Physics-informed Neural Networks Research Articles

A Transformative Approach for Breast Cancer Detection Using Physics-Informed Neural Network and Surface Temperature Data

Abstract Early detection is the most effective defense against breast cancer. Mammography is a well-established X-ray based technique that is used for annual or biennial screening of women above age of 40. Since the dense breast tissue sometimes obscures the cancer in an x-ray image, about 10% of screened women are recalled and undergo additional adjunctive modalities, such as ultrasound, digital breast tomosynthesis or magnetic resonance imaging (MRI). These modalities have drawbacks such as additional radiation dosage, overdiagnosis and high cost. A new concurrent multi-spectral imaging approach is recently presented to eliminate the high recall rates by utilizing the breast surface temperature data with an inverse physics-informed neural network algorithm. The multi-spectral imaging does not use any harmful radiations, such as x-rays, is contact-less and does not require breast compression. It has been validated in 23 patients and offers a cost-effective solution to provide improved detection capability of cancerous cells. It is estimated to reduce the recall rates significantly from the current 10%, with a corresponding reduction in the biopsies. This adjunctive approach builds on the strength of mammography and offers a safe adjunct by relying on the higher metabolic rates of cancer cells.

Development of a cascaded multitask physics-informed neural network (CM-PINN) to construct the muti-physical field model of rubber bushing press fitting

Development of a cascaded multitask physics-informed neural network (CM-PINN) to construct the muti-physical field model of rubber bushing press fitting

A sequential meta-transfer (SMT) learning to combat complexities of physics-informed neural networks: Application to composites autoclave processing

Physics-Informed Neural Networks (PINNs) have gained popularity in solving nonlinear partial differential equations (PDEs) via integrating physical laws into the training of neural networks, making them superior in many scientific and engineering applications. However, conventional PINNs still fall short in accurately approximating the solution of complex systems with strong nonlinearity, especially in long temporal domains. Besides, since PINNs are designed to approximate a specific realization of a given PDE system, they lack the necessary generalizability to efficiently adapt to new system configurations. This entails computationally expensive re-training from scratch for any new change in the system. To address these shortfalls, in this work a sequential meta-transfer (SMT) learning framework is proposed, offering a unified solution for both fast training and efficient adaptation of PINNs in highly nonlinear systems with long temporal domains. Specifically, the framework decomposes PDE's time domain into smaller time segments to create “easier” PDE problems for PINNs training. Then for each time interval, a meta-learner is assigned and trained to achieve an optimal initial state for rapid adaptation to a range of related tasks. Transfer learning principles are then leveraged across time intervals to further reduce the computational cost. Through a composites autoclave processing case study, it is shown that SMT is clearly able to enhance the adaptability of PINNs while significantly reducing computational cost, by a factor of 100.

A gradient-enhanced physics-informed neural networks method for the wave equation

Physics-informed neural networks (PINNs) have been proven to be a useful tool for solving general partial differential equations (PDEs), which is meshless and dimensionally free compared with traditional numerical solvers. Based on PINNs, gradient-enhanced physics-informed neural networks (gPINNs) add the partial derivative loss term of the independent variable and the physical constraint term, which improves the accuracy of network training. In this paper, the gPINNs method is proposed to solve the wave problem. The equation boundary value of the wave problem is added in the network construction, thus the network is forced to satisfy the equation boundary value during each training process. Two examples of wave equations are given in our paper, which are solved numerically by PINNs and gPINNs, respectively. It is found that using fewer data sets, gPINNs can learn data features more fully than PINNs and better results of gPINNs can be obtained.

Investigating the ability of PINNs to solve Burgers’ PDE near finite-time blowup

Physics Informed Neural Networks (PINNs) have been achieving ever newer feats of solving complicated Partial Differential Equations (PDEs) numerically while offering an attractive trade-off between accuracy and speed of inference. A particularly challenging aspect of PDEs is that there exist simple PDEs which can evolve into singular solutions in finite time starting from smooth initial conditions. In recent times some striking experiments have suggested that PINNs might be good at even detecting such finite-time blow-ups. In this work, we embark on a program to investigate this stability of PINNs from a rigorous theoretical viewpoint. Firstly, we derive error bounds for PINNs for Burgers’ PDE, in arbitrary dimensions, under conditions that allow for a finite-time blow-up. Our bounds give a theoretical justification for the functional regularization terms that have been reported to be useful for training PINNs near finite-time blow-up. Then we demonstrate via experiments that our bounds are significantly correlated to the ℓ2 -distance of the neurally found surrogate from the true blow-up solution, when computed on sequences of PDEs that are getting increasingly close to a blow-up.

Reconstruction of dynamic wind turbine wake flow fields from virtual Lidar measurements via physics-informed neural networks

Accurate characterisation of wind turbine wakes is important for the optimal design and operation of wind farms. However, current techniques for full-scale wind measurements are still limited to point characterisation. To address the research challenge in obtaining field characterisation of real-world wind turbine wakes, this work investigates the reconstruction of the dynamic wake flow fields based on a virtual turbine-mounted Lidar and physics-informed neural networks. Specifically, the wake flow field is reconstructed by fusing the sparse measurements with the two-dimensional Navier-Stokes equations without imposing any models for the unsteady wake. Different from supervised machine learning approaches which need the measured values for the quantities of interest in the first place, the proposed method can achieve the prediction of the wind velocity at new locations where there is no measurement available. The reconstruction performance is evaluated via high-fidelity numerical experiments and it is shown that the dynamic wind turbine wake flow fields are predicted accurately, where the main wake features, including the downwind development and crosswind meandering of the wake, are both captured. This work thus paves the way for investigating full-scale in situ wake flow dynamics in real-world wind energy sites.

Physics-informed machine learning for moving load problems

Abstract This paper presents a new approach to simulate forward and inverse problems of moving loads using physics-informed machine learning (PIML). Physics-informed neural networks (PINNs) utilize the underlying physics of moving load problems and aim to predict the deflection of beams and the magnitude of the loads. The mathematical representation of the moving load considered involves a Dirac delta function, to capture the effect of the load moving across the structure. Approximating the Dirac delta function with PINNs is challenging because of its instantaneous change of output at a single point, causing difficulty in the convergence of the loss function. We propose to approximate the Dirac delta function with a Gaussian function. The incorporated Gaussian function physical equations are used in the physics-informed neural architecture to simulate beam deflections and to predict the magnitude of the load. Numerical results show that PIML is an effective method for simulating the forward and inverse problems for the considered model of a moving load.

A physics-informed deep learning description of Knudsen layer reactivity reduction

A physics-informed neural network (PINN) is used to evaluate the fast ion distribution in the hot spot of an inertial confinement fusion target. The use of tailored input and output layers to the neural network is shown to enable a PINN to learn the parametric solution to the Vlasov–Fokker–Planck equation in the absence of any synthetic or experimental data. As an explicit demonstration of the approach, the specific problem of Knudsen layer fusion yield reduction is treated. Here, the predictions from the Vlasov–Fokker–Planck PINN are used to provide a non-perturbative solution of the fast ion tail in the vicinity of the hot spot, thus allowing the spatial profile of the fusion reactivity to be evaluated for a range of collisionalities and hot spot conditions. Excellent agreement is found between the predictions of the Vlasov–Fokker–Planck PINN and the results from traditional numerical solvers with respect to both the energy and spatial distribution of fast ions and the fusion reactivity profile, demonstrating that the Vlasov–Fokker–Planck PINN provides an accurate and efficient means of determining the impact of Knudsen layer yield reduction across a broad range of plasma conditions.

RANS wake surrogate: Impact of Physics Information in Neural Networks

Artificial Neural Networks (ANNs) are being applied as a faster alternative to Computational Fluid Dynamics (CFD) for wind turbine engineering wake models. Unfortunately, ANNs can fail to generalize if the data is insufficient. Physics-Informed Neural Networks (PINNs) can improve convergence while lowering the required data amounts. This paper investigates the PINN methodology systematically by considering varying amounts of data and physics collocation points. This work considers the rotationally symmetric Reynolds Averaged Navier-Stokes (RANS) formulation. Initially, a baseline fully data-driven ANN is studied to determine a suitable network size. Then, multiple PINN-based wake surrogates are trained with continuity and momentum conservation knowledge, varying amounts of data, and physics collocation points. It was found that including physics information under the best circumstances could improve accuracy by 18% at the cost of increasing the training time by a factor of 116. The findings imply that physics information can improve neural network based wake surrogates.

Physics-informed neural networks for fully non-linear free surface wave propagation

This study proposed fully nonlinear free surface physics-informed neural networks (FNFS-PINNs), an advancement within the framework of PINNs, to tackle wave propagation in fully nonlinear potential flows with the free surface. Utilizing the nonlinear fitting capabilities of neural networks, FNFS-PINNs offer an approach to addressing the complexities of modeling nonlinear free surface flows, broadening the scope for applying PINNs to various wave propagation scenarios. The improved quasi-σ coordinate transformation and dimensionless formulation of the basic equations are adopted to transform the time-dependent computational domain into the stationary one and align variable scale changes across different dimensions, respectively. These innovations, alongside a specialized network structure and a two-stage optimization process, enhance the mathematical formulation of nonlinear water waves and solvability of the model. FNFS-PINNs are evaluated through three scenarios: solitary wave propagation featuring nonlinearity, regular wave propagation under high dispersion, and an inverse problem of nonlinear free surface flow focusing on the back-calculation of an initial state from its later state. These tests demonstrate the capability of FNFS-PINNs to compute the propagation of solitary and regular waves in the vertical two-dimensional scenarios. While focusing on two-dimensional wave propagation, this study lays the groundwork for extending FNFS-PINNs to other free surface flows and highlights their potential in solving inverse problems.

Structural damage inverse detection from noisy vibration measurement with physics-informed neural networks

Structural damage inverse detection from noisy vibration measurement with physics-informed neural networks

EcoBlendNet: A physics-informed neural network for optimizing supplementary material replacement to reduce the carbon footprint during cement hydration

The addition of supplementary cementitious materials (SCMs) to cement triggers a complex chemo-physics from intricate mineral admixture interactions. This work develops EcoBlendNet, a novel physics-informed neural network (PINN), to analyze carbon emissions during SCMs-enhanced cement hydration. EcoBlendNet integrates experimental data and the chemo-physical aspects of cement hydration in a heated cement paste for various mixing blends, including Portland cement, cement-fly ash blends, and cement-slag blends. EcoBlendNet accurately predicts concrete maturity and strength, capturing early-age temperature rises. Achieving a remarkable relative L2 error of 0.03 with just 5% of training data, it facilitates efficient mesh-free analysis. The study demonstrates that transitioning from cement-blend to cement-fly ash and cement-slag blends can significantly reduce CO2 emissions without compromising strength development. Quantitative analysis suggests that replacing 45–80% of cement with industrial fly ash and slag can decrease CO2 emissions by 60–80% during cement hydration. Thus, EcoBlendNet, validated through experimentation, offers a practical and eco-friendly approach to concrete construction, bridging the gap between theory and practice.

Boundary integrated neural networks and code for acoustic radiation and scattering

AbstractThis paper presents a novel approach called the boundary integrated neural networks (BINNs) for analyzing acoustic radiation and scattering. The method introduces fundamental solutions of the time‐harmonic wave equation to encode the boundary integral equations (BIEs) within the neural networks, replacing the conventional use of the governing equation in physics‐informed neural networks (PINNs). This approach offers several advantages. First, the input data for the neural networks in the BINNs only require the coordinates of “boundary” collocation points, making it highly suitable for analyzing acoustic fields in unbounded domains. Second, the loss function of the BINNs is not a composite form and has a fast convergence. Third, the BINNs achieve comparable precision to the PINNs using fewer collocation points and hidden layers/neurons. Finally, the semianalytic characteristic of the BIEs contributes to the higher precision of the BINNs. Numerical examples are presented to demonstrate the performance of the proposed method, and a MATLAB code implementation is provided as supplementary material.

Enhancing the accuracy of physics-informed neural networks for indoor airflow simulation with experimental data and Reynolds-averaged Navier–Stokes turbulence model

Enhancing the accuracy of physics-informed neural networks for indoor airflow simulation with experimental data and Reynolds-averaged Navier–Stokes turbulence model

Physics-informed neural networks for parameter estimation and simulation of a two-group epidemiological model

This paper provides a comprehensive exploration of physics-informed neural networks and their core features. It delves into their role in tackling inverse problems inherent in ordinary differential equation-based models. Within this context, we introduce a two-group epidemiological model, elucidating its fundamental attributes. The central objective of this research is to accurately estimate the model parameters for both groups in the epidemiological model. We offer a detailed exposition of the adopted methodology, providing insights into the algorithm and the techniques employed for its implementation. Through this analysis, we illuminate the complexities of our study, contributing to the growing body of knowledge in this field, which intersects epidemiology and neural network-based parameter estimation for an enriched understanding of infectious disease dynamics.

Efficiently Training Physics-Informed Neural Networks via Anomaly-Aware Optimization

Efficiently Training Physics-Informed Neural Networks via Anomaly-Aware Optimization

Splitting Physics-Informed Neural Networks for Inferring the Dynamics of Integer- and Fractional-Order Neuron Models

Splitting Physics-Informed Neural Networks for Inferring the Dynamics of Integer- and Fractional-Order Neuron Models

Empirical loss weight optimization for PINN modeling laser bio-effects on human skin for the 1D heat equation

The application of deep neural networks towards solving problems in science and engineering has demonstrated encouraging results with the recent formulation of physics-informed neural networks (PINNs). Through the development of refined machine learning techniques, the high computational cost of obtaining numerical solutions for partial differential equations governing complicated physical systems can be mitigated. However, solutions are not guaranteed to be unique, and are subject to uncertainty caused by the choice of network model parameters. For critical systems with significant consequences for errors, assessing and quantifying this model uncertainty is essential. In this paper, an application of PINN for laser bio-effects with limited training data is provided for uncertainty quantification analysis. Additionally, an efficacy study is performed to investigate the impact of the relative weights of the loss components of the PINN and how the uncertainty in the predictions depends on these weights. Network ensembles are constructed to empirically investigate the diversity of solutions across an extensive sweep of hyper-parameters to determine the model that consistently reproduces a high-fidelity numerical simulation.

Smoothness: The key factor in well-log information-assisted PINNtomo

Seismic traveltime tomography is popularly used to provide a smooth background model for subsequent depth migration or full waveform inversion (FWI). The core of the traveltime tomography process requires an eikonal solver for seismic traveltime calculation. Most of the conventional eikonal solvers, suffer from first-order convergence errors and difficulties in dealing with irregular topography, which will lead to inaccurate seismic tomography results. To solve these issues, physics-informed neural networks (PINNs) have been developed and demonstrated remarkable success in simultaneous traveltime calculation and velocity construction, which is referred to as PINNtomo. It combines the physics constraint (eikonal equation) and data constraint (traveltime fitting) to form the loss function of the networks. Though PINNtomo can manage to recover a smooth background velocity, it will fail in the inversion for a complicated high-resolution velocity model. We take advantage of the well-log velocity as a prior information to provide an additional model constraint in the loss function to improve the performance of PINNtomo. We found that the well-log information will provide high-resolution components in the inverted velocity model. However, it will destroy the lateral structure of the true model. We propose to use a smoothed version of the well-log velocity as the prior model constraint in PINNtomo. As a result, the accuracy of the inverted background velocity will be improved, which will be beneficial to the subsequent FWI.

Energy-informed graph transformer model for solid mechanical analyses

Physics-informed neural network (PINN) exists some challenges, such as independent and uncorrelated drawbacks leading to convergence impediments, limited interpretability and lack of generalization. In this paper, a novel energy-informed graph transformer model is proposed to overcome the drawbacks of PINN. In the proposed model, the graph neural network-based-attention mechanism is proposed to dynamically calculate weight coefficients between objects of graph-structured data, and then to aggregate weighted combinations of the neighbor objects features to update features of the target objects. The loss function is constructed with homoscedastic uncertainty by introducing trainable scalar parameters, which can be optimized to achieve the best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. Numerical results show that the proposed method can effectively increase the efficiency, robustness and accuracy of the network approximation of forward and inverse problems of solid mechanics. Furthermore, the proposed model demonstrates excellent generalization capabilities when applied to new problem using transfer learning strategy.