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The accurate detection of leukocytes is the basis for the diagnosis of blood system diseases. However, diagnosing leukocyte disorders by doctors is time-consuming and requires extensive experience. Automated detection methods with high accuracy can improve detection efficiency and provide recommendations to inexperienced doctors. Current methods and instruments either fail to automate the identification process fully or have low performance and need suitable leukocyte data sets for further study. To improve the current status, we need to develop more intelligent strategies. This paper investigates fulfilling high-performance automatic detection for leukocytes using a deep learning-based method. We established a new dataset more suitable for leukocyte detection, containing 6273 images (8595 leukocytes) and considering nine common clinical interference factors. Based on the dataset, the performance evaluation of six mainstream detection models is carried out, and a more robust ensemble model is proposed. The mean of average precision (mAP) @IoU = 0.50:0.95 and mean of average recall (mAR)@IoU = 0.50:0.95 of the ensemble model on the test set are 0.853 and 0.922, respectively. The detection performance of poor-quality images is robust. For the first time, it is found that the ensemble model yields an accuracy of 98.84% for detecting incomplete leukocytes. In addition, we also compared the test results of different models and found multiple identical false detections of the models, then provided correct suggestions for the clinic., (© 2023. The Author(s).)

Background: China is progressing towards the goal of schistosomiasis elimination, but there are still some problems, such as difficult management of infection source and snail control. This study aimed to develop deep learning models with high-resolution remote sensing images for recognizing and monitoring livestock bovine, which is an intermediate source of Schistosoma japonicum infection, and to evaluate the effectiveness of the models for real-world application., Methods: The dataset of livestock bovine's spatial distribution was collected from the Chinese National Platform for Common Geospatial Information Services. The high-resolution remote sensing images were further divided into training data, test data, and validation data for model development. Two recognition models based on deep learning methods (ENVINet5 and Mask R-CNN) were developed with reference to the training datasets. The performance of the developed models was evaluated by the performance metrics of precision, recall, and F1-score., Results: A total of 50 typical image areas were selected, 1125 bovine objectives were labeled by the ENVINet5 model and 1277 bovine objectives were labeled by the Mask R-CNN model. For the ENVINet5 model, a total of 1598 records of bovine distribution were recognized. The model precision and recall were 81.9% and 80.2%, respectively. The F1 score was 0.81. For the Mask R-CNN mode, 1679 records of bovine objectives were identified. The model precision and recall were 87.3% and 85.2%, respectively. The F1 score was 0.87. When applying the developed models to real-world schistosomiasis-endemic regions, there were 63 bovine objectives in the original image, 53 records were extracted using the ENVINet5 model, and 57 records were extracted using the Mask R-CNN model. The successful recognition ratios were 84.1% and 90.5% for the respectively developed models., Conclusion: The ENVINet5 model is very feasible when the bovine distribution is low in structure with few samples. The Mask R-CNN model has a good framework design and runs highly efficiently. The livestock recognition models developed using deep learning methods with high-resolution remote sensing images accurately recognize the spatial distribution of livestock, which could enable precise control of schistosomiasis., (© 2023. The Author(s).)

Objective: Deep learning image reconstruction (DLIR) is a new reconstruction method for maintaining image quality at reduced radiation dose. The purpose of this study was to compare image quality of reduced-dose DLIR images with the standard-dose adaptive statistical iterative reconstruction (ASIR-V) images in chest CT., Methods: Our prospective study included 48 adult patients (30 women and 18 men, mean age ±SD, 49.8 ± 14.3 years) who underwent both the standard-dose CT (SDCT) and low-dose CT (LDCT) on a GE Revolution CT scanner. All patients gave written informed consent. All scans were reconstructed with ASIR-V40%. Additionally, LDCT scans were reconstructed with DLIR with high-setting (DLIR-H) and medium-setting (DLIR-M). Image noise and contrast-noise-ratio (CNR) of thoracic aorta with different reconstruction modes were measured and compared., Results: LDCT reduced radiation dose by 96% compared with SDCT (CTDIvol: 0.54mGy vs 12.46mGy). In LDCT, DLIR significantly reduced image noise compared with the state-of-the-art ASIR-V40% with DLIR-H provided the lowest image noise and highest image quality score. In addition, the image noise, CNR of aorta and overall image quality of the low-dose DLIR-H images did not have significant difference compared with the SDCT ASIR-V40% images (all p > 0.05)., Conclusion: DLIR significantly reduces image noise in LDCT chest scans and provides similar image quality as the SDCT ASIR-V images at 4% of the radiation dose., Advances in Knowledge: DLIR uses high-quality FBP data to train deep neural networks to learn how to distinguish between signal and noise, and effectively suppresses noise without affecting anatomical and pathological structures. It opens a new era of CT image reconstruction. DLIR significantly reduces image noise and improves image quality compared with ASIR-V40% under same radiation dose condition. DLIR-H achieves similar image quality at 4% radiation dose as ASIR-V40% at standard-dose level in non-contrast chest CT.

Abstract Deciphering variations in chromosome conformations based on bulk three‐dimensional (3D) genomic data from heterogenous tissues is a key to understanding cell‐type specific genome architecture and dynamics. Surprisingly, computational deconvolution methods for high‐throughput chromosome conformation capture (Hi‐C) data remain very rare in the literature. Here, a deep convolutional neural network (CNN), deconvolve bulk Hi‐C data (deCOOC) that remarkably outperformed all the state‐of‐the‐art tools in the deconvolution task is developed. Interestingly, it is noticed that the chromatin accessibility or the Hi‐C contact frequency alone is insufficient to explain the power of deCOOC, suggesting the existence of a latent embedded layer of information pertaining to the cell type specific 3D genome architecture. By applying deCOOC to in‐house‐generated bulk Hi‐C data from visceral and subcutaneous adipose tissues, it is found that the characteristic chromatin features of M2 cells in the two anatomical loci are distinctively bound to different physiological functionalities. Taken together, deCOOC is both a reliable Hi‐C data deconvolution method and a powerful tool for functional extraction of 3D genome architecture.

Abstract Background Pathway-based analysis of transcriptomic data has shown greater stability and better performance than traditional gene-based analysis. Until now, some pathway-based deep learning models have been developed for bioinformatic analysis, but these models have not fully considered the topological features of pathways, which limits the performance of the final prediction result. Results To address this issue, we propose a novel model, called PathGNN, which constructs a Graph Neural Networks (GNNs) model that can capture topological features of pathways. As a case, PathGNN was applied to predict long-term survival of four types of cancer and achieved promising predictive performance when compared to other common methods. Furthermore, the adoption of an interpretation algorithm enabled the identification of plausible pathways associated with survival. Conclusion PathGNN demonstrates that GNN can be effectively applied to build a pathway-based model, resulting in promising predictive power.

In recent years, segmentation details and computing efficiency have become more important in medical image segmentation for clinical applications. In deep learning, UNet based on a convolutional neural network is one of the most commonly used models. UNet 3+ was designed as a modified UNet by adopting the architecture of full-scale skip connections. However, full-scale feature fusion can result in excessively redundant computations. This study aimed to reduce the network parameters of UNet 3+ while further improving the feature extraction capability. First, to eliminate redundancy and improve computational efficiency, we prune the full-scale skip connections of UNet 3+. In addition, we use the attention module called Convolutional Block Attention Module (CBAM) to capture more essential features and thus improve the feature expression capabilities. The performance of the proposed model was validated by three different types of datasets: skin cancer segmentation, breast cancer segmentation, and lung segmentation. The parameters are reduced by about 36% and 18% compared to UNet and UNet 3+, respectively. The results show that the proposed method not only outperformed the comparison models in a variety of evaluation metrics but also achieved more accurate segmentation results. The proposed models have lower network parameters that enhance feature extraction and improve segmentation performance efficiently. Furthermore, the models have great potential for application in medical imaging computer-aided diagnosis.

Traditional data-driven deep learning models often struggle with high training costs, error accumulation, and poor generalizability in complex physical processes. Physics-informed deep learning (PiDL) addresses these challenges by incorporating physical principles into the model. Most PiDL approaches regularize training by embedding governing equations into the loss function, yet this depends heavily on extensive hyperparameter tuning to weigh each loss term. To this end, we propose to leverage physics prior knowledge by "baking" the discretized governing equations into the neural network architecture via the connection between the partial differential equations (PDE) operators and network structures, resulting in a PDE-preserved neural network (PPNN). This method, embedding discretized PDEs through convolutional residual networks in a multi-resolution setting, largely improves the generalizability and long-term prediction accuracy, outperforming conventional black-box models. The effectiveness and merit of the proposed methods have been demonstrated across various spatiotemporal dynamical systems governed by spatiotemporal PDEs, including reaction-diffusion, Burgers', and Navier-Stokes equations. Most physics-informed deep learning models alleviate the poor generalizability of pure data-driven models by minimizing residuals of the governing equations. In this work the authors propose to leverage physics priors, by embedding the discretized governing equations into the neural network architecture, which improves the generalizability and long-term prediction accuracy. [ABSTRACT FROM AUTHOR]

The powerful parallel computing capability of GPU and the development of matrix processing unit in recent years provide more possibilities to improve the performance of convolutional neural network (CNN) on GPU. For the Winograd convolution algorithm, which is the most widely used in CNN and has the best performance, there are already some tuning results, but they all ignore the utilization of the matrix operation unit and fail to make full use of the computing resources of GPU. This paper introduces a single precision accelerated solution on GPU for CNN. According to the indicators of architecture, the optimal data layout, grid division and block division methods are derived. In order to adapt to a variety of padding in practical application, an efficient dynamic scheme for filling is designed, and by the use of matrix cores, a pipeline algorithm with operator fusion is implemented. The deep learning accelerated library MIOpen in AMD is used as the baseline. Taking several convolutional layers of ResNet50 as the experimental input, the evaluation shows that our approach outperforms MIOpen with the speedup of 1.41x on MI210, and reaches 74% of the peak value of single precision calculations. Applying this method to the training and inference of ResNet50, the speedup of 1.68x is obtained. [ABSTRACT FROM AUTHOR]

Deciphering variations in chromosome conformations based on bulk three‐dimensional (3D) genomic data from heterogenous tissues is a key to understanding cell‐type specific genome architecture and dynamics. Surprisingly, computational deconvolution methods for high‐throughput chromosome conformation capture (Hi‐C) data remain very rare in the literature. Here, a deep convolutional neural network (CNN), deconvolve bulk Hi‐C data (deCOOC) that remarkably outperformed all the state‐of‐the‐art tools in the deconvolution task is developed. Interestingly, it is noticed that the chromatin accessibility or the Hi‐C contact frequency alone is insufficient to explain the power of deCOOC, suggesting the existence of a latent embedded layer of information pertaining to the cell type specific 3D genome architecture. By applying deCOOC to in‐house‐generated bulk Hi‐C data from visceral and subcutaneous adipose tissues, it is found that the characteristic chromatin features of M2 cells in the two anatomical loci are distinctively bound to different physiological functionalities. Taken together, deCOOC is both a reliable Hi‐C data deconvolution method and a powerful tool for functional extraction of 3D genome architecture. [ABSTRACT FROM AUTHOR]

In recent years, segmentation details and computing efficiency have become more important in medical image segmentation for clinical applications. In deep learning, UNet based on a convolutional neural network is one of the most commonly used models. UNet 3+ was designed as a modified UNet by adopting the architecture of full-scale skip connections. However, full-scale feature fusion can result in excessively redundant computations. This study aimed to reduce the network parameters of UNet 3+ while further improving the feature extraction capability. First, to eliminate redundancy and improve computational efficiency, we prune the full-scale skip connections of UNet 3+. In addition, we use the attention module called Convolutional Block Attention Module (CBAM) to capture more essential features and thus improve the feature expression capabilities. The performance of the proposed model was validated by three different types of datasets: skin cancer segmentation, breast cancer segmentation, and lung segmentation. The parameters are reduced by about 36% and 18% compared to UNet and UNet 3+, respectively. The results show that the proposed method not only outperformed the comparison models in a variety of evaluation metrics but also achieved more accurate segmentation results. The proposed models have lower network parameters that enhance feature extraction and improve segmentation performance efficiently. Furthermore, the models have great potential for application in medical imaging computer-aided diagnosis. [ABSTRACT FROM AUTHOR]

This document is an editorial for a special issue on Reliability Engineering in the journal Quality Engineering. The editorial introduces the concept of reliability as "quality over time" and discusses the challenges faced by reliability engineers in dealing with complex data and system complexity. The special issue includes fourteen papers that cover a wide range of topics, including Bayesian data analysis, reliability modeling, system assessment and optimization, and effective system management and maintenance. The guest editors express their enjoyment in reviewing the insightful and innovative research and applications in reliability engineering and hope that readers will find the special issue helpful and enlightening. [Extracted from the article]

Inverse design arises in a variety of areas in engineering such as acoustic, mechanics, thermal/electronic transport, electromagnetism, and optics. Topology optimization is an important form of inverse design, where one optimizes a designed geometry to achieve targeted properties parameterized by the materials at every point in a design region. This optimization is challenging, because it has a very high dimensionality and is usually constrained by partial differential equations (PDEs) and additional inequalities. Here, we propose a new deep learning method---physics-informed neural networks with hard constraints (hPINNs)---for solving topology optimization. hPINN leverages the recent development of PINNs for solving PDEs, and thus does not require a large dataset (generated by numerical PDE solvers) for training. However, all the constraints in PINNs are soft constraints, and hence we impose hard constraints by using the penalty method and the augmented Lagrangian method. We demonstrate the effectiveness of hPINN for a holography problem in optics and a fluid problem of Stokes flow. We achieve the same objective as conventional PDE-constrained optimization methods based on adjoint methods and numerical PDE solvers, but find that the design obtained from hPINN is often smoother for problems whose solution is not unique. Moreover, the implementation of inverse design with hPINN can be easier than that of conventional methods because it exploits the extensive deep-learning software infrastructure. [ABSTRACT FROM AUTHOR]

In recent years, the motion capture system has received a lot of attention because of its wide application, such as movie animation, sport and medical applications. In the field of rehabilitation, motion capture systems are often used to collect the motion information of the patient when he/she is performing rehabilitation tasks. It can be used to quantify the patient’s rehabilitation effectiveness and provide the physician with more objective data as a reference. Using inertial sensors is one of motion capture methods. However, the major challenge to reconstruct accurate human posture with sensor measurements are signal noise, bias and inaccurate gyroscope estimation during long-term wearing. Based on the reason mentioned above, this paper proposes a graph convolutional network (GCN)-based deep learning architecture that uses effective information collected by inertial sensors to predict a sequence of position of each joint of a human’s lower limbs in the 3D space throughout the entire motion. Such motion prediction result based on the deep learning model is to reduce the joint’s tracking error relying only on direct calculations based on measurements of inertial sensors. In the final experiment, the lower limb motion trajectory during walking is used to verify that the method proposed in this work can actually outperform the traditional ones as just mentioned by achieving 2.9 mm drop in mean per joint position error (MPJPE) in 3.6M dataset, resulting in 12.2 mm in MPJPE, and mitigate the drift in real scenario. In our future work, we plan to verify the effectiveness of the proposed model and system for rehabilitation through clinical studies. [ABSTRACT FROM AUTHOR]

Accurate prediction of blood glucose variations in type 2 diabetes (T2D) will facilitate better glycemic control and decrease the occurrence of hypoglycemic episodes as well as the morbidity and mortality associated with T2D, hence increasing the quality of life of patients. Owing to the complexity of the blood glucose dynamics, it is difficult to design accurate predictive models in every circumstance, i.e., hypo/normo/hyperglycemic events. We developed deep-learning methods to predict patient-specific blood glucose during various time horizons in the immediate future using patient-specific every 30-min long glucose measurements by the continuous glucose monitoring (CGM) to predict future glucose levels in 5 min to 1 h. In general, the major challenges to address are (1) the dataset of each patient is often too small to train a patient-specific deep-learning model, and (2) the dataset is usually highly imbalanced given that hypo- and hyperglycemic episodes are usually much less common than normoglycemia. We tackle these two challenges using transfer learning and data augmentation, respectively. We systematically examined three neural network architectures, different loss functions, four transfer-learning strategies, and four data augmentation techniques, including mixup and generative models. Taken together, utilizing these methodologies we achieved over 95% prediction accuracy and 90% sensitivity for a time period within the clinically useful 1 h prediction horizon that would allow a patient to react and correct either hypoglycemia and/or hyperglycemia. We have also demonstrated that the same network architecture and transfer-learning methods perform well for the type 1 diabetes OhioT1DM public dataset. [ABSTRACT FROM AUTHOR]

Deep learning has been shown to be an effective tool in solving partial differential equations (PDEs) through physics-informed neural networks (PINNs). PINNs embed the PDE residual into the loss function of the neural network, and have been successfully employed to solve diverse forward and inverse PDE problems. However, one disadvantage of the first generation of PINNs is that they usually have limited accuracy even with many training points. Here, we propose a new method, gradient-enhanced physics-informed neural networks (gPINNs), for improving the accuracy of PINNs. gPINNs leverage gradient information of the PDE residual and embed the gradient into the loss function. We tested gPINNs extensively and demonstrated the effectiveness of gPINNs in both forward and inverse PDE problems. Our numerical results show that gPINN performs better than PINN with fewer training points. Furthermore, we combined gPINN with the method of residual-based adaptive refinement (RAR), a method for improving the distribution of training points adaptively during training, to further improve the performance of gPINN, especially in PDEs with solutions that have steep gradients. • We propose a new method, gradient-enhanced physics-informed neural networks (gPINNs). • gPINNs leverage gradient information of the PDE residual and embed it into the loss. • We demonstrate the effectiveness of gPINNs in both forward and inverse PDE problems. • We combine gPINN with the residual-based adaptive refinement for further improvement. [ABSTRACT FROM AUTHOR]

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and engineering. Herein, we investigate the performance of two neural operators, which have shown promising results so far, and we develop new practical extensions that will make them more accurate and robust and importantly more suitable for industrial-complexity applications. The first neural operator, DeepONet , was published in 2019 (Lu et al., 2019), and its original architecture was based on the universal approximation theorem of Chen & Chen (1995). The second one, named Fourier Neural Operator or FNO , was published in 2020 (Li et al., 2020), and it is based on parameterizing the integral kernel in the Fourier space. DeepONet is represented by a summation of products of neural networks (NNs), corresponding to the branch NN for the input function and the trunk NN for the output function; both NNs are general architectures, e.g., the branch NN can be replaced with a CNN or a ResNet. According to Kovachki et al. (2021), FNO in its continuous form can be viewed conceptually as a DeepONet with a specific architecture of the branch NN and a trunk NN represented by a trigonometric basis. In order to compare FNO with DeepONet computationally for realistic setups, we develop several extensions of FNO that can deal with complex geometric domains as well as mappings where the input and output function spaces are of different dimensions. We also develop an extended DeepONet with special features that provide inductive bias and accelerate training, and we present a faster implementation of DeepONet with cost comparable to the computational cost of FNO, which is based on the Fast Fourier Transform. We consider 16 different benchmarks to demonstrate the relative performance of the two neural operators, including instability wave analysis in hypersonic boundary layers, prediction of the vorticity field of a flapping airfoil, porous media simulations in complex-geometry domains, etc. We follow the guiding principles of FAIR (Findability, Accessibility, Interoperability, and Reusability) for scientific data management and stewardship. The performance of DeepONet and FNO is comparable for relatively simple settings, but for complex geometries the performance of FNO deteriorates greatly. We also compare theoretically the two neural operators and obtain similar error estimates for DeepONet and FNO under the same regularity assumptions. • We develop new practical extensions of DeepONet and FNO that make them more accurate and robust. • We consider 16 different benchmarks to demonstrate the performance of DeepONet and FNO. • We obtain theoretical error estimates of DeepONet and FNO. [ABSTRACT FROM AUTHOR]

• Efficient DeepONets are developed for the non-equilibrium chemistry at high Mach numbers. • We obtain good prediction when the Mach number is out of the input. • We develop a new inference tool, DeepMMnet for complex multiphysics and multiscale models. • DeepMMnets assimilate sparse data using pre-trained DeepONets in a "plug-and-play" mode. • The codes are compact and easy to adopt in diverse domains as well as maintain or enhance further. In high-speed flow past a normal shock, the fluid temperature rises rapidly triggering downstream chemical dissociation reactions. The chemical changes lead to appreciable changes in fluid properties, and these coupled multiphysics and the resulting multiscale dynamics are challenging to resolve numerically. Using conventional computational fluid dynamics (CFD) requires excessive computing cost. Here, we propose a totally new efficient approach, assuming that some sparse measurements of the state variables are available that can be seamlessly integrated in the simulation algorithm. We employ a special neural network for approximating nonlinear operators, the DeepONet [23] , which is used to predict separately each individual field, given inputs from the rest of the fields of the coupled multiphysics system. We demonstrate the effectiveness of DeepONet for a benchmark hypersonic flow involving seven field variables. Specifically we predict five species in the non-equilibrium chemistry downstream of a normal shock at high Mach numbers as well as the velocity and temperature fields. We show that upon training, DeepONets can be over five orders of magnitude faster than the CFD solver employed to generate the training data and yield good accuracy for unseen Mach numbers within the range of training. Outside this range, DeepONet can still predict accurately and fast if a few sparse measurements are available. We then propose a composite supervised neural network, DeepM&Mnet, that uses multiple pre-trained DeepONets as building blocks and scattered measurements to infer the set of all seven fields in the entire domain of interest. Two DeepM&Mnet architectures are tested, and we demonstrate the accuracy and capacity for efficient data assimilation. DeepM&Mnet is simple and general: it can be employed to construct complex multiphysics and multiscale models and assimilate sparse measurements using pre-trained DeepONets in a "plug-and-play" mode. [ABSTRACT FROM AUTHOR]

Abstract Background China is progressing towards the goal of schistosomiasis elimination, but there are still some problems, such as difficult management of infection source and snail control. This study aimed to develop deep learning models with high-resolution remote sensing images for recognizing and monitoring livestock bovine, which is an intermediate source of Schistosoma japonicum infection, and to evaluate the effectiveness of the models for real-world application. Methods The dataset of livestock bovine’s spatial distribution was collected from the Chinese National Platform for Common Geospatial Information Services. The high-resolution remote sensing images were further divided into training data, test data, and validation data for model development. Two recognition models based on deep learning methods (ENVINet5 and Mask R-CNN) were developed with reference to the training datasets. The performance of the developed models was evaluated by the performance metrics of precision, recall, and F1-score. Results A total of 50 typical image areas were selected, 1125 bovine objectives were labeled by the ENVINet5 model and 1277 bovine objectives were labeled by the Mask R-CNN model. For the ENVINet5 model, a total of 1598 records of bovine distribution were recognized. The model precision and recall were 81.9% and 80.2%, respectively. The F1 score was 0.81. For the Mask R-CNN mode, 1679 records of bovine objectives were identified. The model precision and recall were 87.3% and 85.2%, respectively. The F1 score was 0.87. When applying the developed models to real-world schistosomiasis-endemic regions, there were 63 bovine objectives in the original image, 53 records were extracted using the ENVINet5 model, and 57 records were extracted using the Mask R-CNN model. The successful recognition ratios were 84.1% and 90.5% for the respectively developed models. Conclusion The ENVINet5 model is very feasible when the bovine distribution is low in structure with few samples. The Mask R-CNN model has a good framework design and runs highly efficiently. The livestock recognition models developed using deep learning methods with high-resolution remote sensing images accurately recognize the spatial distribution of livestock, which could enable precise control of schistosomiasis. Graphical Abstract

• DeepONets can learn the electroconvection operator using a small number of data. • DeepONets achieve high accuracy at 1000X speed for the unseen testing data. • DeepM&Mnet is proposed as a new data assimilation framework. • DeepM&Mnet enables the combination of data measurements and pre-trained DeepONets. • A comparison between two DeepM&Mnet architectures is performed. Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. Here, we use electroconvection as a benchmark problem to put forward a new data assimilation framework, the DeepM&Mnet, for simulating multiphysics and multiscale problems at speeds much faster than standard numerical methods using pre-trained neural networks. We first pre-train DeepONets that can predict independently each field, given general inputs from the rest of the fields of the coupled system. DeepONets can approximate nonlinear operators and are composed of two sub-networks, a branch net for the input fields and a trunk net for the locations of the output field. DeepONets, which are extremely fast, are used as building blocks in the DeepM&Mnet and form constraints for the multiphysics solution along with some sparse available measurements of any of the fields. We demonstrate the new methodology and document the accuracy of each individual DeepONet, and subsequently we present two different DeepM&Mnet architectures that infer accurately and efficiently 2D electroconvection fields for unseen electric potentials. The DeepM&Mnet framework is general and can be applied for building any complex multiphysics and multiscale models based on very few measurements using pre-trained DeepONets in a "plug-and-play" mode. [ABSTRACT FROM AUTHOR]

Full waveform inversion (FWI) infers the subsurface structure information from seismic waveform data by solving a non-convex optimization problem. Data-driven FWI has been increasingly studied with various neural network architectures to improve accuracy and computational efficiency. Nevertheless, the applicability of pre-trained neural networks is severely restricted by potential discrepancies between the source function used in the field survey and the one utilized during training. Here, we develop a Fourier-enhanced deep operator network (Fourier-DeepONet) for FWI with the generalization of seismic sources, including the frequencies and locations of sources. Specifically, we employ the Fourier neural operator as the decoder of DeepONet, and we utilize source parameters as one input of Fourier-DeepONet, facilitating the resolution of FWI with variable sources. To test Fourier-DeepONet, we develop three new and realistic FWI benchmark datasets (FWI-F, FWI-L, and FWI-FL) with varying source frequencies, locations, or both. Our experiments demonstrate that compared with existing data-driven FWI methods, Fourier-DeepONet obtains more accurate predictions of subsurface structures in a wide range of source parameters. Moreover, the proposed Fourier-DeepONet exhibits superior robustness when handling data with Gaussian noise or missing traces and sources with Gaussian noise, paving the way for more reliable and accurate subsurface imaging across diverse real conditions. [ABSTRACT FROM AUTHOR]

Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural operators such as deep operator networks (DeepONets) provide a new simulation paradigm in science and engineering. Pure data-driven neural operators and deep learning models, in general, are usually limited to interpolation scenarios, where new predictions utilize inputs within the support of the training set. However, in the inference stage of real-world applications, the input may lie outside the support, i.e., extrapolation is required, which may result to large errors and unavoidable failure of deep learning models. Here, we address this challenge of extrapolation for deep neural operators. First, we systematically investigate the extrapolation behavior of DeepONets by quantifying the extrapolation complexity, via the 2-Wasserstein distance between two function spaces and propose a new strategy of bias–variance trade-off for extrapolation with respect to model capacity. Subsequently, we develop a complete workflow, including extrapolation determination, and we propose five reliable learning methods that guarantee a safe prediction under extrapolation by requiring additional information—the governing PDEs of the system or sparse new observations. The proposed methods are based on either fine-tuning a pre-trained DeepONet or multifidelity learning. We demonstrate the effectiveness of the proposed framework for various types of parametric PDEs. Our systematic comparisons provide practical guidelines for selecting a proper extrapolation method depending on the available information, desired accuracy, and required inference speed. [ABSTRACT FROM AUTHOR]