composed of infrared and optical image fusion, semantic segmentation and temperature clustering networks improves significantly the fault temperature detection on different blower components.