GINNs: Graph-Informed Neural Networks for multiscale physics

Hall, Eric Joseph; Taverniers, Søren; Katsoulakis, Markos A.; Tartakovsky, Daniel M.

doi:10.1016/j.jcp.2021.110192

Cited by 28 publications

(24 citation statements)

References 48 publications

(39 reference statements)

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“…As highlighted in the introduction, our MI-based approach to GSA is applicable to any black-box surrogate model. To illustrate the ability of MI-based GSA to deal with correlated CVs, for which variance-based GSA approaches are of limited value, we combine it with a GINN, a domain-aware DNN surrogate introduced in [6] to overcome computational bottlenecks in complex multiscale and multiphysics systems. A multiscale formulation of electrodiffusion in nanoporous media serves as a testbed.…”

Section: Mi-based Gsa With Black-box Surrogatesmentioning

confidence: 99%

“…Electrolyte (an ionized fluid) fills the nanopores and contributes to the formation of the EDL at the electrolyte-electrode interface (see, e.g., Fig. A8 in [6]). Identification of an optimal pore structure of the carbon electrodes holds the promise of manufacturing EDLCs which boast high power and high energy density [58,59].…”

Section: Multiscale Supercapacitor Dynamicsmentioning

confidence: 99%

“…The joint PDF of the random CVs X systematically quantifies uncertainties and errors arising in the physics-based representation. This key quantity for decision support is captured by a Bayesian Network (BN) [6,29], which encodes both physical relationships and available domain knowledge (Fig. 1).…”

Section: Multiscale Supercapacitor Dynamicsmentioning

confidence: 99%

“…This agnosticism makes DNNs suitable for dependent/correlated inputs and non-Gaussian, skewed, multimodal, and/or mutually correlated output QoIs, typically observed in complex real-world systems. While DNNs (e.g., see [2][3][4][5][6]) can tremendously speed up the design pipeline by accelerating and fully automating the prediction of QoIs, they represent black boxes that do not shed any light on the form of the function they are approximating. They provide no clear link between this function and the network weights.…”

Section: Introduction: Gsa and Deep Learning For Simulation-aided Designmentioning

confidence: 99%

“…Our MI-based GSA is compatible with any black-box model including DNNs such as physics-informed NNs [5,[32][33][34][35] and "data-free" physics-constrained NNs [4,[36][37][38]. Here, we leverage a Graph-Informed Neural Network (GINN) [6] that is tailored for multiscale physics and systems with correlated CVs. The GINN's ability to generate "big data" allows us to consider higher-order effects due to interactions between the CVs.…”

Section: Introduction: Gsa and Deep Learning For Simulation-aided Designmentioning

confidence: 99%

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Mutual information for explainable deep learning of multiscale systems

Taverniers

Hall

Katsoulakis

et al. 2021

Journal of Computational Physics

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Timely completion of design cycles for multiscale and multiphysics systems ranging from consumer electronics to hypersonic vehicles relies on rapid simulation-based prototyping. The latter typically involves high-dimensional spaces of possibly correlated control variables (CVs) and quantities of interest (QoIs) with non-Gaussian and/or multimodal distributions. We develop a model-agnostic, moment-independent global sensitivity analysis (GSA) that relies on differential mutual information to rank the effects of CVs on QoIs. Large amounts of data, which are necessary to rank CVs with confidence, are cheaply generated by a deep neural network (DNN) surrogate model of the underlying process. The DNN predictions are made explainable by the GSA so that the DNN can be deployed to close design loops. Our information-theoretic framework is compatible with a wide variety of black-box models. Its application to multiscale supercapacitor design demonstrates that the CV rankings facilitated by a domain-aware Graph-Informed Neural Network are better resolved than their counterparts obtained with a physics-based model for a fixed computational budget. Consequently, our information-theoretic GSA provides an "outer loop" for accelerated product design by identifying the most and least sensitive input directions and performing subsequent optimization over appropriately reduced parameter subspaces.

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Section: Mi-based Gsa With Black-box Surrogatesmentioning

confidence: 99%

Section: Multiscale Supercapacitor Dynamicsmentioning

confidence: 99%

Section: Multiscale Supercapacitor Dynamicsmentioning

confidence: 99%

Section: Introduction: Gsa and Deep Learning For Simulation-aided Designmentioning

confidence: 99%

Section: Introduction: Gsa and Deep Learning For Simulation-aided Designmentioning

confidence: 99%

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Mutual information for explainable deep learning of multiscale systems

Taverniers

Hall

Katsoulakis

et al. 2021

Journal of Computational Physics

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Multi-scale Modelling of Natural Composites Using Thermodynamics-Based Artificial Neural Networks and Dimensionality Reduction Techniques

Piunno

Stefanou

Jommi

2023

Springer Series in Geomechanics and Geoengineering

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Modelling natural composites, as the majority of real geomaterials, requires facing their intrinsic multiscale nature. This allows to consider multiphysics coupling occurring at the microscale, then reflected onto the macroscopic behavior. Geotechnics is constantly requiring reliable constitutive models of natural composites to solve large-scale engineering problems accurately and efficiently. This need motivates the contribution. To capture in detail the macroscopic effects of microscopic processes, many authors have developed multi-scale numerical schemes. A common drawback of such methods is the prohibitive computational cost. Recently, Machine Learning based approaches have raised as promising alternatives to traditional methods. Artificial Neural Networks -ANNs -have been used to predict the constitutive behaviour of complex, heterogeneous materials, with reduced calculation costs. However, a major weakness of ANN is the lack of a rigorous framework based on principles of physics. This often implies a limited capability to extrapolate values ranging outside the training set and the need of large, high-quality datasets, on which performing the training. This work focuses on the use of Thermodynamics-based Artificial Neural Networks -TANN -to predict the constitutive behaviour of natural composites. Dimensionality reduction techniques -DRTs -are used to embed information of microscopic processes into a lower dimensional manifold. The obtained set of variables is used to characterize the state of the material at the macroscopic scale. Entanglement of DRTs with TANN allows to reproduce the complex nonlinear material response with reduced computational costs and guarantying thermodynamic admissibility. To demonstrate the method capabilities an application to a heterogeneous material model is presented.

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A Review of Physics Informed Neural Networks for Multiscale Analysis and Inverse Problems

Kim,

Lee

2024

Multiscale Sci. Eng.

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GINNs: Graph-Informed Neural Networks for multiscale physics

Cited by 28 publications

References 48 publications

Mutual information for explainable deep learning of multiscale systems

Mutual information for explainable deep learning of multiscale systems

Multi-scale Modelling of Natural Composites Using Thermodynamics-Based Artificial Neural Networks and Dimensionality Reduction Techniques

A Review of Physics Informed Neural Networks for Multiscale Analysis and Inverse Problems

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