Physics-based Surrogate Modeling Research Articles

Quantification of elastic incompatibilities at triple junctions via physics-based surrogate models

Stresses resulting from elastic incompatibilities at grain boundaries have long been known to drive the premature failure and loss of desirable macroscopic properties in polycrystalline materials. In this work, we employ machine learning to create a surrogate model that furnishes a functional relationship between grain boundary configurational data and metrics of incompatibility. A planar triple junction geometry composed of cubic grains rotated about their [001] axis was adopted as the grain boundary model. High-fidelity finite element simulations of this triple junction under hydrostatic extension were used to generate a synthetic dataset for training the surrogate model. A set of J integrals computed around microcracks placed along the triple junction boundaries were used to quantify the elastic incompatibilities between the grains. Using the grain rotation angles and J integrals as the feature and label data respectively, a multi-layer perceptron network was trained using the synthetic data produced with the physics-based model. We demonstrate that the network trained using data from the physics-based model establishes an accurate functional dependence between the triple junction angles and the J integrals that enables direct and fast evaluation. We use the surrogate model to efficiently sweep the configuration space and create contour maps of the largest stress intensification at the triple junction as a function of the grain rotation angles. Furthermore, we show that the analytical properties of the surrogate model can be utilized to identify the most and least compatible triple junction configurations via optimization.

Physics-informed neural networks for solving the Helmholtz equation

Discretization-based methods like the finite element method have proven to be effective for solving the Helmholtz equation in computational acoustics. However, it is very challenging to incorporate measured data into the model or infer model input parameters based on observed response data. Machine learning approaches have shown promising potential in data-driven modeling. In practical applications, purely supervised approaches suffer from poor generalization and physical interpretability. Physics-informed neural networks (PINNs) incorporate prior knowledge of the underlying partial differential equation by including the residual into the loss function of an artificial neural network. Training the neural network minimizes the residual of both the differential equation and the boundary conditions and learns a solution that satisfies the corresponding boundary value problem. In this contribution, PINNs are applied to solve the Helmholtz equation within a two-dimensional acoustic duct and mixed boundary conditions are considered. The results show that PINNs are able to solve the Helmholtz equation very accurately and provide a promising data-driven method for physics-based surrogate modeling.

Do all roads lead to Rome? A comparison of knowledge-based, data-driven, and physics-based surrogate models for performance-based early design

A performance-based early design must assess the life cycle performance of a sizable design space at low computational cost and limited data. This paper evaluates the relative capabilities of three surrogate modeling approaches to estimate seismic loss under complete and incomplete design information scenarios. Three surrogate models of knowledge-based (i.e., from prior published assessments), data-driven (i.e., support vector machine trained on a simulation-based building inventory), and physics-based (i.e., equivalent single-degree-of-freedom systems) are systematically used to estimate bounds on direct seismic loss for four hypothetical concrete office construction projects in Charleston, South Carolina. Subsequently, a framework is presented that implements these surrogate models as a sequence to explore design alternatives consistent with divergence-convergence cycles of early design exploration. The results show that all different surrogate models provide reasonable accuracy for the complete design information case, whereas data-driven models provided higher accuracy than the other models. For incomplete design information, the data-driven models demarcated the performance space and estimated the same median loss values as detailed loss analysis. In contrast, physics-based surrogate models were more accurate in capturing the relationship between loss and design parameters for smaller sets of design alternatives. Nevertheless, all different surrogate modeling techniques were inadequate to capture loss variability between different designs of the same geometry.

Integrated membrane material design and system synthesis

In designing membrane systems, the synergy between membrane materials and the process design is often overlooked. We present a mixed-integer nonlinear programming (MINLP) model for synthesizing membrane systems while simultaneously designing the respective membrane materials for multicomponent gas separation. The approach considers superstructure representations for systems with: (1) same, (2) potentially different, and (3) property-targeting membrane materials. In the first two systems, the selection of membrane material is a decision, while in the final type, membrane permeances are subject to optimization. Physics-based surrogate models are used to describe permeation in crossflow and countercurrent flow permeators. We show that, through a case study of biogas upgrading, our approach obtains high quality solutions. Furthermore, we use the proposed approach while considering permeance-based production cost to find the optimal membrane.

Neural network ensembles and uncertainty estimation for predictions of inelastic mechanical deformation using a finite element method-neural network approach

Abstract The finite element method (FEM) is widely used to simulate a variety of physics phenomena. Approaches that integrate FEM with neural networks (NNs) are typically leveraged as an alternative to conducting expensive FEM simulations in order to reduce the computational cost without significantly sacrificing accuracy. However, these methods can produce biased predictions that deviate from those obtained with FEM, since these hybrid FEM-NN approaches rely on approximations trained using physically relevant quantities. In this work, an uncertainty estimation framework is introduced that leverages ensembles of Bayesian neural networks to produce diverse sets of predictions using a hybrid FEM-NN approach that approximates internal forces on a deforming solid body. The uncertainty estimator developed herein reliably infers upper bounds of bias/variance in the predictions for a wide range of interpolation and extrapolation cases using a three-element FEM-NN model of a bar undergoing plastic deformation. This proposed framework offers a powerful tool for assessing the reliability of physics-based surrogate models by establishing uncertainty estimates for predictions spanning a wide range of possible load cases.

Generalized optimization-based synthesis of membrane systems for multicomponent gas mixture separation

Synthesizing a membrane system to separate multicomponent gas mixture is challenging due to the combinatorial number of feasible configurations and the difficulties in describing the multicomponent permeators. We present a mixed-integer nonlinear programming (MINLP) model for synthesizing membrane systems for multicomponent gas mixture separation. The approach employs a richly connected superstructure to represent numerous potential system configurations, and different physics-based surrogate permeator models, such as countercurrent flow or crossflow, to be used in each stage. Moreover, to describe realistic systems, pressure drop equations can be included. We also present solution methods to accelerate the solution process. Through a case study of natural gas sweetening, we demonstrate that the proposed approach is able to obtain good solutions using an off-the-shelf global optimization solver. Finally, we expand the conventional membrane system synthesis problem by introducing feed variability in our model through a case study of an integrated reactor-separation system.

A Hybrid Surrogate Modeling Approach for Vehicle Crash Simulations

Integrated vehicle safety – a combination of active and passive vehicle safety systems has the potential to increase occupant safety dramatically. To adapt the passive safety components such as belt and airbag to a given collision scenario, the system requires a priori knowledge of the collision consequences, i.e. via a camera, radar or lidar system. Therefore, real-time capable surrogate models are needed, that predict the vehicle decelerations during a crash with high accuracy. To combine the strength of both data-driven and physics-based surrogate modeling techniques, a hybrid surrogate model consisting of a machine learning-enhanced spring-damper-mass model, is developed in this work. Thereby, the spring-damper-mass model describes the deformation behavior of the vehicle structure. A neural network is then trained to predict the stiffness and damping parameters of the simplified physical model based on the impact angle, the velocity and the offset of the vehicles.

Optimization of thin electric propeller using physics-based surrogate model with space mapping

The propulsion system greatly effects the performance of small electric powered Unmanned Aerial Vehicles (UAV). The propeller is one of the key elements of an electric propulsion system. The present research aims to optimize the propeller shape by utilizing the physics-based surrogate modeling strategy along with a space mapping method. A quasi-global construction is made that perceptively links a low-fidelity (coarse) model and a high-fidelity (fine) model, thus avoiding the direct optimization of the fine model. The space mapping utilizes a parameter extraction process that assist the surrogate model to locally realign itself with the fine model. For coarse model, an open source propeller analyses and design program (QPROP) is used. This program uses an extension of the classical blade element formulation. The fine model is based on the computational fluid dynamics analysis utilizing the finite-volume discretization of the Reynolds-averaged Navier–Stokes equations. The computed results have been verified by comparing them with the available propeller performance data. After a successful validation, geometric parameters for the propeller are varied to study their effect on performance and carry out parametric sensitivity analysis. The selected design variables control the section airfoil shape and the propeller geometry. The optimized design has been achieved with few iterations of the fine model reducing the overall computational cost of optimization process. The results indicate that the space mapping surrogate modeling is an effective strategy for propeller shape optimization.

Global optimization of benchmark aerodynamic cases using physics-based surrogate models

The paper proposes the combination of physics-based surrogate models, adaptive sampling of the design space and evolutionary optimization towards the solution of aerodynamic design problems. The Proper Orthogonal Decomposition is used to extract the main features of the flow field and Radial Basis Function networks allow the surrogate model to predict the target response over the entire design space. In order to train accurate and usable surrogates, ad hoc in-fill criteria are provided which smartly rank and select new samples to enrich the model database. The solution of two aerodynamic benchmark problems is proposed within the framework of the AIAA Aerodynamic Design Optimization Discussion Group. The two benchmark problems consist respectively in the drag minimization of the RAE 2822 airfoil in transonic viscous flow and of the NACA 0012 airfoil in transonic inviscid flow. The shape parameterization approach is based on the Class-Shape Transformation (CST) method with a sufficient degree of Bernstein polynomials to cover a wide range of shapes. Mesh convergence is demonstrated on single-block C-grid structured meshes. The in-house ZEN flow solver is used for Euler/RANS aerodynamic solution. Results show that, thanks to the combined usage of surrogate models and adaptive training in an evolutionary optimization framework, optimal candidates may be located even with limited computational resources with respect to plain evolutionary approaches and similar standard methodologies.

Surrogate Modeling of Ultrasonic Nondestructive Evaluation Simulations

Ultrasonic testing (UT) is used to detect internal flaws in materials or to characterize material properties. Computational simulations are an important part of the UT process. Fast models are essential for UT applications such as inverse design or model-assisted probability of detection. This paper presents investigations of using surrogate modeling techniques to create fast approximate models of UT simulator responses. In particular, we propose to use data-driven surrogate modeling techniques (kriging interpolation), and physics-based surrogate modeling techniques (space mapping), as well a mixture of the two approaches. These techniques are investigated for two cases involving UT simulations of metal components immersed in a water bath during the inspection process.

Supersonic Airfoil Shape Optimization by Variable-fidelity Models and Manifold Mapping

Supersonic vehicles are an important type of potential transports. Analysis of these vehicles requires the use of accurate models, which are also computationally expensive, to capture the highly nonlinear physics. This paper presents results of numerical investigations of using physics-based surrogate models to design supersonic airfoil shapes. Variable-fidelity models are generated using inviscid computational fluid dynamics simulations and analytical models. By using response correction techniques, in particular, the manifold mapping technique, fast surrogate models are constructed. The effectiveness of the approach is investigated using lift-constrained drag minimization problems of supersonic airfoil shapes. Compared with direct optimization, the results show that an order of magnitude speed up can be obtained. Furthermore, we investigate the effectiveness of the variable-fidelity technique in terms of speed and design quality using several combinations of medium-fidelity and low-fidelity models.

Multi-fidelity design optimization of transonic airfoils using physics-based surrogate modeling and shape-preserving response prediction

A computationally efficient design methodology for transonic airfoil optimization has been developed. In the optimization process, a numerically cheap physics-based low-fidelity surrogate (the transonic small-disturbance equation) is used in lieu of an accurate, but computationally expensive, high-fidelity (the compressible Euler equations) simulation model. Correction of the low-fidelity model is achieved by aligning its corresponding airfoil surface pressure distribution with that of the high-fidelity model using a shape-preserving response prediction technique. The resulting method requires only a single high-fidelity simulation per iteration of the design process. The method is applied to airfoil lift maximization in two-dimensional inviscid transonic flow, subject to constraints on shock-induced pressure drag and airfoil cross-sectional area. The results showed that more than a 90% reduction in high-fidelity function calls was achieved when compared to direct high-fidelity model optimization using a pattern-search algorithm.