GINNs: Graph-Informed Neural Networks for Multiscale Physics (2006.14807v1)

Abstract: We introduce the concept of a Graph-Informed Neural Network (GINN), a hybrid approach combining deep learning with probabilistic graphical models (PGMs) that acts as a surrogate for physics-based representations of multiscale and multiphysics systems. GINNs address the twin challenges of removing intrinsic computational bottlenecks in physics-based models and generating large data sets for estimating probability distributions of quantities of interest (QoIs) with a high degree of confidence. Both the selection of the complex physics learned by the NN and its supervised learning/prediction are informed by the PGM, which includes the formulation of structured priors for tunable control variables (CVs) to account for their mutual correlations and ensure physically sound CV and QoI distributions. GINNs accelerate the prediction of QoIs essential for simulation-based decision-making where generating sufficient sample data using physics-based models alone is often prohibitively expensive. Using a real-world application grounded in supercapacitor-based energy storage, we describe the construction of GINNs from a Bayesian network-embedded homogenized model for supercapacitor dynamics, and demonstrate their ability to produce kernel density estimates of relevant non-Gaussian, skewed QoIs with tight confidence intervals.

• The paper presents the GINN framework, which embeds probabilistic graphical models into neural networks to produce physically realistic surrogate models.
• It replaces computational bottlenecks in traditional physics-based simulations with efficient neural network surrogates that capture non-Gaussian, skewed outputs.
• Implemented in supercapacitor energy storage, the approach delivers tight confidence intervals and improved simulation efficiency for uncertainty quantification.

An Overview of "GINNs: Graph-Informed Neural Networks for Multiscale Physics"

The paper presents a hybrid model framework, termed Graph-Informed Neural Networks (GINNs), integrating deep learning with probabilistic graphical models (PGMs) to act as surrogates for physics-based representations in multiscale systems. The GINN framework addresses significant computational challenges associated with traditional physics-based models, particularly in scenarios involving complex and nonlinear multiscale and multiphysics systems, by replacing computational bottlenecks with neural networks (NNs).

In multiscale physics, accurate modeling often requires extensive data collection and robust computational resources due to the intrinsically high-dimensional nature of these models and the typically skewed, non-Gaussian distributions of quantities of interest (QoIs). GINNs are designed to accelerate these processes by serving as efficient surrogates, informed by domain-specific structured priors encoded in PGMs, to generate large data sets swiftly and with computational parsimony. This approach is demonstrated in the context of supercapacitor-based energy storage.

Key Contributions and Methodology

Traditional physics-based modeling involves deterministic systems that often need reformulation in a probabilistic framework. This paper explores methods to transform these models into streamlined and efficient surrogates without sacrificing accuracy or physical soundness. The proposed GINN framework particularly distinguishes itself by embedding probabilistic hierarchical models into deterministic physics-based models to account for mutual correlations among control variables (CVs) and to ensure physically plausible distributions of CVs and QoIs.

1. Graph-Informed Neural Networks (GINNs): The innovation lies in embedding PGMs to guide NN learning and prediction. A PGM allows the exploitation of structured dependencies between variables, contrasting with the norm where inputs to NNs are regarded as independent. This approach ensures the physical realism of generated distributions, which is critical in applications such as energy storage where the distribution characteristics are non-trivial.
2. Efficient Surrogate Modeling: GINNs replace the expensive-to-compute components of physics-based models with learned neural-network-based representations, transforming computational bottlenecks into simpler problems that NNs can efficiently manage. The resultant output distributions maintain high fidelity, enabling decision-making in design and optimization without necessitating exorbitant computation times.
3. Use Case - Supercapacitor-based Energy Storage: The GINN framework is applied in modeling supercapacitor dynamics, wherein the physical complexities of the non-linear multiscale physics are distilled into a Bayesian-network-embedded model serving as the GINN foundation. The paper confirms the capability of GINNs to produce tight confidence intervals and accurate kernel density estimates for non-Gaussian, skewed QoIs, endorsing its practical applicability and predictive accuracy.

Implications and Future Work

The proposed GINN framework holds significant promise for broader application across varied domains requiring multiscale and multiphysics modeling. Its ability to maintain computational simplicity without sacrificing accuracy opens possibilities for advancements in data-driven uncertainty quantification (UQ) and data-centric engineering. By reducing computational loads drastically, GINNs facilitate accelerated simulation-aided design and development, prompting further exploration into their utility in other complex systems prominently featuring stochastic processes.

Future research could extend into validating GINN configurations across additional multi-fidelity setups or exploring causal inference effects in probabilistic graphical models. Additionally, fine-tuning the balance between the NN complexity and probabilistically motivated model constraints represents a potential avenue to enhance both predictive accuracy and interpretability across more intricate systems.

Overall, the paper pushes the boundaries of surrogate modeling by integrating hybrid techniques and leverages machine learning in conjunction with traditional physics-based modeling to lay the groundwork for more cost-effective and efficient predictive systems in complex physics simulations.