Neural blind deconvolution to reconstruct high-resolution ground-based solar observations

For the 3D localization problem using point spread function (PSF) engineering, we propose an enhancement of our previously introduced localization neural network, LocNet. The improved network is a physics-informed neural network that we call PiLocNet. Previous works on the localization problem may be categorized separately into model-based optimization and neural network approaches. Our PiLocNet combines the strengths of both approaches by incorporating forward-model-based information into the network via a data-fitting loss term that constrains the neural network to yield results that are physically sensible. We additionally incorporate certain regularization terms from the variational method, which further improves the robustness of the network in the presence of image noise, as we show for the Poisson and Gaussian noise models. This framework accords interpretability to the neural network, and the results we obtain show its superiority. Although this paper focuses on the use of a single-lobe rotating PSF to encode the full 3D source location, we expect the method to be widely applicable to other PSFs and imaging problems that are constrained by well-modeled forward processes.

Adaptive optics (AO) enhances astronomical images by correcting perturbations in the optical system, resulting in complex point spread function (PSF) shapes, which provide critical information for optical design, calibration, and diagnostics. This paper presents a parametric model for an AO-corrected long-exposure PSF that adapts to complex shapes and various seeing conditions. A complementary estimation method is also introduced, addressing the inverse problem of estimating the atmospheric PSF or power spectral density (PSD) from observed PSF data. The model, based on Gaussian sum approximation (GSA), was tested using simulated PSF data from the OOMAO toolbox for Fried parameter (r0) values ranging from 0.10 to 0.20 m and on-sky data from the Very Large Telescope’s MUSE instrument. Two approaches were analyzed: (i) direct PSF estimation using GSA, and (ii) PSF estimation derived from atmospheric PSD estimation. Both methods were evaluated using root mean square error (RMSE). While approach (i) provided the best performance, approach (ii) produced more accurate atmospheric PSF estimates compared to the Moffat approximation and the Fetick method. Additionally, approach (ii) enabled the estimation of key physical parameters, such as the Fried parameter (r0) and residual AO variance ($\sigma _{AO}^2$). The proposed methods effectively estimate atmospheric PSF and PSD, even for complex PSF shapes influenced by spiders, central obstructions, or static aberrations.

A Physics-Informed Neural Network (PINN) was developed to solve the complex Navier-Stokes (N-S) equations for multiphase flow measurement including flowrates of individual phases in the multiphase mixture, and phase ratios. The results were compared against a mathematical based multiphase flow measurement approach and validated through a controlled loop test using oil, water, and gas. The PINN embeds fundamental fluid dynamics principles into its learning process, ensuring that the neural network adheres to the governing physical laws of motion, continuity, and conservation. Unlike traditional neural networks that rely solely on data-driven learning, PINNs incorporate fluid dynamics driven differential equations, to enhance model accuracy and reliability. This study evaluates the accuracy, efficiency, and repeatability of PINNs by comparing their results against traditional mathematical-based multiphase flow measurement (MPFM) technology and controlled test cases. The developed PINN successfully solved the Navier- Stokes (N-S) equations in their closest approximation to the original form, with minimal assumptions and simplifications, to estimate multiphase flow rates, integrating fundamental fluid dynamics principles into its learning process. The results demonstrated that the PINN-based approach achieved accuracy comparable to traditional mathematical multiphase flow measurement (MPFM) technologies, while significantly improving computational efficiency. During controlled loop tests with oil, water, and gas, the PINN model consistently captured flow dynamics with high precision, validating its effectiveness under real-world conditions. Moreover, the PINN method exhibited strong generalization capabilities, adapting to various flow regimes without the need for extensive empirical calibration. Compared to conventional MPFM technologies, PINN reduced reliance on predefined correlations and offered greater adaptability to changing fluid properties. The repeatability of results confirmed the model's reliability, positioning PINNs as a promising alternative for complex multiphase flow measurement applications. These findings highlight the potential of PINNs as an innovative, physics-guided, and data-efficient solution, effectively bridging the gap between traditional physics-based methods and modern machine learning techniques. This paper presents an innovative application of Physics-Informed Neural Networks (PINNs) for multiphase flow measurement, offering a data-driven yet physics-guided alternative to traditional mathematical MPFM technologies. By embedding fundamental physical laws into the neural network training process, the proposed approach enhances accuracy, computational efficiency, and adaptability, while minimizing reliance on extensive empirical calibration. This advancement significantly improves real-time flow monitoring, equipping practicing engineers with a more reliable, data-efficient, and scalable solution for complex multiphase flow measurement in industrial applications.

Biochemically recurrent prostate cancer (BCR) is the main indication to perform prostate-specific membrane antigen PET/CT. However, localizing BCR with prostate-specific membrane antigen PET/CT remains challenging in patients with low prostate-specific antigen (PSA) values. Here, we studied the impact of advanced PET image reconstruction methods on BCR localization and interobserver agreement with 18F-DCFPyL PET/CT scans in patients with BCR and low PSA values. Methods: Twenty-four patients with BCR and a PSA level of less than 2.0 ng/mL were included. PET images were reconstructed with 4-mm voxels and 2-mm voxels, both with and without point-spread function. All scans were interpreted by 4 nuclear medicine physicians. Additionally, PET examinations of 5 patients with primary prostate cancer and confirmed absence of lymph node metastases (after lymph node dissection) were included, to assess the risk of introducing false-positive findings when using advanced reconstruction. Calculation of BCR localization rates (scan positivity) was based on consensus among our readers (≥3 readers regarding a scan positive for BCR), as well as the individual scan interpretations of the readers. Results: In the consensus analysis, BCR localization rates were not higher using advanced reconstruction (62.5%-66.7%) than using 4-mm reconstruction (62.5%). On the basis of individual readings, however, more scans were positive using 2-mm reconstruction (74.0%; 95% confidence interval [CI], 65.0%-82.9%) (P = 0.027) and 2-mm reconstruction with point-spread function (75.0%; 95% CI, 66.2%-83.8%) (P = 0.014) than 4-mm reconstruction (65.6%; 95% CI, 56.0%-75.3%). A higher number of lesions was detected on the 2-mm scans (median, 2 lesions; interquartile range, 1-3) than the 4-mm scans (median, 1; interquartile range, 0-3; P = 0.008). The advanced reconstruction methods did not increase interobserver agreement (80.6%-84.7%), compared with the 4-mm scans (75.7%, P = 0.08-0.25). In the patients with primary prostate cancer, an equal number of false-positive lesions was observed among the different reconstruction methods (overall, n = 13). Conclusion: Applying advanced image reconstruction for 18F-DCFPyL PET/CT scans did not increase BCR localization in patients with BCR and low PSA values (reader consensus). Yet, the increased number of positive individual readings may imply that further development of image reconstruction methods holds potential to improve BCR localization. No improved interobserver agreement was observed with advanced reconstruction compared with standard 4-mm reconstruction.

3D concrete printing (3DCP) is an innovative construction method that extrudes cementitious materials layer-by-layer to fabricate building components based on a digital model. 3DCP has gained increasing adoption globally for projects like buildings, bridges, retaining walls, and stormwater management systems. However, 3DCP places stringent demands on the rheological properties of the printable cementitious materials. Rheology is critical for the flow and buildability of fresh concrete during extrusion. The mixture must have a low yield stress for pumping, moderate viscosity to hold its shape after deposition, minimal bleeding and segregation of aggregates, as well as responsive rheology that can transition from fluid to solid state as layers are printed sequentially. In this dissertation, we aim to solve the challenges mentioned above including: (1) accurate and efficient quantification of rheological and thixotropic properties of cementitious materials, (2) evaluation of flow behavior of fresh concrete during extrusion. Using traditional experimental methods to evaluate rheological properties of cement paste is labor-intensive and time-consuming. Numerical simulations like Finite Element Method (FEM) or Computational Fluid Dynamics (CFD) can help increase the speed of finding the most suitable material for 3DCP. However, these simulation methods are costly in computing power, making them less desirable for simulating the dynamic and complex process of 3DCP. Moreover, mesh-based approaches are not suitable for complex geometries as the mesh generation would be challenging with curved boundaries, small features, holes or thin regions. Physics-Informed Neural Network (PINN) is introduced in the work as an innovative solution to simulate and model the whole process of 3DCP. It can leverage the flexibility and computational efficiency of data-based neural networks, which can accelerate the learning and convergence speed. At the same time, Partial Differential Equations (PDEs) would be embedded in the network structure to increase the accuracy of its prediction. The integrated governing physical laws can help the neural network understanding the underlying physics of the 3DCP process, potentially increasing the accuracy and reliability of simulations. A significant part of the research is dedicated to understanding the rheological and thixotropic behavior of cementitious materials, which is critical for the material design in 3DCP. We developed a Rheology-informed Neural Network, RheologyNet, where we embedded the rheological constitutive laws into the loss function. These physical laws can help the network focus on simulating the rheological properties of cementitious materials. Moreover, a thixotropic evaluation system has been established based on the proposed model to evaluate the thixotropic property of cement paste. This study is presented in Chapter 2. Then, we proposed a Navier-Stokes Informed Neural Network (NSINN) to study the flow behavior of cement paste in the 3DCP barrel and nozzle since it involves complicated Multiscale or Multiphysics behaviors, such as anisotropy and non-uniform shear rate distribution. The Navier Stokes Equation and the rheological constitutive equations are coupled and embedded into the NSINN architecture to simulate the flow behavior in the barrel during 3D-printing extrusion process. This approach demonstrates the potential of PINNs to provide high-accuracy simulations of velocity and pressure fields in a computationally efficient manner compared to traditional mesh-based models. Also, we used the NSINN to learn the relationship between the nozzle size and the printing quality. The details of the study are presented in Chapter 3. At last, a multi-subnetwork PINN architecture (MultiSubPINN) is proposed to address the limitations of traditional PINNs. This is because traditional PINNs used Fully-connected Neural Network (FNN) as main bone. It has problems like different outputs must share parameters within the network structure. However, this parameter sharing nature might lead to potential errors and decrease the model performance. The main architecture of this network is consisted of multiple separated sub-networks and the loss function of each sub-network is calculated separately to update the parameters in each sub-network. By doing this, we can ensure that the optimization for one output doesn't negatively impact others, therefore providing a more flexible, scalable, and potentially more accurate alternative for the evaluation. Besides, using randomly distributed training points in the computational domain for PINNs is a common way. However, many physical problems exhibit non-uniform behavior, with certain regions of the domain having more complex dynamics or sharper gradients than others. Randomly distributed training points might not adequately capture these regions, leading to a model that misrepresents the underlying physics in critical areas. We proposed a Physical-based sampling strategy to optimize the training of the PINNs. This study is presented in Chapter 4. In summary, this dissertation has established a new platform that is enabled by interpretable NN to accurately quantify cement paste’s rheological properties and simulate the flow behavior of 3D concrete printing process. The findings suggest that PINNs can not only improve the efficiency and accuracy of simulations but also provide a more profound understanding of the material behaviors and process dynamics critical to 3DCP. The novel PINN structure developed from this dissertation is a powerful general platform that could be applicable to a variety of material domains for complex rheological behavior predictions.

In order to improve underwater range-gated imagery quality, image restoration and super-resolution reconstruction techniques based on maximum a posteriori framework are combined with the point spread function (PSF) of the system. A model based on beam propagation considering time-dependent backscatter is established including the extreme attenuation properties of water and the diffraction limit of sensor for obtaining the PSF. The proposed method is applied for an underwater range-gated imaging system. Performance of the approach is compared with the traditional restoration and reconstruction algorithms. Objective image quality metrics are used to quantify the effectiveness of the restoration and reconstruction. Experimental results showed that the proposed method can effectively improve the resolution and quality of underwater range-gated imaging.

Modern methods for MR image reconstruction, denoising, and parameter mapping are becoming increasingly nonlinear, black-box, and at risk of "hallucination." These trends mean that traditional tools for judging confidence in an image (visual quality assessment, point-spread functions (PSFs), g-factor maps, etc.) are less helpful than before. This paper describes and evaluates an approach that can help with assessing confidence in images produced by arbitrary nonlinear methods. We propose to characterize nonlinear methods by examining the images they produce before and after applying controlled perturbations to the measured data. This results in functions known as local perturbation responses (LPRs) that can provide useful insight into sensitivity, spatial resolution, and aliasing characteristics. LPRs can be viewed as generalizations of classical PSFs, and are are very flexible-they can be applied to arbitary nonlinear methods and arbitrary datasets across a range of different reconstruction, denoising, and parameter mapping applications. Importantly, LPRs do not require a ground truth image. Impulse-based and checkerboard-pattern LPRs are demonstrated in image reconstruction and denoising scenarios. We observe that these LPRs provide insights into spatial resolution, signal leakage, and aliasing that are not available with other methods. We also observe that popular reference-based image quality metrics (eg, mean-squared error and structural similarity) do not always correlate with good LPR characteristics. LPRs are a useful tool that can be used to characterize and assess confidence in nonlinear MR methods, and provide insights that are distinct from and complementary to existing quality assessments.

As Li-ion batteries become more essential in today's economy, tools need to be developed to accurately and rapidly diagnose a battery's internal state-of-health. Using a Li-ion battery's (high-rate) voltage response, it is proposed to determine a battery's internal state through Bayesian calibration.However, Bayesian calibration is notoriously slow and requires thousands of model runs. To accelerate parameter inference using Bayesian calibration, a surrogate model is developed to replace the underlying physics-based Li-ion model. Developing a surrogate model for rapid Bayesian calibration analysis is discussed for both the single particle model (SPM) and the pseudo two-dimensional (P2D) model.Surrogate models are constructed using physics-informed neural networks (PINNs) that encode the influence of internal properties on observed voltage responses. In practice, a neural network can be trained by: 1) using simulation results of the physics-based model (i.e., a data-loss approach); 2) using the residuals of the governing equations themselves (i.e., a physics-loss approach); or 3) using a combination of simulation results and governing equation residuals. In the present work, PINNs are developed using a variety of training losses and neural network architectures. In this analysis, it is shown that a PINN surrogate model can be reliably trained with only physics-informed loss. However, using a coupled data-informed and physics-loss approach produced the most accurate PINNs. Figure~\\ref{fig:spm_2d} illustrates the absolute relative errors of trained PINN networks using several different training losses and neural network architectures.After determining a consistent training strategy for both the SPM and P2D PINN surrogate models, the PINNs are extended to determine additional internal state-of-health parameters. As more and more parameters were introduced, the PINN training suffered from ``the curse of dimensionality", which was mitigated by using a hierarchical training approach (where a PINN trained with fewer variable model parameters was used to train a PINN with more variable model parameters).Next, the high-dimensionality PINN surrogates are then integrated into Bayesian calibration schemes to identify internal Li-ion battery properties from experimentally measured voltages. Interpreting the high-dimensional parameter posteriors is discussed with respect to model error, parameter prior choices, and experimental errors. Figure 1

A novel sequential method to train physics informed neural networks for Allen Cahn and Cahn Hilliard equations

This thesis investigates two physics informed neural network (PINN) approaches for two mechanistic problems via the performance metrics of model parameter estimation and system state prediction. The PINNs are compared to Bayesian inference (BI) tested under similar conditions. The first PINN studied is the loss-based PINN, which embeds physics into a standard feedforward neural network within the loss function of this network. The second PINN investigated is the hybrid-recurrent physics informed neural network, which uses a recurrent neural network (RNN) that embeds physics in RNN architecture. The BI used as a point of comparison uses a Transitional Markov Chain Monte Carlo algorithm to estimate the posterior distributions. The applications studied are a compartmental model for an infectious disease, and a mass-spring-damper model. It is found that BI performs better in ideal data conditions and the PINNs perform better in weak data conditions.

In recent years, the artificial intelligence computing paradigm represented by physics-informed neural networks (PINNs) has received great attention in the field of plasma numerical simulation. However, the plasma chemical system considered in related research is relatively simplified, and the research on solving the more complex multi-particle low-temperature fluid model based on PINNs is still blank. In more complex chemical systems, the coupling relationship between particle densities and between particle densities and mean electron energy become more intricate. Therefore, the applicability of PINNs in dealing with sophisticated reaction systems needs further exploring and improving. In this work, we propose a general PINN framework (source term decoupled PINNs, Std-PINNs) for solving multi-particle low-temperature plasma fluid model. By introducing equivalent positive ions and replacing each particle transport equation with the current continuity equation as a physical constraint, Std-PINN splits the entire solution process into the training processes of two neural networks, realizing the decoupling of the source term of the heavy particle transport equation from the electron density and mean electron energy, which greatly reduces the complexity of neural network training. In this work, the application of Std-PINNs to solving multi-particle low-temperature plasma fluid models is demonstrated through two classic discharge cases with different complexity of reaction systems (low-pressure argon glow discharge and atmospheric-pressure helium glow discharge) and the performance of Std-PINN is compared with that of conventional PINN and finite element method (FEM). The results show that the training results output from the traditional PINN are completely incorrect due to the strong coupling correlation of each physical variable through the source terms of each particle transport equation, while the <i>L</i><sub>2</sub> relative error between Std-PINN and FEM results can reach up to ~10<sup>–2</sup> , thus verifying the feasibility of Std-PINN in simulating multi-particle plasma fluid model. Std-PINN expands the application of deep learning method to modeling complex physical systems and provides new ideas for conducting low-temperature plasma simulations. In addition, this study provides novel insights into the field of artificial intelligence scientific computing: the mathematical form that describes the state of a physical system is not unique. By introducing equivalent physical variables, equations suitable for neural network solutions can be derived and combined with observable data to simplify problems.

In recent years, successful applications of deep learning (DL) have inspired scientists to explore the possibilities of applying DL approaches to modeling scientific problems. Existing studies have revealed that to bake the physics into the DL makes a good supplement to the traditional numerical methods (e.g., finite element, finite volume method) which primarily rely on partial differential equations (PDEs). While DL models are ordinarily trained in a purely data-driven manner, integrating physics into them for simulating scientific problems has several benefits such as (i) physics constraints could regularize the over-parameterized model and hence mitigate the overfitting issue commonly seen in DL; (ii) physics information could also effectively reduce the amount of data needed for training the model; (iii) the resultant physics-informed DL models feature better interpretability and generalizability compared with the conventional black-box model. Furthermore, the powerful expressiveness of the deep network, guaranteed by the universal approximation theorem, makes it a suitable approximator for the solution to a physical system. In this dissertation, we develop two different DL architectures (or approaches), one being continuous scheme-based while the other discrete scheme-based, that leverage physics knowledge for modeling scientific problems. Through comprehensive numerical experiments, we demonstrate the proposed models can be used in solving general PDEs, establishing predictive data-driven models for dynamical systems, identifying the parameters in governing PDEs or even discovering the entire governing PDEs of dynamical systems from scarce and noisy measurements. The continuous model roots on the physics-informed neural network (PINN) which uses a fully connected neural network (FCNN) to approximate the physical fields of a system globally. This model is mesh-free as the residual of the physics (e.g., PDEs, initial/boundary values) is evaluated on a set of collocation points within the physical domain. Several applications including the forward simulations, data-driven simulations and solving inverse problems are presented to exemplify the advantages of PINN over traditional numerical methods. However, the original PINN suffers from inaccurate initial/boundary values due to the weak enforcement of the initial/boundary conditions (I/BCs). To overcome this issue, we propose an improved PINN model by utilizing multiple deep neural networks (DNNs) to construct the solution. Through a DNN pre-trained to represent the initial/boundary values, the approximated solution would obey the given I/BCs forcibly. With several numerical examples, we show that the improved PINN is characterized with much better accuracy on the I/BCs. Though the PINN shows great promise in data-driven modeling and solving inverse problems, some inherent limitations of PINN still exist, such as (i) the solution might lacks fine-scale details due to the global approximation of FCNN; (ii) high computational expense caused by the FCNN it roots on; (iii) incapability to incorporate existing PDE terms (e.g., $\Delta u$) into the network architecture. To overcome these drawbacks, this dissertation also proposes a discrete model - Physics-encoded Recurrent Convolutional Neural Network (PeRCNN) which recurrently updates the solution (or state variable) for time marching. Specifically, it utilizes convolutional neural network (CNN) to capture the spatial patterns of the solution while the recurrent network mimics the forward Euler scheme (or Runge-Kutta scheme) in numerical methods. PeRCNN is a mesh-based and discrete model due to the discretization in time and spatial dimension. The local connectivity of CNN makes PeRCNN more computationally efficient. In addition, the coercive encoding mechanism of physics in PeRCNN, fundamentally different from the PINN relying on soft penalty, ensures the network to rigorously obey given physics. The proposed PeRCNN is successfully applied to solving general PDEs, the data-driven modeling of dynamical systems and the data-driven discovery of governing PDEs from scarce and noisy measurements. Comparisons with the state-of-the-art DL models demonstrate that the proposed PeRCNN possesses excellent computational efficiency, accuracy and generalizability. --Author's abstract

Identifying optimal architectures of physics-informed neural networks by evolutionary strategy

In recent engineering applications using deep learning, physics-informed neural network (PINN) is a new development as it can exploit the underlying physics of engineering systems. The novelty of PINN lies in the use of partial differential equations (PDE) for the loss function. Most PINNs are implemented using automatic differentiation (AD) for training the PDE loss functions. A lesser well-known study is the use of finite difference method (FDM) as an alternative. Unlike an AD based PINN, an immediate benefit of using a FDM based PINN is low implementation cost. In this paper, we propose the use of finite difference method for estimating the PDE loss functions in PINN. Our work is inspired by computational analysis in electromagnetic systems that traditionally solve Laplace’s equation using successive over-relaxation. In the case of Laplace’s equation, our PINN approach can be seen as taking the Laplacian filter response of the neural network output as the loss function. Thus, the implementation of PINN can be very simple. In our experiments, we tested PINN on Laplace’s equation and Burger’s equation. We showed that using FDM, PINN consistently outperforms non-PINN based deep learning. When comparing to AD based PINNs, we showed that our method is faster to compute as well as on par in terms of error reduction.

A camera shake of the relative motion between cameras and original scenes often occurs during a shoot, resulting in blurred images. This paper presents a method of restoring blurred images based on patch-based PSF (Point Spread Function) estimation and channel-dependent image deblurring. Initially, a pair of noisy and blurred images is acquired by consecutive shooting under short and long exposures to more accurately estimate the 2D trajectory formed by the camera shake, which is also known as PSF. From the noisy image, one patch with strong edges is extracted using gradient operators and the corresponding blurry patch is found within the blurry image. The boundaries of both patches are padded in a specified tile pattern to prevent the appearance of vertical or horizontal lines due to boundary discontinuity. Tikhonov regularization is then iteratively conducted on Gaussian pyramid images with adaptive noise thresholding to get the optimized PSF. Finally, the color conversion of the blurred image into a luminance and two chrominance images is done to apply the channel dependent image deblurring where the spatial resolution of the chrominance images is reduced based on the natural gradient distribution to abandon the valueless data regardless of the restoration quality. Moreover, another artificially blurred image made by the convolution of the known Gaussian PSF and the noisy image is used to reduce undesirable ringing-artifacts and increase the sharpness. The experimental results show that the proposed method can provide more improved PSFs and restored images accompanied by the reduction of computing time and ring artifacts.