Physics-based Constraints Research Articles

Isotropic Growth on Cartesian Voxel Grids with von Neumann Neighborhoods for Rapid Generation of Synthetic Microstructures

Randomized instantiations of synthetic microstructures are needed to assess the statistical significance of microstructure variability. Algorithms that use Voronoi tessellations of random points produce synthetic polycrystalline microstructures with a less realistic appearance than random packing of spheroidal particles followed by growth-until-impingement. Additionally, Voronoi tessellations offer limited control of morphological parameters and are challenging to implement when the desired volume fraction is less than unity. However, unless additional physics-based constraints are applied, growth on a Cartesian voxel grid utilizing a von Neumann neighborhood element results in anisotropic growth that is generally not observable along the primary axes. The present work describes both analytical and empirically optimized corrections for directional growth rates and a framework for their inclusion in a synthetic microstructure generation algorithm. The presented algorithm can produce synthetic microstructures similar to those produced by random seed Monte Carlo techniques in a fraction of the computational time.

Super-Resolving and Denoising 4D flow MRI of Neurofluids Using Physics-Guided Neural Networks.

To obtain high-resolution velocity fields of cerebrospinal fluid (CSF) and cerebral blood flow by applying a physics-guided neural network (div-mDCSRN-Flow) to 4D flow MRI. The div-mDCSRN-Flow network was developed to improve spatial resolution and denoise 4D flow MRI. The network was trained with patches of paired high-resolution and low-resolution synthetic 4D flow MRI data derived from computational fluid dynamic simulations of CSF flow within the cerebral ventricles of five healthy cases and five Alzheimer's disease cases. The loss function combined mean squared error with a binary cross-entropy term for segmentation and a divergence-based regularization term for the conservation of mass. Performance was assessed using synthetic 4D flow MRI in one healthy and one Alzheimer' disease cases, an in vitro study of healthy cerebral ventricles, and in vivo 4D flow imaging of CSF as well as flow in arterial and venous blood vessels. Comparison was performed to trilinear interpolation, divergence-free radial basis functions, divergence-free wavelets, 4DFlowNet, and our network without divergence constraints. The proposed network div-mDCSRN-Flow outperformed other methods in reconstructing high-resolution velocity fields from synthetic 4D flow MRI in healthy and AD cases. The div-mDCSRN-Flow network reduced error by 22.5% relative to linear interpolation for in vitro core voxels and by 49.5% in edge voxels. The results demonstrate generalizability of our 4D flow MRI super-resolution and denoising approach due to network training using flow patches and physics-based constraints. The mDCSRN-Flow network can facilitate MRI studies involving CSF flow measurements in cerebral ventricles and association of MRI-based flow metrics with cerebrovascular health.

A reality-augmented adaptive physics informed machine learning method for efficient heat transfer prediction in laser melting

Physics informed neural network (PINN) method is proposed to alleviate problems in many science and engineering scenarios when data-collection is difficult, or traditional numerical calculations are lack of convenience because more time-consuming numerical calculations are required whenever one or more parameters of the process is changed. However, for advanced manufacturing processes like laser melting (LM), a basis of laser metal additive manufacturing, involve many complex physical phenomena (e.g. melting, convection, solidification, vaporization and interface evolution), the full equations of which are too complex to be solved by current PINN. This paper proposes a reality-augmented adaptive physics informed machine learning (RAA-PIML) method to meet the objectives of precise and fast predictive LM. It applies adaptive function, integrating heat transfer law and boundary condition equations to loss function, which has fast convergence and strong physics-based constraints. The reality-augmented data are acquired by few experiments and an accurate 3D heat transfer model covering turbulence. The conducted experimental results demonstrate that the developed solution exhibits higher efficiency than simulation, and superior performance than state-of-the-art methods, which shows outstanding potential in industry applications.

Physics-informed data-driven discovery of constitutive models with application to strain-rate-sensitive soft materials

AbstractA novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on strain-rate-sensitive soft materials. This model is based on the viscous dissipation-based visco-hyperelasticity framework where the total stress is decomposed into volumetric, isochoric hyperelastic, and isochoric viscous overstress contributions. It is shown that each of these stress components can be written as linear combinations of the components of an irreducible integrity basis. Three Gaussian process regression-based surrogate models are trained (one per stress component) between principal invariants of strain and strain rate tensors and the corresponding coefficients of the integrity basis components. It is demonstrated that this type of model construction enforces key physics-based constraints on the predicted responses: the second law of thermodynamics, the principles of local action and determinism, objectivity, the balance of angular momentum, an assumed reference state, isotropy, and limited memory. The three surrogate models that constitute our constitutive model are evaluated by training them on small-size numerically generated data sets corresponding to a single deformation mode and then analyzing their predictions over a much wider testing regime comprising multiple deformation modes. Our physics-informed data-driven constitutive model predictions are compared with the corresponding predictions of classical continuum thermodynamics-based and purely data-driven models. It is shown that our surrogate models can reasonably capture the stress–strain-strain rate responses in both training and testing regimes and improve prediction accuracy, generalizability to multiple deformation modes, and compatibility with limited data.

Multi-Physics Three-Dimensional Component Placement and Routing Optimization Using Geometric Projection

Abstract This article presents a novel three-dimensional topology optimization framework developed for 3D spatial packaging of interconnected systems using a geometric projection method (GPM). The proposed gradient-based topology optimization method simultaneously optimizes the locations and orientations of system components (or devices) and lengths, diameters, and trajectories of interconnects to reduce the overall system volume within the prescribed 3D design domain. The optimization is subject to geometric and physics-based constraints dictated by various system specifications, suited for a wide range of transportation (aerospace or automotive), heating, ventilation, air-conditioning, and refrigeration, and other complex system applications. The system components and interconnects are represented using 3D parametric shapes such as cubes, cuboids, and cylinders. These objects are then projected onto a three-dimensional finite element mesh using the geometric projection method. Sensitivities are calculated for the objective function (bounding box volume) with various geometric and physics-based (thermal and hydraulic) constraints. Several case studies were performed with different component counts, interconnection topologies, and system boundary conditions and are presented to exhibit the capabilities of the proposed 3D multi-physics spatial packaging optimization framework.

Physically constrained eigenspace perturbation for turbulence model uncertainty estimation

Aerospace design is increasingly incorporating design under uncertainty-based approaches to lead to more robust and reliable optimal designs. These approaches require dependable estimates of uncertainty in simulations for their success. The key contributor of predictive uncertainty in computational fluid dynamics (CFD) simulations of turbulent flows are the structural limitations of Reynolds-averaged Navier–Stokes models, termed model-form uncertainty. Currently, the common procedure to estimate turbulence model-form uncertainty is the eigenspace perturbation framework (EPF), involving perturbations to the modeled Reynolds stress tensor within physical limits. The EPF has been applied with success in design and analysis tasks in numerous prior works from the industry and academia. Owing to its rapid success and adoption in several commercial and open-source CFD solvers, in-depth verification and validation of the EPF is critical. In this work, we show that under certain conditions, the perturbations in the EPF can lead to Reynolds stress dynamics that are not physically realizable. This analysis enables us to propose a set of necessary physics-based constraints, leading to a realizable EPF. We apply this constrained procedure to the illustrative test case of a converging-diverging channel, and we demonstrate that these constraints limit physically implausible dynamics of the Reynolds stress tensor, while enhancing the accuracy and stability of the uncertainty estimation procedure.

Super-resolution flow-field reconstruction in rotating detonation combustors

The high-resolution flow field information is crucial for understanding the operational mechanisms of rotating detonation combustors (RDCs). However, due to limitations in sensor technology and observation techniques, the present experimental methods face great challenges in obtaining high-resolution data of RDCs. In the study, a novel physics-informed deep generative model is proposed for super-resolution flow-field reconstruction with low-resolution inputs. Compare to other methods, the application of physics-based constraints in this method enables accurate reconstruction of critical phenomena in RDCs while maintaining physics consistency. Additionally, the proposed super-resolution reconstruction method can be further employed for low sampling depth even binary input data, thereby evidently reducing the sampling depth per measurement point, which helps to overcome the challenges associated with high-frequency data acquisition and facility the implementation of larger-scale measurement arrays. As an extension to the measurement capabilities in reactive flow systems, the presented model possesses notable engineering significance.

Physics-Guided Deep Learning for Prediction of Energy Production from Geothermal Reservoirs

Predictive models are traditionally used for the development and management of geothermal reservoirs. While field operation optimization based on physics-based simulations offers dependable strategies, simulation models require detailed descriptions of reservoir conditions and properties and entail extensive computational efforts. As efficient alternatives to traditional physics-based simulation, data-driven predictive models such as deep learning-based models can provide fast predictions to facilitate complex iterative tasks that otherwise entail high computation time. However, purely data-driven models that are trained using limited data often provide physically inconsistent predictions and fail to generalize beyond the training data. This has important consequences in optimization applications where, during optimization, the well control strategies are likely to fall beyond the training data. These limitations undermine the suitability and strength of data-driven models in scientific and engineering applications, where the amount of data is typically limited but physical laws are well-established and frequently used. To address the above challenges, we propose a novel physics-guided machine learning model by incorporating the general structure of the physics-based equations into deep learning models. A typical approach for incorporating physics is adding physics-based constraints in the loss function to regularize the trainable parameters. However, this approach does not exploit or adapt the architecture of the neural network. In this work, the architecture of the proposed recurrent neural networks (RNN) is designed to represent the differential equations of the subsurface flow system. We present the physics-guided RNN models in detail and demonstrate their connection to the underlying differential equations describing the fluid flow physics. We investigate the prediction performance of the proposed models by first applying them to controlled example to evaluate their extrapolation power, before using them with simulated and field datasets.

Effects of mass balance, energy balance, and storage-discharge constraints on LSTM for streamflow prediction

We investigate the effects of physics-based constraints, added to the loss function of a Long Short-Term Memory (LSTM) network, on its performance in daily streamflow prediction. Three types of constraints (mass balance, energy balance, and storage-discharge relationship), along with their combinations, are tested across 34 river basins in Nebraska. We found that the addition of constraints improves the model performance in several basins, but there are also cases where the performance drops or does not differ significantly. Mass and energy balance constraints improve the performance in 38% and 32% of catchments, respectively, while storage-discharge constraints improve the performance in 12% of catchments. The combination of mass and energy balance constraints has a positive effect on 41% of catchments, while the combination of mass balance and storage-discharge constraints improves the performance in 26% of catchments. We recommend the use of constraints in cases where they boost the LSTM performance.

Neural Volumetric Reconstruction for Coherent Synthetic Aperture Sonar

Synthetic aperture sonar (SAS) measures a scene from multiple views in order to increase the resolution of reconstructed imagery. Image reconstruction methods for SAS coherently combine measurements to focus acoustic energy onto the scene. However, image formation is typically under-constrained due to a limited number of measurements and bandlimited hardware, which limits the capabilities of existing reconstruction methods. To help meet these challenges, we design an analysis-by-synthesis optimization that leverages recent advances in neural rendering to perform coherent SAS imaging. Our optimization enables us to incorporate physics-based constraints and scene priors into the image formation process. We validate our method on simulation and experimental results captured in both air and water. We demonstrate both quantitatively and qualitatively that our method typically produces superior reconstructions than existing approaches. We share code and data for reproducibility.

Utilising physics-informed neural networks for optimisation of diffusion coefficients in pseudo-binary diffusion couples

ABSTRACT We propose a numerical inverse method based on physics-informed neural networks (PINN) for calculating composition-dependent diffusion coefficients in pseudo-binary (PB) diffusion couples in multicomponent alloys. Traditional methods rely solely on experimental diffusion profiles as design targets, which can lead to unreliable estimates. In contrast, PINN uses a combination of available data and physics-based constraints to obtain optimised design parameters and exact solutions for constrained governing differential equations. The constraints in PINN include governing partial differential equations, initial and boundary conditions, and any other equality/inequality relations obeyed by physical parameters. Our study shows the necessity of experimentally estimated intrinsic diffusion coefficients for the prediction of reliable composition-dependent mobility data. In the absence of such data, different combinations of unknown intrinsic diffusion coefficients can also produce reasonable approximations of diffusion profiles and interdiffusion coefficients while wrongly predicting more fundamental quantities (i.e. intrinsic diffusivities). Our method utilises PINN to simultaneously obtain optimised design parameters (diffusion coefficients) and exact solutions for governing diffusion equations. The implementation of PINN uses experimentally estimated diffusion coefficients obtained by the PB diffusion couple method, in addition to diffusion profiles, as design targets. The method is extended to non-ideal PB diffusion profiles, such as conventional diffusion couples in which all the components develop diffusion profiles, by incorporating additional constraints such as zero composition gradient of certain component(s) and experimentally estimated interdiffusion coefficients at extrema in the composition profiles. PINN is found to be a promising approach for obtaining reliable estimates of diffusion coefficients in multicomponent alloys.

Incorporating Physics-Based Models into Equivalent Circuit Analysis of EIS Data from Organic Coatings

Electrochemical impedance spectroscopy (EIS) is a widely used method for monitoring coatings because it can be done in situ and causes little damage to the coating. However, interpreting the impedance data from coatings in order to determine the state of the coating and its protective abilities is challenging. A modified version of the rapid electrochemical assessment of paint (REAP) equivalent circuit is developed here, along with a method to calculate the impedance of a circuit using matrix algebra. This new equivalent circuit and the calculation method are used to analyze EIS data obtained from a two-layer commercial organic coating system immersed in NaCl solutions with different concentrations and at different temperatures. The matrix calculation method is validated by comparing results obtained from commercial analysis software to this method for two different equivalent circuits, and the parameter values are nearly equal. Physics-based models of the equivalent circuit elements are derived and used to obtain both initial estimates for the regressions and physics-based constraints on the model parameters. These models are integrated into the regression procedure, and the corrected Akaike information criterion (AICc) is used to compare fits between the new circuit and classic equivalent circuits. The AICc values indicate the new circuit results in better fits than classic equivalent circuits used for coatings analysis.

A Physics-Based Algorithm to Universally Standardize Routinely Obtained Clinical T2-Weighted Images

MR images can be challenging for machine learning and other large-scale analyses because most clinical images, for example, T2-weighted (T2w) images, reflect not only the biologically relevant T2 of tissue but also hardware and acquisition parameters that vary from site to site. Quantitative T2 mapping avoids these confounds because it quantitatively isolates the biological parameter of interest, thus representing a universal standardization across sites. However, efforts to incorporate quantitative mapping sequences into routine clinical practice have seen slow adoption. Here we show, for the first time, that the routine T2w complex raw dataset can be successfully regarded as a quantitative mapping sequence that can be reconstructed with classical optimization methods and physics-based constraints. While previous constrained reconstruction methods are unable to reconstruct a T2 map based on this data, the expanding-constrained alternating minimization for parameter mapping (e-CAMP), which employs stepwise initialization, a linearized version of the exponential model and a phase conjugacy constraint, is demonstrated to provide useful quantitative maps directly from a vendor T2w single image data. This paper introduces the method and demonstrates its performance using simulations, retrospectively undersampled brain images, and prospectively acquired T2w images taken on both phantom and brain. Because T2w scans are included in nearly every protocol, this approach could open the door to creating large, standardized datasets without requiring widespread changes in clinical protocols.

Physics-Informed Neural Networks with Group Contribution Methods.

Thermophysical properties of organic compounds are used in countless scientific, engineering, and industrial settings in developing theories, designing new systems and devices, analyzing costs and risks, and improving existing infrastructure. Often, due to costs, safety, prior interest, or procedural difficulties, experimental values for desired properties are not available and must be predicted. The literature is filled with prediction techniques, but even the best traditional methods have significant errors compared to what is possible considering experimental uncertainty. Recently, machine learning and artificial intelligence techniques have been applied to the property prediction problem, but the examples to date do not extrapolate well outside the data set used for training the model. This work demonstrates a solution to this problem by combining chemistry and physics when training the model and builds upon prior traditional and machine learning methods. Two case studies are presented. The first is for parachor which is used for surface tension prediction. Surface tensions are needed to design distillation columns, adsorption processes, gas-liquid reactors, liquid-liquid extractors, improve oil reservoir recovery, and undertake environmental impact studies or remediation actions. A set of 277 compounds is divided into training, validation, and test sets, and a multilayered physics-informed neural network (PINN) is developed. The results demonstrate that better extrapolation by deep learning models can be developed by adding in physics-based constraints. Second, a set of 1600 compounds is utilized for training, validating, and testing a PINN to improve normal boiling point predictions based on group contribution methods and physics-based constraints. The results show that the PINN performs better than any other method with a normal boiling point mean absolute error of 6.95 °C on training and 11.2 °C on test data. Key observations are that (1) a balanced split by compound type is important to have representative compound families in each of the train, validation, and test sets and (2) constraining group contributions being positive improves predictions on the test set. While this work demonstrates improvements for only surface tension and normal boiling point, the results offer significant hope that PINNs can improve prediction of other relevant thermophysical properties over existing approaches.

Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations

We develop a fully data-driven model of anisotropic finite viscoelasticity using neural ordinary differential equations as building blocks. We replace the Helmholtz free energy function and the dissipation potential with data-driven functions that a priori satisfy physics-based constraints such as objectivity and the second law of thermodynamics. Our approach enables modeling viscoelastic behavior of materials under arbitrary loads in three-dimensions even with large deformations and large deviations from the thermodynamic equilibrium. The data-driven nature of the governing potentials endows the model with much needed flexibility in modeling the viscoelastic behavior of a wide class of materials. We train the model using stress–strain data from biological and synthetic materials including human brain tissue, blood clots, natural rubber and human myocardium and show that the data-driven method outperforms traditional, closed-form models of viscoelasticity.

Multilayer Perceptron-Based Stress Evolution Analysis Under DC Current Stressing for Multisegment Wires

Electromigration (EM) is one of the major concerns in the reliability analysis of very large-scale integration (VLSI) systems due to the continuous technology scaling. Accurately predicting the time-to-failure of integrated circuits (ICs) becomes increasingly important for modern IC design. However, traditional methods are often not sufficiently accurate, leading to undesirable over-design especially in advanced technology nodes. In this article, we propose an approach using multilayer perceptrons (MLPs) to compute stress evolution in the interconnect trees during the void nucleation phase. The availability of a customized trial function for neural network training holds the promise of finding dynamic mesh-free stress evolution on complex interconnect trees under time-varying temperatures. Specifically, we formulate a new objective function considering the EM-induced coupled partial differential equations (PDEs), boundary conditions (BCs), and initial conditions to enforce the physics-based constraints in the spatial–temporal domain. The proposed model avoids meshing and reduces temporal iterations compared with conventional numerical approaches like finite element method. Numerical results confirm its advantages on accuracy and computational performance.

Physics-informed graph neural network for spatial-temporal production forecasting

Production forecast based on historical data provides essential value for developing hydrocarbon resources. Classic history matching workflow is often computationally intense and geometry-dependent. Analytical data-driven models like decline curve analysis (DCA) and capacitance resistance models (CRM) provide a grid-free solution with a relatively simple model capable of integrating some degree of physics constraints. However, the analytical solution may ignore subsurface geometries and is appropriate only for specific flow regimes and otherwise may violate physics conditions resulting in degraded model prediction accuracy. Machine learning-based predictive model for time series provides non-parametric, assumption-free solutions for production forecasting, but are prone to model overfit due to training data sparsity; therefore may be accurate over short prediction time intervals.We propose a grid-free, physics-informed graph neural network (PI-GNN) for production forecasting. A customized graph convolution layer aggregates neighborhood information from historical data and has the flexibility to integrate domain expertise into the data-driven model. The proposed method relaxes the dependence on close-form solutions like CRM and honors the given physics-based constraints. Our proposed method is robust, with improved performance and model interpretability relative to the conventional CRM and GNN baseline without physics constraints.

Deep estimation of viscoelastic and backscatter quantitative ultrasound

Deep learning is an ideal tool to solve inverse problems, which are often ill-posed and require incorporation of a priori information. We focus on solving two well-known inverse problems that entail the estimation of (1) viscoelastic (VE) and (2) backscatter quantitative ultrasound (QUS). These properties are of critical clinical value but are not currently available from B-mode images. On the first front, we propose a novel technique called PICTURE (Physically Inspired ConsTraint for Unsupervised Regularized Elastography) [Tehrani, Rivaz, MICCAI, (2022)], where we impose additional physics-based constraints on the deformation vector field within our loss function and show that it substantially improves the quality of lateral displacement estimation. We develop semi- and unsupervised methods to tackle the problem of lack of ground truth training datasets in real experiments. On the second front, we propose a novel method for segmenting regions of ultrasound images without any patching based on scatterer number densities [Tehrani et al. TUFFC (2022)]. Our segmentation maps can divide the image into irregular regions of fully developed speckle (FDS) or underdeveloped speckle. When moving from simulation to real datasets, we exploit domain adaptation methods using concepts similar to the popular reference phantom method in QUS.

Physics-Informed Quantum Communication Networks: A Vision Toward the Quantum Internet

Quantum communications is a promising technology that will play a fundamental role in the design of future networks. In fact, significant efforts are being undertaken by both the quantum physics and the classical communications communities on developing new architectures, solutions, and practical implementations of quantum communication networks (QCNs). Although these efforts led to various advances in today's technologies, there still exists a non-trivial gap between the research efforts of the two communities on designing and optimizing the performance of QCNs. For instance, most prior works by the classical communications community ignore important quantum physics-based constraints when designing QCNs. For example, many existing works on entanglement distribution do not account for the decoherence of qubits inside quantum memories and, thus, their designs become impractical since they assume an infinite lifetime of quantum states. In this article, we bring forth a novel analysis of the performance of QCNs in a physics-informed manner, by relying on the quantum physics principles that underly the different components of QCNs. The need for the physics-informed approach is then assessed and its fundamental role in designing practical QCNs is analyzed across various open research areas. Moreover, we identify novel physics-informed performance metrics and controls that enable QCNs to leverage the state-of-theart advancements in quantum technologies to enhance their performance. Finally, we analyze multiple pressing challenges and open research directions in QCNs that must be treated using a physics-informed approach to lead practically viable results. Ultimately, this work attempts to bridge the gap between the classical communications and the quantum physics communities in the area of QCNs to foster the development of the future communication networks toward the quantum Internet.

Generalized Labeled Multi-Bernoulli Multi-Target Tracking with Doppler-Only Measurements

The paper addresses the problem of tracking multiple targets with Doppler-only measurements in multi-sensor systems. It is well known that the observability of the target state measured using Doppler-only measurements is very poor, which makes it difficult to initialize the tracking target and produce the target trajectory in any tracking algorithm. Within the framework of random finite sets, we propose a novel constrained admissible region (CAR) based birth model that instantiates the birth distribution using Doppler-only measurements. By combining physics-based constraints in the unobservable subspace of the state space, the CAR based birth model can effectively reduce the ambiguity of the initial state. The CAR based birth model combines physics-based constraints in the unobservable subspace of the state space to reduce the ambiguity of the initial state. We implement the CAR based birth model with the generalized labeled multi-Bernoulli tracking filter to demonstrate the effectiveness of our proposed algorithm in Doppler-only tracking. The performance of the proposed approach is tested in two simulation scenarios in terms of the optimal subpattern assignment (OSPA) error, OSPA(2) (2)error, and computing efficiency. The simulation results demonstrate the superiority of the proposed approach. Compared to the approach taken by the state-of-the-art methods, the proposed approach can at most reduce the OSPA error by 58.77%, reduce the OSPA(2) error by 43.51%, and increase the computing efficiency by 9.56 times in the first scenario. In the second scenario, the OSPA error is reduced by 62.80%, the OSPA(2) (2)error is reduced by 43.65%, and the computing efficiency is increased by 2.61 times at most.