Adaptive Model Reduction Research Articles

Dual Digital Twin: Cloud–edge collaboration with Lyapunov-based incremental learning in EV batteries

The soaring potential of edge computing leads to the emergence of cloud–edge collaboration. This hierarchy enables the deployment of artificial intelligence models in the cyber–physical venue. This paper presents Dual Digital Twin, the next level of digital twin, in the presence of two levels of communication availability, for battery system real-time monitoring and control in electric vehicles. To implement the dual digital twin concept, an online adaptive model reduction problem is formulated with time scale differences induced by the time sensitivity property of industrial applications and limitations of infrastructure. To minimize the model reduction error and battery system control penalty, the online adaptive battery reduced order model framework is proposed, consisting of the gated recurrent unit neural network to construct battery internal states given Internet of things sensor measurements, and incremental learning techniques to facilitate the update of the reduced-order model given data stream. Moreover, we design the physics-informed update of the neural network using the Lyapunov stability theorem to enhance the synchronization with the physical battery behavior. A Li-ion battery and single particle digital twin model with electrolyte and thermal dynamics are utilized in the simulation to justify the effectiveness of the proposed framework. Numerical results demonstrate 1.70% average reduced-order model prediction error and 43.3% accuracy improvement with the novel physics-informed online adaptive framework. The method is also robust concerning varying environmental factors and noise.

Lookahead data-gathering strategies for online adaptive model reduction of transport-dominated problems

Online adaptive model reduction efficiently reduces numerical models of transport-dominated problems by updating reduced spaces over time, which leads to nonlinear approximations on latent manifolds that can achieve a faster error decay than classical linear model reduction methods that keep reduced spaces fixed. Critical for online adaptive model reduction is coupling the full and reduced model to judiciously gather data from the full model for adapting the reduced spaces so that accurate approximations of the evolving full-model solution fields can be maintained. In this work, we introduce lookahead data-gathering strategies that predict the next state of the full model for adapting reduced spaces toward dynamics that are likely to be seen in the immediate future. Numerical experiments demonstrate that the proposed lookahead strategies lead to accurate reduced models even for problems where previously introduced data-gathering strategies that look back in time fail to provide predictive models. The proposed lookahead strategies also improve the robustness and stability of online adaptive reduced models.

An Adaptive Model Reduction Method Leveraging Locally Supported Basis Functions

We propose a new method, the continuous Galerkin method with globally and locally supported basis functions (CG-GL), to address the parametric robustness issues of reduced-order models (ROMs) by incorporating solution-based adaptivity with locally supported finite element basis functions. The CG-GL method combines the accuracy of locally supported basis functions with the efficiency of globally supported data-driven basis functions. Efficient output-based dual-weighted residual error estimates are derived and implemented for the CG-GL method and used to drive efficient online trial space adaptation. An empirical quadrature procedure is introduced for rapid evaluation of nonlinear terms that does not require retraining throughout the adaptation process. Two numerical experiments demonstrate the potential of the CG-GL method to produce accurate approximations with limited training and its tunable trade-off between accuracy and computational cost.

Adaptive Model Reduction of High-Order Solutions of Compressible Flows via Optimal Transport

The solution of conservation laws with parametrised shock waves presents challenges for both high-order numerical methods and model reduction techniques. We introduce an r-adaptivity scheme based on optimal transport and apply it to develop reduced order models for compressible flows. The optimal transport theory allows us to compute high-order r-adaptive meshes from a starting reference mesh by solving the Monge–Ampère equation. A high-order discretization of the conservation laws enables high-order solutions to be computed on the resulting r-adaptive meshes. Furthermore, the Monge–Ampère solutions contain mappings that are used to reduce the spatial locality of the resulting solutions and make them more amenable to model reduction. We use a non-intrusive model reduction method to construct reduced order models of both the mesh and the solution. The procedure is demonstrated on three supersonic and hypersonic test cases, with the hybridisable discontinuous Galerkin method being used as the full order model.

Dynamic reanalysis of structures with geometric variability and parametric uncertainties via an adaptive model reduction method

In this paper, a model reduction method is proposed for the dynamic reanalysis of structures with geometric variability and parametric uncertainties. Geometric variability is introduced by distorting the finite element meshes for some substructures via arbitrary shape functions. Parametric uncertainties are also considered to describe local variations of the stiffnesses of the substructures. The proposed approach involves expressing the substructure transformation matrices using interpolated matrices of Craig–Bampton component modes together with matrices of enrichment vectors. These enrichment vectors are parameter-independent and, as such, they only need to be computed once. This, as a result, leads to reduced substructure models which can be quickly updated to reanalyze structures with geometric and parametric changes. The accuracy and numerical efficiency of the proposed approach are highlighted through numerical experiments.

Adaptive mixture approximation for target tracking in clutter

Target tracking is a state estimation problem common in many practical scenarios like air traffic control, autonomous vehicles, marine radar surveillance and so on. In a Bayesian perspective, when phenomena like clutter are present, most existing tracking algorithms must deal with association hypotheses which may grow in number over time. In that case, the posterior state distribution can quickly become computationally intractable, and approximations must necessarily be introduced. In this work, the impact of the number of hypotheses and of reduction procedures is investigated both in terms of computational resources and tracking performances. For this purpose, a recently developed adaptive mixture model reduction algorithm is considered in order to assess its performances when applied to the problem of single object tracking in the presence of clutter and to provide some interesting insights into the addressed problem.

Adaptive Model Reduction and State Estimation of Agro-hydrological Systems

• An adaptive model reduction approach for agro-hydrological systems. • An adaptive state estimation approach based on the adaptive model reduction. • Extensive simulations with real field data showing the efficiency of the proposed approaches. Closed-loop irrigation can deliver a promising solution for precision irrigation. The accurate soil moisture (state) estimation is critical in implementing a closed-loop agricultural irrigation system. The water dynamics in an agro-hydrological system may be modeled using the Richards equation. Due to the high dimensionality of the Richards equation, it is very challenging to solve an optimization-based advanced state estimator like moving horizon estimation (MHE). This work addresses the aforementioned challenge and proposes a systematic approach for state estimation of large agricultural fields. We first propose a structure-preserving adaptive model reduction method using trajectory-based unsupervised machine learning techniques. The adaptively reduced model is then used in the design of an adaptive MHE algorithm. The performance of the proposed algorithms is first compared with a standard MHE based on a small simulated field. Then, the proposed approach is applied to a large-scale real agricultural field and extensive simulations are carried out to show its effectiveness and applicability.

Resilient Adaptive Parallel sImulator for griD (RAPID): An Open Source Power System Simulation Toolbox

This paper describes an open source power system simulation toolbox: Resilient Adaptive Parallel sImulator for griD (RAPID), a package of Python codes that implements an advanced power system dynamic simulation framework. The main function of RAPID is time-domain simulation, and it contains details of the solution process, including the quasi-steady-state power flow analysis, to solve nonlinear differential algebraic equations describing the detailed representation of network and transient stability models of dynamic devices in a computationally efficient manner. In particular, RAPID utilizes and incorporates emerging solution techniques; a novel “parallel-in-time” (Parareal) algorithm, adaptive model reduction, and semi-analytical solution methods as well as the standard numerical solution methods. Moreover, the whole simulation process for the transmission network has been coupled with OpenDSS, a widely used open-source distribution system simulator, to enable the co-simulation of integrated transmission and distribution systems. Basic structure and features of RAPID are presented to provide an easy-to-understand guideline for the usage of the tool and illustrate its unique capabilities. This paper also presents simulation results for a number of test scenarios and demonstrates RAPID’s values for advancing power systems research in dynamic modeling and simulation techniques toward researchers as well as educators and students.

A Block Arnoldi Algorithm Based Reduced-Order Model Applied to Large-Scale Algebraic Equations of a 3-D Field Problem

In simulations of three-dimensional transient physics filled through a numerical approach, the order of the equation set of high-fidelity models is extremely high. To eliminate the large dimension of equations, a model order reduction (MOR) technique is introduced. In the existing MOR methods, the block Arnoldi algorithm-based MOR method is numerically stable, achieving a passively reduced order model. Nevertheless, this method performs poorly when it is applied to very wide-frequency transients. To eliminate this deficiency, multipoint MOR methods are emerging. However, it is hard to directly apply an existing multipoint MOR method to a 3-D transient field equation set. The implementation issues in a reduction process (such as the selection of expansion points, the number of moments matched at a point and the error bound) have not been explored in detail. In this respect, an adaptive multipoint model reduction model based on the Arnoldi algorithm is proposed to obtain the reduced-order models of a 3-D temperature field. The originality of this study is the proposal of a novel adaptive algorithm for selecting expansion points, matching moments automatically, using a posterior-error estimator based on temperature response coupled with a network topological method (NTM). The computational efficiency and accuracy of the proposed method are evaluated by the numerical results from solving the temperature field of a prototype insulated-gate bipolar transistor (IGBT).

Design and Optimization of Numerical Methods for Solving Inverse Problems

. The purpose of inverse problems is to identify the unknown causes or parameters based on observable effects or measurements in a variety of scientific and technical domains. To arrive at precise and trustworthy solutions, numerical algorithms for inverse problems must be designed and optimised. The creation and optimisation of numerical algorithms specifically created for solving inverse issues are presented in detail in this abstract.The formulation of inverse issues and the mathematical models that explain the underlying processes are the primary topics of the first part of this work. We examine many inverse issues, such as ill-posed, parameter estimation, and linear and nonlinear ones. Prior information and regularisation methods must be used to increase the stability and uniqueness of the answers.The creation and application of numerical algorithms for the solution of inverse problems is the focus of the second component. We study in depth a number of iterative techniques, including the conjugate gradient method, Levenberg-Marquardt algorithm, and Gauss-Newton method. There is also discussion of sophisticated methods such variational methods, Bayesian inference, and approaches based on optimisation.The third consideration focuses on optimising numerical techniques to raise their effectiveness and precision. To hasten convergence and lower computational costs, methods like adaptive mesh refinement, parallel processing, and model reduction are examined. Additionally, methods for handling noisy or missing data are looked at, as well as methods for choosing the right regularisation settings.

Stein Variational Reduced Basis Bayesian Inversion

We propose and analyze a Stein variational reduced basis method (SVRB) to solve large-scale PDE-constrained Bayesian inverse problems. To address the computational challenge of drawing numerous samples requiring expensive PDE solves from the posterior distribution, we integrate an adaptive and goal-oriented model reduction technique with an optimization-based Stein variational gradient descent method. We present detailed analyses for the reduced basis approximation errors of the potential and its gradient, the induced errors of the posterior distribution measured by Kullback--Leibler divergence, as well as the induced errors of the Stein variational samples. To demonstrate the computational accuracy and efficiency of SVRB, we report results of numerical experiments on a Bayesian inverse problem governed by a diffusion PDE with random parameters with both uniform and Gaussian prior distributions. Over 100X speedups can be achieved while the accuracy of the approximation of the potential and its gradient is preserved.

Model Reduction for Transport-Dominated Problems via Online Adaptive Bases and Adaptive Sampling

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 19 April 2019Accepted: 09 June 2020Published online: 21 September 2020Keywordsmodel reduction, transport-dominated problems, empirical interpolation, online adaptive model reduction, sparse sampling, proper orthogonal decompositionAMS Subject Headings65M22, 65N22, 65F99, 49M15Publication DataISSN (print): 1064-8275ISSN (online): 1095-7197Publisher: Society for Industrial and Applied MathematicsCODEN: sjoce3

Efficient reliability analysis coupling importance sampling using adaptive subset simulation and PGD model reduction

AbstractOne of the most important goals in civil engineering is to guaranty the safety of constructions. National standards prescribe a required failure probability in the order of 10−6 (e.g. DIN EN 199:2010‐12). The estimation of these failure probabilities is the key point of structural reliability analysis. Generally, it is not possible to compute the failure probability analytically. Therefore, simulation‐based methods as well as methods based on surrogate modeling or response surface methods have been developed. Nevertheless, these methods still require a few thousand evaluations of the structure, usually with finite element (FE) simulations, making reliability analysis computationally expensive for relevant applications.The aim of this contribution is to increase the efficiency of structural reliability analysis by using the advantages of model reduction techniques. Model reduction is a popular concept to decrease the computational effort of complex numerical simulations while maintaining a reasonable accuracy. Coupling a reduced model with an efficient variance reducing sampling algorithm significantly reduces the computational cost of the reliability analysis without a relevant loss of accuracy.

An Efficient, Globally Convergent Method for Optimization Under Uncertainty Using Adaptive Model Reduction and Sparse Grids

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of in...

Adaptive Nonlinear Model Reduction for Fast Power System Simulation

The paper proposes a new adaptive approach to power system model reduction for fast and accurate time-domain simulation. This new approach is a compromise between linear model reduction for faster simulation and nonlinear model reduction for better accuracy. During the simulation period, the approach adaptively switches among detailed and linearly or nonlinearly reduced models based on variations of the system state: it employs unreduced models for the fault-on period, uses weighted column norms of the admittance matrix to decide which functions to be linearized in power system differential-algebraic equations for large changes of the state, and adopts a linearly reduced model for small changes of the state. Two versions of the adaptive model reduction approach are introduced. The first version uses traditional power system partitioning where the model reduction is applied to a defined large external area in a power system and the other area defined as the study area keeps full detailed models. The second version applies the adaptive model reduction to the whole system. The paper also conducts comprehensive case studies comparing simulation results using the proposed adaptively reduced models with the linearly reduced model and coherency-based reduced model on the Northeast Power Coordinating Council 140-bus 48-machine system.

Enhancements of the G-Scheme Framework

The G-Scheme is a well established framework for multi-scale adaptive model reduction, whose effectiveness was demonstrated with reference to a number of test models, together with an identification of the critical areas that were in need of further theoretical and computational refinement. In this communication, we report on how we enhanced the solver performance. Two new features involving (i) the criteria to identify the fast and slow subspace dimensions, and (ii) a criterion to decide if and when the reuse of the CSP Basis is feasible without deteriorating the overall performance of the solver, have been proved able to increase significantly the computational efficiency of the solver without sacrificing its accuracy.

Adaptive model reduction technique for large-scale dynamical systems with frequency-dependent damping

In many engineering problems, it is customary to use viscoelastic materials in the passive control of structural vibration and noise radiation. The most commonly used numerical tool to obtain detailed information on the performance of complex structures is the finite element (FE) method. However, structures with viscoelastic materials often require very large-scale FE computational models to obtain reliable predictions, which makes original full-order system evaluation intractable due to memory and time limitations. In order to alleviate these problems, model order reduction techniques have become indispensable. Most of them, however, often do not handle complex-valued and especially frequency-dependent system matrices well. Due to the frequency dependency of the material properties, the FE equations of motion for viscoelastic models are not of a standard second-order form as that for regular elastic FE models. In this paper, a new transformation technique based on Taylor’s theorem is introduced to treat the frequency-dependent shear modulus. After transforming the problem into a second-order system equation with remainder term, an adaptive second-order Arnoldi method is applied for the reduction of the computational complexity of structures, incorporating classical free- and constrained-layer damping treatments. In support, a relative error indicator is developed to iteratively enrich the reduced model and determine the position of expansion points used in next step. Three widely used models, the Golla–Hughes–McTavish model, Generalized Maxwell model and Fractional Derivative model for describing the frequency-dependent property of viscoelastic materials are investigated in order to demonstrate the simplicity, versatility and efficiency of the proposed approach.

Adaptive POD model reduction for solute transport in heterogeneous porous media

We study the applicability of a model order reduction technique to the solution of transport of passive scalars in homogeneous and heterogeneous porous media. Transport dynamics are modeled through the advection-dispersion equation (ADE) and we employ Proper Orthogonal Decomposition (POD) as a strategy to reduce the computational burden associated with the numerical solution of the ADE. Our application of POD relies on solving the governing ADE for selected times, termed snapshots. The latter are then employed to achieve the desired model order reduction. We introduce a new technique, termed Snapshot Splitting Technique (SST), which allows enriching the dimension of the POD subspace and damping the temporal increase of the modeling error. Coupling SST with a modeling strategy based on alternating over diverse time scales the solution of the full numerical transport model to its reduced counterpart allows extending the benefit of POD over a prolonged temporal window so that the salient features of the process can be captured at a reduced computational cost. The selection of the time scales across which the solution of the full and reduced model are alternated is linked to the Péclet number (P e), representing the interplay between advective and dispersive processes taking place in the system. Thus, the method is adaptive in space and time across the heterogenous structure of the domain through the combined use of POD and SST and by way of alternating the solution of the full and reduced models. We find that the width of the time scale within which the POD-based reduced model solution provides accurate results tends to increase with decreasing P e. This suggests that the effects of local-scale dispersive processes facilitate the POD method to capture the salient features of the system dynamics embedded in the selected snapshots. Since the dimension of the reduced model is much lower than that of the full numerical model, the methodology we propose enables one to accurately simulate transport at a markedly reduced computational cost.

Entropy production and timescales

Spatially homogeneous reactive systems are characterised by the simultaneous presence of a wide range of timescales. When the dynamics of such reactive systems develop very slow and very fast timescales separated by a range of active timescales, with large gaps in the fast/active and slow/active timescales, then it is possible to attain a multi-scale adaptive model reduction along with the integration of the governing ordinary differential equations using the G-Scheme framework. The G-Scheme assumes that the dynamics is decomposed into active, slow, fast, and when applicable, invariant subspaces. We derive expressions that reveal the direct link between timescales and entropy production by resorting to the estimates of the contributions of the fast and slow subspaces provided by the G-Scheme. With reference to a constant pressure adiabatic batch reactor, we compute the contribution to entropy production by the four subspaces. These numerical experiments show that, as indicated by the theoretical derivation, the contribution to entropy production of the fast subspace is of the same magnitude as the error threshold chosen for the numerical integration, and that the contribution of the slow subspace is generally much smaller than that of the active subspace. We explicitly exploit this property to identify the slow and fast subspace dimensions differently from the method adopted in the G-Scheme, where the dimensions of the subspaces are defined on the basis of the asymptotic approximations of the contributions of the fast and slow subspaces. Comparison of the outcome of the analyses performed using two types of criteria underlines the substantial equivalence of the two. This property opens the door to a number of possible applications that will be explored in future work. For example, it is possible to utilise the information on entropy production associated with reactions within each subspace to define an entropy participation index that can be utilised for model reduction.

Online adaptive local multiscale model reduction for heterogeneous problems in perforated domains

In this paper, we develop and analyze an adaptive multiscale approach for heterogeneous problems in perforated domains. We consider commonly used model problems including the Laplace equation, the elasticity equation, and the Stokes system in perforated regions. In many applications, these problems have a multiscale nature arising because of the perforations, their geometries, the sizes of the perforations, and configurations. Typical modeling approaches extract average properties in each coarse region, that encapsulate many perforations, and formulate a coarse-grid problem. In some applications, the coarse-grid problem can have a different form from the fine-scale problem, e.g. the coarse-grid system corresponding to a Stokes system in perforated domains leads to Darcy equations on a coarse grid. In this paper, we present a general offline/online procedure, which can adequately and adaptively represent the local degrees of freedom and derive appropriate coarse-grid equations. Our approaches start with the offline procedure, which constructs multiscale basis functions in each coarse region and formulates coarse-grid equations. We presented the offline simulations without the analysis and adaptive procedures, which are needed for accurate and efficient simulations. The main contributions of this paper are (1) the rigorous analysis of the offline approach, (2) the development of the online procedures and their analysis, and (3) the development of adaptive strategies. We present an online procedure, which allows adaptively incorporating global information and is important for a fast convergence when combined with the adaptivity. We present online adaptive enrichment algorithms for the three model problems mentioned above. Our methodology allows adding and guides constructing new online multiscale basis functions adaptively in appropriate regions. We present the convergence analysis of the online adaptive enrichment algorithm for the Stokes system. In particular, we show that the online procedure has a rapid convergence with a rate related to the number of offline basis functions, and one can obtain fast convergence by a sufficient number of offline basis functions, which are computed in the offline stage. The convergence theory can also be applied to the Laplace equation and the elasticity equation. To illustrate the performance of our method, we present numerical results with both small and large perforations. We see that only a few (1 or 2) online iterations can significantly improve the offline solution.