Physics-informed Framework Research Articles

AI-Aristotle: A physics-informed framework for systems biology gray-box identification.

Discovering mathematical equations that govern physical and biological systems from observed data is a fundamental challenge in scientific research. We present a new physics-informed framework for parameter estimation and missing physics identification (gray-box) in the field of Systems Biology. The proposed framework-named AI-Aristotle-combines the eXtreme Theory of Functional Connections (X-TFC) domain-decomposition and Physics-Informed Neural Networks (PINNs) with symbolic regression (SR) techniques for parameter discovery and gray-box identification. We test the accuracy, speed, flexibility, and robustness of AI-Aristotle based on two benchmark problems in Systems Biology: a pharmacokinetics drug absorption model and an ultradian endocrine model for glucose-insulin interactions. We compare the two machine learning methods (X-TFC and PINNs), and moreover, we employ two different symbolic regression techniques to cross-verify our results. To test the performance of AI-Aristotle, we use sparse synthetic data perturbed by uniformly distributed noise. More broadly, our work provides insights into the accuracy, cost, scalability, and robustness of integrating neural networks with symbolic regressors, offering a comprehensive guide for researchers tackling gray-box identification challenges in complex dynamical systems in biomedicine and beyond.

A cusp-capturing PINN for elliptic interface problems

In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve discontinuous-coefficient elliptic interface problems whose solution is continuous but has discontinuous first derivatives on the interface. To find such a solution using neural network representation, we introduce a cusp-enforced level set function as an additional feature input to the network to retain the inherent solution properties; that is, capturing the solution cusps (where the derivatives are discontinuous) sharply. In addition, the proposed neural network has the advantage of being mesh-free, so it can easily handle problems in irregular domains. We train the network using the physics-informed framework in which the loss function comprises the residual of the differential equation together with certain interface and boundary conditions. We conduct a series of numerical experiments to demonstrate the effectiveness of the cusp-capturing technique and the accuracy of the present network model. Numerical results show that even using a one-hidden-layer (shallow) network with a moderate number of neurons and sufficient training data points, the present network model can achieve prediction accuracy comparable with traditional methods. Besides, if the solution is discontinuous across the interface, we can simply incorporate an additional supervised learning task for solution jump approximation into the present network without much difficulty.

A novel physics-informed framework for real-time adaptive modal parameters estimation of offshore structures

Singular value decomposition provides a rigorous mathematical foundation for these monitoring methods, such as modal analysis, damage detection, etc. As substantial limitations including computational efficiency and adaptive capabilities have been identified in the matrix process, data-driven algorithms with enhanced efficiency and accuracy to adapt the rapid development of information and technologies have been highly required in offshore structures monitoring. To meet this demand, a novel physics-informed frame work enabling the real-time adaptive monitoring has been proposed in this paper. The working principle of the developed framework has been represented by the smart conversion of physics-informed modal identification into the optimal process of fast and accurate solving an eigensystem governed by differential equations via recurrent neural network. The ingenious design of the proposed framework has complied with the rule of singular value decomposition used for modal identification and therefore, learning capabilities of the physics-informed framework have been remarkably enhanced by successfully addressing two bottleneck problems including proper initialized input values and the optimal time increment of the developed recurrent neural network. Both numerical simulations and the field-data based study of a mono-pile offshore wind turbine structure have been presented to examine the superior performance of the proposed framework. Results have shown that the proposed framework has the ability to adaptively identify modal parameters with a higher level of computational efficiency as compared with traditional methods. Furthermore, the computational advantage of the develop framework has demonstrated the potential to integrate with sensor networks and edge computing for smart monitoring and maintenance in various engineering subjects.

A data-driven physics-informed stochastic framework for hurricane-induced risk estimation of transmission tower-line systems under a changing climate

Hurricanes are one of the most devastating natural hazards which result in significant damage to civil infrastructure. The transmission tower-line system is specifically highly vulnerable to hurricane effects. Recent studies have indicated that the collapse of the transmission tower-line system during hurricane events is mainly due to the joint occurrence of wind and rain. Therefore, it is important to assess the failure probabilities of these structures under wind and rain-induced loads. With climate change, those probabilities are expected to significantly change where the brunt of the damage and economic losses would be disproportionately borne by coastal communities. This study proposes a hybrid risk-responsive, data-driven and physics-informed framework which evaluates the hurricane-induced damage to transmission lines in vulnerable regions and communities under several climate scenarios. The framework is founded upon an advanced physics informed hurricane simulation model followed by a Gaussian kernel density technique to efficiently estimate the intensity measures and quantify the associated uncertainties accurately. The generated hazard intensities are coupled with fragility surfaces expressed in terms of wind speed and rain intensity. Then, the failure probabilities are obtained for the transmission tower-line system under the joint excitation and future climate scenario. The framework is applied to several coastal cities along the US east coast. It is shown that, due to the involved system nonlinearity, the obtained failure probabilities change drastically with the future climate scenario. In addition, rainfall-induced loads which significantly impact the failure probabilities of the transmission tower-line systems are not only function of the selected sites, but also depend on the considered limit state and climate scenario. Therefore, their consideration is important for the structural design and estimation of the system performance.

A novel physics-informed framework for reconstruction of structural defects

The ultrasonic guided wave technology plays a significant role in the field of non-destructive testing as it employs acoustic waves with the advantages of high propagation efficiency and low energy consumption during the inspect process. However, the theoretical solutions to guided wave scattering problems with assumptions such as the Born approximation have led to the poor quality of the reconstructed results. Besides, the scattering signals collected from industry sectors are often noised and nonstationary. To address these issues, a novel physics-informed framework (PIF) for the quantitative reconstruction of defects by means of the integration of the data-driven method with the guided wave scattering analysis is proposed in this paper. Based on the geometrical information of defects and initial results obtained by the PIF-based analysis of defect reconstructions, a deep-learning neural network model is built to reveal the physical relationship between the defects and the noisy detection signals. This learning model is then adopted to assess and characterize the defect profiles in structures, improve the accuracy of the analytical model, and eliminate the impact of the noise pollution in the process of inspection. To demonstrate the advantages of the developed PIF for the complex defect reconstructions with the capability of denoising, several numerical examples are carried out. The results show that the PIF has greater accuracy for the reconstruction of defects in the structures than the analytical method, and provides a valuable insight into the development of artificial intelligence (AI)-assisted inspection systems with high accuracy and efficiency in the fields of structural integrity and condition monitoring.

DRVN (deep random vortex network): A new physics-informed machine learning method for simulating and inferring incompressible fluid flows

We present the deep random vortex network (DRVN), a novel physics-informed framework for simulating and inferring the fluid dynamics governed by the incompressible Navier–Stokes equations. Unlike the existing physics-informed neural network (PINN), which embeds physical and geometry information through the residual of equations and boundary data, DRVN automatically embeds this information into neural networks through neural random vortex dynamics equivalent to the Navier–Stokes equation. Specifically, the neural random vortex dynamics motivates a Monte Carlo-based loss function for training neural networks, which avoids the calculation of derivatives through auto-differentiation. Therefore, DRVN can efficiently solve Navier–Stokes equations with non-differentiable initial conditions and fractional operators. Furthermore, DRVN naturally embeds the boundary conditions into the kernel function of the neural random vortex dynamics and, thus, does not need additional data to obtain boundary information. We conduct experiments on forward and inverse problems with incompressible Navier–Stokes equations. The proposed method achieves accurate results when simulating and when inferring Navier–Stokes equations. For situations that include singular initial conditions and agnostic boundary data, DRVN significantly outperforms the existing PINN method. Furthermore, compared with the conventional adjoint method when solving inverse problems, DRVN achieves a 2 orders of magnitude improvement for the training time with significantly precise estimates.

Physics-informed distribution transformers via molecular dynamics and deep neural networks

Generating quasirandom points with high uniformity is a fundamental task in many fields. Existing number-theoretic approaches produce evenly distributed points in [0,1]d in asymptotic sense but may not yield a good distribution for a given set size. It is also difficult to extend those techniques to other geometries like a disk or a manifold. In this paper, we present a novel physics-informed framework to transform a given set of points into a distribution with better uniformity. We model each point as a particle and assign the system with a potential energy. Upon minimizing the energy, the uniformity of distribution can be improved correspondingly. Two kinds of schemes are introduced: one based on molecular dynamics and another based on deep neural networks. The new physics-informed framework serves as a black-box transformer that is able to improve given distributions and can be easily extended to other geometries such as disks, spheres, complex manifolds, etc. Various experiments with different geometries are provided to demonstrate that the new framework is able to transform poorly distributed input into one with superior uniformity.

Physics-informed PointNet: A deep learning solver for steady-state incompressible flows and thermal fields on multiple sets of irregular geometries

We present a novel physics-informed deep learning framework for solving steady-state incompressible flow on multiple sets of irregular geometries by incorporating two main elements: using a point-cloud based neural network to capture geometric features of computational domains, and using the mean squared residuals of the governing partial differential equations, boundary conditions, and sparse observations as the loss function of the network to capture the physics. While the solution of the continuity and Navier-Stokes equations is a function of the geometry of the computational domain, current versions of physics-informed neural networks have no mechanism to express this functionally in their outputs, and thus are restricted to obtain the solutions only for one computational domain with each training procedure. Using the proposed framework, three new facilities become available. First, the governing equations are solvable on a set of computational domains containing irregular geometries with high variations with respect to each other but requiring training only once. Second, after training the introduced framework on the set, it is now able to predict the solutions on domains with unseen geometries from seen and unseen categories as well. The former and the latter both lead to savings in computational costs. Finally, all the advantages of the point-cloud based neural network for irregular geometries, already used for supervised learning, are transferred to the proposed physics-informed framework. The effectiveness of our framework is shown through the method of manufactured solutions and thermally-driven flow for forward and inverse problems.

A physics-informed data reconciliation framework for real-time electricity and emissions tracking

To encourage and guide decarbonization efforts, better tools are needed to monitor real-time CO2 and criteria air pollutant emissions from electricity consumption, production, imports, and exports. Using real-time data from the electricity system is especially challenging for quantitative applications requiring high quality and physically consistent data. Until now, time-intensive, ad-hoc and manual data verification and cleaning strategies have been used to prepare the data for quantitative analysis. As an alternative to existing techniques, here we provide a physics-informed framework to greatly accelerate and automate data processing to enable internally consistent electric system consumption, production, import, and export data in near real-time. A key component of this framework is an optimization program to minimize the data adjustments required to satisfy energy conservation equations. The effectiveness of this method is demonstrated by applying it to the continental United States electricity network. The resulting publicly-available data set, which provides in near-real time, hourly updates on electricity generation, consumption, imports, exports and associated emissions, is the first of this nature.

A data-driven, physics-informed framework for forecasting the spatiotemporal evolution of chaotic dynamics with nonlinearities modeled as exogenous forcings

We introduce a data-driven, linear method for the spatiotemporal prediction of high-dimensional and chaotic dynamical systems. In this method, the observables are vector-valued and delay-embedded, and the nonlinearities are treated as external forcings. The proper representation of the nonlinear terms is found in a physics-informed way or a purely data-driven fashion, depending on whether any knowledge of governing dynamics is available or not. The unknown matrices appearing in the method are found using the dynamic mode decomposition with control technique. The distinctive features of the method enable it to accurately capture the system's dynamically important unstable modes while suppressing their unbounded growth via the included nonlinearities. The predictive capabilities of the method are demonstrated for well-known prototypes of chaotic dynamics such as the Kuramoto-Sivashinsky equation and Lorenz-96 system, for which the method predictions are accurate for several Lyapunov timescales. Similar performance is shown for two-dimensional lid-driven cavity flows at high Reynolds numbers.

Physically Based Modeling of Cyclic Plasticity for Highly Oriented Nanotwinned Metals

Abstract Fatigue resistance is crucial for the engineering application of metals. Polycrystalline metals with highly oriented nanotwins have been shown to exhibit a history-independent, stable, and symmetric cyclic response [Pan et al., 2017, Nature 551, pp. 214-217]. However, a constitutive model that incorporates the cyclic deformation mechanism of highly oriented nanotwinned metals is currently lacking. This study aims to develop a physically based model to describe the plastic deformation of highly oriented nanotwinned metals under cyclic loading parallel to the twin boundaries. The theoretical analysis is conducted based on non-uniform distribution of twin boundary spacing measured by experiments. During cyclic plasticity, each twin lamella is discretely regarded as a perfect elastoplastic element with a yielding strength depending on its thickness. The interaction between adjacent nanotwins is not taken into consideration according to the cyclic plasticity mechanism of highly oriented nanotwins. The modeling results are well consistent with the experiments, including the loading-history independence, Masing behavior, and back stress evolution. Moreover, the dissipation energy during cyclic deformation can be evaluated from a thermodynamics perspective, which offers an approach for the prediction of the fatigue life of highly oriented nanotwins. The cyclic plasticity modeling and fatigue life prediction are unified without additional fatigue damage parameters. Overall, our work lays down a physics-informed framework that is critical for the precise prediction of the unique cyclic behaviors of highly oriented nanotwins.

A physics-informed Run-to-Run control framework for semiconductor manufacturing

For decades, Run-to-Run (R2R) controllers have been widely implemented in semiconductor manufacturing. They operate over key process parameters on the basis of the metrological measurements acquired from the process and their deviations from the target setpoints. Conventionally, R2R controllers have been implemented independently of the actual equipment condition, which is obviously affecting the process stability and performance. Therefore, both equipment signals and process states shall be considered to make the R2R controllers more robust to the equipment condition drifts. In this paper, we propose a novel physics-informed framework to integrate the real-time equipment condition, based on the Fault Detection and Classification (FDC) data, into the R2R controllers. By utilizing Dynamic Bayesian Networks (DBN), the implicit relationship structure between metrology measurements, FDC indicators, and R2R regulators can be learned and reviewed explicitly. The structure shall be further reviewed to valid with the existing relationships and expert knowledge. Infeasible causalities on the structure will be constrained via setting up the blacklist at the structure learning stage. The proposed framework consists of the offline modeling stage, which incorporates the process, equipment variables, and the expert knowledge in the structure learning, and the online control stage, which constructs the Structured R2R controller (SRC) based on the relationship structure. As a result, the model is consistent by design with empirically known relationships and fundamental physical laws. The proposed SRC not only optimizes the operation with respect to the target control values but also considers the equipment and process states simultaneously. The effectiveness of SRC and the derivative control strategy are validated through a real dataset of a Chemical-Mechanical Polishing (CMP) process, and two simulated studies.