From Physics-Based Models to Predictive Digital Twins via Interpretable Machine Learning

Kapteyn, Michael G.; Willcox, Karen

doi:10.48550/arxiv.2004.11356

Cited by 12 publications

(12 citation statements)

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“…A similar argument holds for the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm developed by Brunton et al [38][39][40][41]. An ML-based method more closely related to (physically interpretable) model updating is found in the work of Willcox et al [42][43][44][45][46]. Here, a (first-principles) model is selected from a predefined library of models, representing systems with various fault types, using an optimal decision tree.…”

Section: Introductionmentioning

confidence: 94%

Real-time parameter updating for nonlinear digital twins using inverse mapping models and transient-based features

Kessels

Fey

Wouw

2022

Preprint

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In the context of digital twins, it is essential that a model gives an accurate description of the (controlled) dynamic behavior of a physical system during the system’s entire operational life. Therefore, model updating techniques are required that enable real-time updating of physically interpretable parameter values and are applicable to a wide range of (nonlinear) dynamical systems. As traditional, iterative, parameter updating methods may be computationally too expensive for real-time updating, the Inverse Mapping Parameter Updating (IMPU) method is proposed as an alternative. For this method, first, an Artificial Neural Network (ANN) is trained offline using novel features of simulated transient response data. Then, in the online phase, this ANN maps, with little computational cost, a set of measured output response features to parameter estimates enabling real-time model updating. In this paper, various types of transient response features are introduced to update parameter values of nonlinear dynamical systems with increased computational efficiency and accuracy. To analyze the efficacy of these features, the IMPU method is applied to a (simulated) nonlinear multibody system. It is shown that a smart selection of features, based on, e.g., the frequency content of the transient response, can improve the accuracy of the estimated parameter values, leading to more accurate updated models. Furthermore, the generalization capabilities of the ANNs are analyzed for these feature types, by varying the number of training samples and assessing the effect of incomplete training data. It is shown that the IMPU method can predict parameter values that are not part of the training data with acceptable accuracy as well.

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Section: Introductionmentioning

confidence: 94%

Real-time parameter updating for nonlinear digital twins using inverse mapping models and transient-based features

Kessels

Fey

Wouw

2022

Preprint

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“…Meanwhile, their applications in engineering disciplines mostly focus on scientific data, which resulted in a burgeoning discipline called scientific machine learning (SciML) [1] that blends scientific computing and ML. Typical examples for SciML are data-driven modeling [2] and digital twins [3] which have obtained significant interest in the nuclear engineering area in the last few years.…”

Section: Ia Background and Motivationmentioning

confidence: 99%

Quantification of Deep Neural Network Prediction Uncertainties for VVUQ of Machine Learning Models

Mahmoud¹,

Xu²

2022

Preprint

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Recent performance breakthroughs in Artificial intelligence (AI) and Machine learning (ML), especially advances in Deep learning (DL), the availability of powerful, easy-to-use ML libraries (e.g., scikit-learn, TensorFlow, PyTorch.), and increasing computational power have led to unprecedented interest in AI/ML among nuclear engineers. For physics-based computational models, Verification, Validation and Uncertainty Quantification (VVUQ) have been very widely investigated and a lot of methodologies have been developed.However, VVUQ of ML models has been relatively less studied, especially in nuclear engineering. In this work, we focus on UQ of ML models as a preliminary step of ML VVUQ, more specifically, Deep Neural Networks (DNNs) because they are the most widely used supervised ML algorithm for both regression and classification tasks. This work aims at quantifying the prediction, or approximation uncertainties of DNNs when they are used as surrogate models for expensive physical models. Three techniques for UQ of DNNs are compared, namely Monte Carlo Dropout (MCD), Deep Ensembles (DE) and Bayesian Neural Networks (BNNs). Two nuclear engineering examples are used to benchmark these methods, (1) timedependent fission gas release data using the Bison code, and (2) void fraction simulation based on the BFBT benchmark using the TRACE code. It was found that the three methods typically require different DNN architectures and hyperparameters to optimize their performance. The UQ results also depend on the amount of training data available and the nature of the data. Overall, all these three methods can provide reasonable estimations of the approximation uncertainties. The uncertainties are generally smaller when the mean predictions are close to the test data, while the BNN methods usually produce larger uncertainties than MCD and DE.

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“…Combining data-driven modeling and machine learning with physics-based simulations provides a hybrid modeling strategy [121] with high potential in multiscale modeling of biological systems [118]. Advancements in each of these fields and their coupling will produce predictive digital twins [122] that could facilitate treatment planning, patient management, and ultimately transform personalized cardiovascular medicine [123].…”

Section: Opportunities and Challengesmentioning

confidence: 99%

Data-driven cardiovascular flow modeling: examples and opportunities

Arzani,

Dawson

2020

Preprint

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High-fidelity modeling of blood flow is crucial for enhancing our understanding of cardiovascular disease. Despite significant advances in computational and experimental characterization of blood flow, the knowledge that we can acquire from such investigations remains limited by the presence of uncertainty in parameters, low spatiotemporal resolution, and measurement noise. Additionally, extracting useful information from these datasets is challenging. Datadriven modeling techniques have the potential to overcome these challenges and transform cardiovascular flow modeling. In this paper, we review several data-driven modeling techniques, highlight the common ideas and principles that emerge across numerous such techniques, and provide illustrative examples of how they could be used in the context of cardiovascular fluid mechanics. In particular, we discuss principal component analysis (PCA), robust PCA, compressed sensing, the Kalman filter for data assimilation, low-rank data recovery, and several additional methods for reduced-order modeling for cardiovascular flows, including the dynamic mode decomposition (DMD), and the sparse identification of nonlinear dynamics (SINDy). All of these techniques are presented in the context of cardiovascular flows with simple examples. These data-driven modeling techniques have the potential to transform computational and experimental cardiovascular flow research, and we discuss challenges and opportunities in applying these techniques in the field, looking ultimately towards data-driven patient-specific blood flow modeling.

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From Physics-Based Models to Predictive Digital Twins via Interpretable Machine Learning

Cited by 12 publications

References 0 publications

Real-time parameter updating for nonlinear digital twins using inverse mapping models and transient-based features

Real-time parameter updating for nonlinear digital twins using inverse mapping models and transient-based features

Quantification of Deep Neural Network Prediction Uncertainties for VVUQ of Machine Learning Models

Data-driven cardiovascular flow modeling: examples and opportunities

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