Physics-informed Machine Learning Approach Research Articles

A physics-informed machine learning approach for predicting acoustic convergence zone features from limited mesoscale eddy data

A physics-informed machine learning approach for predicting acoustic convergence zone features from limited mesoscale eddy data

The development of thermodynamically consistent and physics-informed equation-of-state model through machine learning

Ab initio molecular dynamics (AIMD) simulations have become an important tool used in the construction of equations of state (EOS) tables for warm dense matter. Due to computational costs, only a limited number of system state conditions can be simulated, and the remaining EOS surface must be interpolated for use in radiation-hydrodynamic simulations of experiments. In this work, we develop a thermodynamically consistent EOS model that utilizes a physics-informed machine learning approach to implicitly learn the underlying Helmholtz free-energy from AIMD generated energies and pressures. The model, referred to as PIML-EOS, was trained and tested on warm dense polystyrene producing a fit within a 1% relative error for both energy and pressure and is shown to satisfy both the Maxwell and Gibbs–Duhem relations. In addition, we provide a path toward obtaining thermodynamic quantities, such as the total entropy and chemical potential (containing both ionic and electronic contributions), which are not available from current AIMD simulations.

AFSD-Nets: A Physics-Informed Machine Learning Model for Predicting the Temperature Evolution During Additive Friction Stir Deposition

Abstract This study models the temperature evolution during additive friction stir deposition (AFSD) using machine learning. AFSD is a solid-state additive manufacturing technology that deposits metal using plastic flow without melting. However, the ability to predict its performance using the underlying physics is in the early stage. A physics-informed machine learning approach, AFSD-Nets, is presented here to predict temperature profiles based on the combined effects of heat generation and heat transfer. The proposed AFSD-Nets includes a set of customized neural network approximators, which are used to model the coupled temperature evolution for the tool and build during multi-layer material deposition. Experiments are designed and performed using 7075 aluminum feedstock deposited on a substrate of the same material for 30 layers. A comparison of predictions and measurements shows that the proposed AFSD-Nets approach can accurately describe and predict the temperature evolution during the AFSD process.

Microstructure-Sensitive Deformation Modeling and Materials Design with Physics-Informed Neural Networks

Microstructure-sensitive materials design has become popular among materials engineering researchers in the last decade because it allows the control of material performance through the design of microstructures. In this study, the microstructure is defined by an orientation distribution function. A physics-informed machine learning approach is integrated into microstructure design to improve the accuracy, computational efficiency, and explainability of microstructure-sensitive design. When data generation is costly and numerical models need to follow certain physical laws, machine learning models that are domain-aware perform more efficiently than conventional machine learning models. Therefore, a new paradigm called the physics-informed neural network (PINN) is introduced in the literature. This study applies the PINN to microstructure-sensitive modeling and inverse design to explore the material behavior under deformation processing. In particular, we demonstrate the application of PINN to small-data problems driven by a crystal plasticity model that needs to satisfy the physics-based design constraints of the microstructural orientation space. For the first problem, we predict the microstructural texture evolution of copper during a tensile deformation process as a function of initial texturing and strain rate. The second problem aims to calibrate the crystal plasticity parameters of the Ti-7Al alloy by solving an inverse design problem to match the PINN-predicted final texture prediction and the experimental data.

Performance analysis of data-driven and physics-informed machine learning methods for thermal-hydraulic processes in Full-scale Emplacement experiment

This study centers on the critical aspect of thermal management in deep geological repositories, particularly concerning the heat induced by radioactive nuclear waste. It evaluates eight machine learning methods to analyze thermal-hydraulic processes, focusing on their accuracy in predicting temperature and relative humidity, computational efficiency, robustness, and sensitivity to parameters. These methods are applied to data from the Full-scale Emplacement experiment in the Mont Terri underground laboratory. Notably, the Physics-Informed Machine Learning approach incorporates the experiment's heater power output conditions. The results demonstrate the effectiveness of these methods, especially the Physics-Informed Machine Learning model, in simulating complex processes typical of deep geological repository systems. The study highlights the k-Nearest Neighbor model's efficacy due to its proximity-based decision-making and the superior performance of the Physics-Informed model, suggesting its broader applicability. Our findings offer valuable insights for enhancing the design, management, and safety of underground facilities, contributing novel tools for precision and computational efficiency in energy process simulations.

A Physics-Informed General Convolutional Network for the Computational Modeling of Materials with Damage

Abstract Despite their effectiveness in modeling complex phenomena, the adoption of machine learning (ML) methods in computational mechanics has been hindered by the lack of availability of training datasets, limitations on accuracy of out-of-sample predictions, and computational cost. This work presents a physics-informed ML approach and network architecture that addresses these challenges in the context of modeling the behavior of materials with damage. The proposed methodology is a novel Physics-Informed General Convolutional Network (PIGCN) framework that features (1) the fusion of a dense edge network with a convolutional neural network (CNN) for specifying and enforcing boundary conditions and geometry information, (2) a data augmentation approach for learning more information from a static dataset that significantly reduces the necessary data for training, and (3) the use of a CNN for physics-informed ML applications, which is not as well explored as graph networks in the current literature. The PIGCN framework is demonstrated for a simple two-dimensional, rectangular plate with a hole or elliptical defect in a linear elastic material, but the approach is extensible to three dimensions and more complex problems. The results presented in the paper show that the PIGCN framework improves physics-based loss convergence and predictive capability compared to ML-only (physics-uninformed) architectures. A key outcome of this research is the significant reduction in training data requirements compared to ML-only models, which could reduce a considerable hurdle to using data-driven models in materials engineering where material experimental data is often limited.

Physics Informed Machine Learning Approach for Performance Degradation Monitoring of Gas Turbine

The heavy-duty gas turbine is playing an increasingly significant role on power generation due to its lower-emission, higher flexibility and thermo-efficiency. Main subsystems of the gas turbine like compressor, combustor and turbine degrade over the operating time under the harsh environmental conditions, which largely impacts the efficiency and productivity of the system. Therefore, it is critical to develop effective approaches to monitor performance degradation of a heavy-duty gas turbine for system predictive maintenance thus improving the efficiency and productivity of the machine. This paper presents a new physics informed machine learning methodology to predict the degradation of gas turbine by seamlessly integrating thermodynamic heat balancing mechanism, component characteristics, multi-source data and artificial neural network model. The mechanism-based thermodynamic model is established for multiple subsystems considering the balance of flow, mass and energy, and then integrated to a system level for performance simulation of the gas turbine under different conditions. The system model is able to effectively simulate values for those parameters that are not measurable (e.g. GT exhaust flow) or inaccurately measured (e.g. fuel flow). Machine learning based data cleaning approach is employed to preprocess the multivariate raw data of the gas turbine. The difference between design performance data and corrected value obtained from the physics-informed model under ISO conditions is utilized to assess the performance degradation. A Long Short-Term Memory (LSTM) model is established from the fusion of the actual and simulation data to predict the performance degradation of the gas turbine. A comparison study with the classical Nonlinear Autoregressive Network with External Input (NARX) neural network is conducted to demonstrate the advantage of the proposed method. Key Word: Gas Turbine, Thermodynamic Balance, Performance Degradation Predict, Machine Learning, LSTM

A framework for Li-ion battery prognosis based on hybrid Bayesian physics-informed neural networks

Li-ion batteries are the main power source used in electric propulsion applications (e.g., electric cars, unmanned aerial vehicles, and advanced air mobility aircraft). Analytics-based monitoring and forecasting for metrics such as state of charge and state of health based on battery-specific usage data are critical to ensure high reliability levels. However, the complex electrochemistry that governs battery operation leads to computationally expensive physics-based models; which become unsuitable for prognosis and health management applications. We propose a hybrid physics-informed machine learning approach that simulates dynamical responses by directly implementing numerical integration of principle-based governing equations through recurrent neural networks. While reduced-order models describe part of the voltage discharge under constant or variable loading conditions, model-form uncertainty is captured through multi-layer perceptrons and battery-to-battery aleatory uncertainty is modeled through variational multi-layer perceptrons. In addition, we use a Bayesian approach to merge fleet-wide data in the form of priors with battery-specific discharge cycles, where the battery capacity is fully available or only partially available. We illustrate the effectiveness of our proposed framework using the NASA Prognostics Data Repository Battery dataset, which contains experimental discharge data on Li-ion batteries obtained in a controlled environment.

Long-term fatigue estimation on offshore wind turbines interface loads through loss function physics-guided learning of neural networks

Offshore wind turbines are exposed during their serviceable lifetime to a wide range of loads from aero-, hydro- and structural dynamics. This complex loading scenario will have an impact on the lifetime of the asset, with fatigue remaining the key structural design driver for the substructure, e.g. the monopile. The ability to monitor the progression of fatigue life of these assets has recently become an operational concern. To achieve a monitoring alternative to strain gauges (cost-prohibitive farm-wide installation), supervisory control and data acquisition (SCADA) systems, often coupled with acceleration measurements, have been used. Existing work focused primarily on ten-minute fatigue load estimation. However, fatigue accumulates over time and the ability to accurately monitor this accumulation of fatigue over a longer time-window is paramount. In this contribution we investigate a novel approach using nine months of real-world SCADA and acceleration ten-minute statistics as inputs of a neural network model for long-term DEM estimation. This is further enhanced by including physical information relative to the problem at hand into the neural network model, in a so-called physics-informed machine learning approach. Specifically, we employ a custom loss function – the Minkowski logarithmic error – which prioritizes conservativeness (over-prediction of fatigue rates) and to embed the damage accumulation into the machine learning model.In the results and discussion section, we use Tower-TP interface load measurements for three real-world turbines to demonstrate the concept. First a model is trained on one turbine, before being applied to all three locations. The model performance is compared to direct measurements of fatigue progression at all three locations and a control loss function (the mean squared logarithm error) in both the Fore-Aft and Side-Side loading directions. The novel physics-informed model clearly outperforms the control loss function in accumulated fatigue predictions with errors below 3% on accumulated damage equivalent moment estimates. Additionally, the model’s long-term performance is checked according to varying timescales (hourly, daily, weekly or monthly accumulation of DEM) and it is seen that the spread on the error rapidly reduces and converges to zero. Finally, the long-term DEM is accumulated into a monthly accumulated fatigue damage. We also see how the error on this begins to converge after 6+ months, which opens the door for extrapolation.

A physics-informed machine learning approach for notch fatigue evaluation of alloys used in aerospace

Within this work, a unified physics-informed machine learning (PIML) framework is proposed for notch fatigue life prediction and key feature parameters identification of aerospace polycrystalline alloys. The unified PIML approach reaches a capable accuracy in notch fatigue life prediction of the polycrystalline alloys under a wide range of notch geometries and loading conditions compared with physics-based life models. In addition, the global sensitivity analysis method is used to accurately identify the key feature parameters that affect the notch fatigue life. The nominal maximum stress and unnotched specimen reference life are recognized as highly relevant features for notch fatigue life whereas the notch root radius is the key parameter among the notch parameters. Finally, life uncertainty induced by the notch geometry parameters is performed by using the proposed PIML model based on Latin hypercube sampling, which accomplishes the probabilistic estimation of notch fatigue life well. In practical applications, the PIML framework can be applied efficiently to notch fatigue life prediction of a new material dataset due to its powerful generalization ability without additional parameter fitting or finite element analysis. The well-trained PIML model and the uncertainty assessment method provide potential tools for notch fatigue evaluation under complex loading conditions.

A physics‐informed learning technique for fault location of DC microgrids using traveling waves

Fast and accurate fault location in DC power systems is of particular importance to ensure their reliable operation. One of the approaches for implementing a fast-tripping protection scheme is to use Traveling waves (TW) initiated by a fault scenario. This paper proposes a physics-informed machine learning approach that utilizes TWs for fault location in DC microgrids. TWs are extracted by the so-called multiresolution analysis which identifies the TW's wavelet coefficients for multiple frequency ranges. This paper deploys Parseval's theorem to find the energy of wavelet coefficients as a quantitative metric for describing TWs. The hypothesis of this paper is that once the Parseval energy curves for a specific cable are extracted, they can be utilized to locate faults along with that cable regardless of the DC system in which the cable is deployed. The fault location algorithm uses Parseval energy curves to train a Gaussian Process (GP) estimator. With the Parseval energy values of measured current at the protection device location, the GP estimator is able to estimate fault locations with high accuracy. The effectiveness of the proposed algorithm is verified by simulating a DC microgrid system in PSCAD/EMTDC.

Probabilistic physics-informed machine learning for dynamic systems

This paper develops a physics-informed machine learning approach for response prediction in dynamic systems, by augmenting a physics-based model with a machine learning model for model error; both models are probabilistic. The physics-based dynamic system model has discrepancy in the predicted output (due to incomplete physics or model form error in the physics-based model) when compared against observation data. The model form error is quantified using Bayesian state estimation with observation data, and a probabilistic machine learning model is trained to predict the output discrepancy for untrained inputs. Two different computational options are developed to implement this overall approach, with different levels of sophistication and computational effort. The methods are developed for problems with stationary and non-stationary, and Gaussian and non-Gaussian random process inputs. Strategies for computational effort reduction at different stages, such as model training, model error quantification, and reliability prediction, are discussed. The proposed approach is demonstrated using two numerical illustrations: (a) a deep beam subjected to dynamic loading (a single physics system), and (b) hypersonic flow over a flexible aircraft panel (a multi-physics system).

Velocity reconstruction in puffing pool fires with physics-informed neural networks

Pool fires are canonical representations of many accidental fires which can exhibit an unstable unsteady behavior, known as puffing, which involves a strong coupling between the temperature and velocity fields. Despite their practical relevance to fire research, their experimental study can be limited due to the complexity of measuring relevant quantities in parallel. In this work, we analyze the use of a recent physics-informed machine learning approach, called hidden fluid mechanics (HFM), to reconstruct unmeasured quantities in a puffing pool fire from measured quantities. The HFM framework relies on a physics-informed neural network (PINN) for this task. A PINN is a neural network that uses both the available data, here the measured quantities, and the physical equations governing the system, here the reacting Navier–Stokes equations, to infer the full fluid dynamic state. This framework is used to infer the velocity field in a puffing pool fire from measurements of density, pressure, and temperature. In this work, the dataset used for this test was generated from numerical simulations. It is shown that the PINN is able to reconstruct the velocity field accurately and to infer most features of the velocity field. In addition, it is shown that the reconstruction accuracy is robust with respect to noisy data, and a reduction in the number of measured quantities is explored and discussed. This study opens up the possibility of using PINNs for the reconstruction of unmeasured quantities from measured ones, providing the potential groundwork for their use in experiments for fire research.

Designing acoustofluidic devices using a simplified physics-informed machine learning approach

The safe positioning of particles within an acoustofluidic device is critical in biomedical and biological applications. Relating the design of acoustofluidic device walls and the internal acoustic field is a complex, nonlinear problem. The field of Physics-Informed Machine Learning (PIML) offers a number of potential approaches to simplify the design of these devices. One such PIML approach is learning from synthetic data. With large scientific data sets with rich spatial-temporal data and high-performance computing providing large amounts of data to be inferred and interpreted, the task of PIML is to ensure that these predictions and inferences are enforced by, and conform to the limits imposed by physical laws. The tools employed in PIML can include large, deep neural networks, Bayesian modeling, and deep reinforcement learning with sophisticated simulations of the environment. In this work, we show a simplified version of PIML using a combination of a small fully connected neural network and a 2D meshfree simulator of acoustic devices to predict the boundary shape for an acoustically actuated device. We will discuss the real-world results and applications, as well as the current limitations of this approach and the path ahead to scale and include more complexity for more applications and designs.

Hydrologic similarity based on width function and hypsometry: An unsupervised learning approach

The prediction of hydrologic conditions in watersheds has manifold applications, ranging from flood disaster preparedness to water supply and environmental flow management. In watersheds with scarce or no flow data, it is difficult to make accurate hydrologic predictions. Past work has used similarity in single-valued properties of the terrain (for example, drainage area, mean slope) as the basis to relate flow conditions in gauged watersheds to the ungauged ones. The resulting predictions show modest accuracy and have a weak physical basis. In this study, we develop a physics-informed machine learning approach to extract features that represent the hydrologic dynamics — width function and hypsometric curve. These two geomorphometric measures are computed using functional forms fitted to estimates derived from digital elevation data. Furthermore, dynamically-similar groups are identified based on results from unsupervised clustering and divergence measures. Our approach paves the way towards a flexible and scalable machine learning approach that can be used to assess hydrologic similarity and improve prediction, one informed by physics of surface flow generation and transport in watersheds. A case study involving 72 sub-watersheds in the Narmada River Basin (India) is used to illustrate the new methodology.

Predicting performance of in-situ microbial enhanced oil recovery process and screening of suitable microbe-nutrient combination from limited experimental data using physics informed machine learning approach

Screening of suitable microbe-nutrient combination and prediction of oil recovery at the initial stage is essential for the success of Microbial Enhanced Oil Recovery (MEOR) technique. However, experimental and physics-based modelling approaches are expensive and time-consuming. In this study, Physics Informed Machine Learning (PIML) framework was developed to screen and predict oil recovery at a relatively lesser time and cost with limited experimental data. The screening was done by quantifying the influence of parameters on oil recovery from correlation and feature importance studies. Results revealed that microbial kinetic, operational and reservoir parameters influenced the oil recovery by 50%, 32.6% and 17.4%, respectively. Higher oil recovery is attained by selecting a microbe-nutrient combination having a higher ratio of value between biosurfactant yield and microbial yield parameters, as they combinedly influence the oil recovery by 27%. Neural Network is the best ML model for MEOR application to predict oil recovery (R2≈0.99).

Toward Model Reduction for Power System Transients With Physics-Informed PDE

This manuscript reports the first step towards building a robust and efficient model reduction methodology to capture transient dynamics in a transmission level electric power system. Such dynamics is normally modeled on seconds-to-tens-of-seconds time scales by the so-called swing equations, which are ordinary differential equations defined on a spatially discrete model of the power grid. Following Seymlyen (1974) and Thorpe, Seyler, and Phadke (1999), we suggest to map the swing equations onto a linear, inhomogeneous Partial Differential Equation (PDE) of parabolic type in two space and one time dimensions with time-independent coefficients and properly defined boundary conditions. We illustrate our method on the synchronous transmission grid of continental Europe. We show that, when properly coarse-grained, i.e., with the PDE coefficients and source terms extracted from a spatial convolution procedure of the respective discrete coefficients in the swing equations, the resulting PDE reproduces faithfully and efficiently the original swing dynamics. We finally discuss future extensions of this work, where the presented PDE-based modeling will initialize a physics-informed machine learning approach for real-time modeling, $n-1$ feasibility assessment and transient stability analysis of power systems.

Increasing the Safety of Adaptive Cruise Control Using Physics-Guided Reinforcement Learning

This paper presents a novel approach for improving the safety of vehicles equipped with Adaptive Cruise Control (ACC) by making use of Machine Learning (ML) and physical knowledge. More exactly, we train a Soft Actor-Critic (SAC) Reinforcement Learning (RL) algorithm that makes use of physical knowledge such as the jam-avoiding distance in order to automatically adjust the ideal longitudinal distance between the ego- and leading-vehicle, resulting in a safer solution. In our use case, the experimental results indicate that the physics-guided (PG) RL approach is better at avoiding collisions at any selected deceleration level and any fleet size when compared to a pure RL approach, proving that a physics-informed ML approach is more reliable when developing safe and efficient Artificial Intelligence (AI) components in autonomous vehicles (AVs).

A physics-informed machine learning approach for solving heat transfer equation in advanced manufacturing and engineering applications

A physics-informed neural network is developed to solve conductive heat transfer partial differential equation (PDE), along with convective heat transfer PDEs as boundary conditions (BCs), in manufacturing and engineering applications where parts are heated in ovens. Since convective coefficients are typically unknown, current analysis approaches based on trial-and-error finite element (FE) simulations are slow. The loss function is defined based on errors to satisfy PDE, BCs and initial condition. An adaptive normalizing scheme is developed to reduce loss terms simultaneously. In addition, theory of heat transfer is used for feature engineering. The predictions for 1D and 2D cases are validated by comparing with FE results. While comparing with theory-agnostic ML methods, it is shown that only by using physics-informed activation functions, the heat transfer beyond the training zone can be accurately predicted. Trained models were successfully used for real-time evaluation of thermal responses of parts subjected to a wide range of convective BCs.

Physics-informed machine learning with conditional Karhunen-Loève expansions

We present a new physics-informed machine learning approach for the inversion of partial differential equation (PDE) models with heterogeneous parameters. In our approach, the space-dependent partially observed parameters and states are approximated via Karhunen-Loève expansions (KLEs). Each of these KLEs is then conditioned on their corresponding measurements, resulting in low-dimensional models of the parameters and states that resolve observed data. Finally, the coefficients of the KLEs are estimated by minimizing the norm of the residual of the PDE model evaluated at a finite set of points in the computational domain, ensuring that the reconstructed parameters and states are consistent with both the observations and the PDE model to an arbitrary level of accuracy.In our approach, KLEs are constructed using the eigendecomposition of covariance models of spatial variability. For the model parameters, we employ a parameterized covariance model calibrated on parameter observations; for the model states, the covariance is estimated from a number of forward simulations of the PDE model corresponding to realizations of the parameters drawn from their KLE. We apply the proposed approach to identify heterogeneous diffusion coefficients in diffusion equations from sparse measurements of the diffusion coefficient and the solution of the diffusion equation. We find that the proposed approach compares favorably against state-of-the-art point estimates such as maximum a posteriori estimation and physics-informed neural networks.