Phong C. H. Nguyen

Phong C. H. Nguyen, Joseph B. Choi, H. S. Udaykumar et al.

Many mechanical engineering applications call for multiscale computational modeling and simulation. However, solving for complex multiscale systems remains computationally onerous due to the high dimensionality of the solution space. Recently, machine learning (ML) has emerged as a promising solution that can either serve as a surrogate for, accelerate or augment traditional numerical methods. Pioneering work has demonstrated that ML provides solutions to governing systems of equations with comparable accuracy to those obtained using direct numerical methods, but with significantly faster computational speed. These high-speed, high-fidelity estimations can facilitate the solving of complex multiscale systems by providing a better initial solution to traditional solvers. This paper provides a perspective on the opportunities and challenges of using ML for complex multiscale modeling and simulation. We first outline the current state-of-the-art ML approaches for simulating multiscale systems and highlight some of the landmark developments. Next, we discuss current challenges for ML in multiscale computational modeling, such as the data and discretization dependence, interpretability, and data sharing and collaborative platform development. Finally, we suggest several potential research directions for the future.

Joseph B. Choi, Phong C. H. Nguyen, Oishik Sen et al.

Artificial intelligence (AI) is rapidly emerging as an enabling tool for solving various complex materials design problems. This paper aims to review recent advances in AI-driven materials-by-design and their applications to energetic materials (EM). Trained with data from numerical simulations and/or physical experiments, AI models can assimilate trends and patterns within the design parameter space, identify optimal material designs (micro-morphologies, combinations of materials in composites, etc.), and point to designs with superior/targeted property and performance metrics. We review approaches focusing on such capabilities with respect to the three main stages of materials-by-design, namely representation learning of microstructure morphology (i.e., shape descriptors), structure-property-performance (S-P-P) linkage estimation, and optimization/design exploration. We provide a perspective view of these methods in terms of their potential, practicality, and efficacy towards the realization of materials-by-design. Specifically, methods in the literature are evaluated in terms of their capacity to learn from a small/limited number of data, computational complexity, generalizability/scalability to other material species and operating conditions, interpretability of the model predictions, and the burden of supervision/data annotation. Finally, we suggest a few promising future research directions for EM materials-by-design, such as meta-learning, active learning, Bayesian learning, and semi-/weakly-supervised learning, to bridge the gap between machine learning research and EM research.

Phong C. H. Nguyen, Yen-Thi Nguyen, Pradeep K. Seshadri et al.

Predictive simulations of the shock-to-detonation transition (SDT) in heterogeneous energetic materials (EM) are vital to the design and control of their energy release and sensitivity. Due to the complexity of the thermo-mechanics of EM during the SDT, both macro-scale response and sub-grid mesoscale energy localization must be captured accurately. This work proposes an efficient and accurate multiscale framework for SDT simulations of EM. We introduce a new approach for SDT simulation by using deep learning to model the mesoscale energy localization of shock-initiated EM microstructures. The proposed multiscale modeling framework is divided into two stages. First, a physics-aware recurrent convolutional neural network (PARC) is used to model the mesoscale energy localization of shock-initiated heterogeneous EM microstructures. PARC is trained using direct numerical simulations (DNS) of hotspot ignition and growth within microstructures of pressed HMX material subjected to different input shock strengths. After training, PARC is employed to supply hotspot ignition and growth rates for macroscale SDT simulations. We show that PARC can play the role of a surrogate model in a multiscale simulation framework, while drastically reducing the computation cost and providing improved representations of the sub-grid physics. The proposed multiscale modeling approach will provide a new tool for material scientists in designing high-performance and safer energetic materials.

Phong C. H. Nguyen, Yen-Thi Nguyen, Joseph B. Choi et al.

The thermo-mechanical response of shock-initiated energetic materials (EM) is highly influenced by their microstructures, presenting an opportunity to engineer EM microstructure in a "materials-by-design" framework. However, the current design practice is limited, as a large ensemble of simulations is required to construct the complex EM structure-property-performance linkages. We present the Physics-Aware Recurrent Convolutional (PARC) Neural Network, a deep-learning algorithm capable of learning the mesoscale thermo-mechanics of EM from a modest number of high-resolution direct numerical simulations (DNS). Validation results demonstrated that PARC could predict the themo-mechanical response of shocked EM with a comparable accuracy to DNS but with notably less computation time. The physics awareness of PARC enhances its modeling capabilities and generalizability, especially when challenged in unseen prediction scenarios. We also demonstrate that visualizing the artificial neurons at PARC can shed light on important aspects of EM thermos-mechanics and provide an additional lens for conceptualizing EM.

Phong C. H. Nguyen, Xinlun Cheng, Shahab Azarfar et al.

Modeling unsteady, fast transient, and advection-dominated physics problems is a pressing challenge for physics-aware deep learning (PADL). The physics of complex systems is governed by large systems of partial differential equations (PDEs) and ancillary constitutive models with nonlinear structures, as well as evolving state fields exhibiting sharp gradients and rapidly deforming material interfaces. Here, we investigate an inductive bias approach that is versatile and generalizable to model generic nonlinear field evolution problems. Our study focuses on the recent physics-aware recurrent convolutions (PARC), which incorporates a differentiator-integrator architecture that inductively models the spatiotemporal dynamics of generic physical systems. We extend the capabilities of PARC to simulate unsteady, transient, and advection-dominant systems. The extended model, referred to as PARCv2, is equipped with differential operators to model advection-reaction-diffusion equations, as well as a hybrid integral solver for stable, long-time predictions. PARCv2 is tested on both standard benchmark problems in fluid dynamics, namely Burgers and Navier-Stokes equations, and then applied to more complex shock-induced reaction problems in energetic materials. We evaluate the behavior of PARCv2 in comparison to other physics-informed and learning bias models and demonstrate its potential to model unsteady and advection-dominant dynamics regimes.

Hiep Vo Dang, Phong C. H. Nguyen

Reconstructing high-fidelity fluid flow fields from sparse sensor measurements is vital for many science and engineering applications but remains challenging because of dimensional disparities between state and observational spaces. Due to such dimensional differences, the measurement operator becomes ill-conditioned and non-invertible, making the reconstruction of flow fields from sensor measurements extremely difficult. Although sparse optimization and machine learning address the above problems to some extent, questions about their generalization and efficiency remain, particularly regarding the discretization dependence of these models. In this context, deep operator learning offers a better solution as this approach models mappings between infinite-dimensional functional spaces, enabling superior generalization and discretization-independent reconstruction. We introduce FLRONet, a deep operator learning framework that is trained to reconstruct fluid flow fields from sparse sensor measurements. FLRONet employs a branch-trunk network architecture to represent the inverse measurement operator that maps sensor observations to the original flow field, a continuous function of both space and time. Validation performed on the CFDBench dataset has demonstrated that FLRONet consistently achieves high levels of reconstruction accuracy and robustness, even in scenarios where sensor measurements are inaccurate or missing. Furthermore, the operator learning approach endows FLRONet with the capability to perform zero-shot super-resolution in both spatial and temporal domains, offering a solution for rapid reconstruction of high-fidelity flow fields.

Phong C. H. Nguyen, Joseph B. Choi, Quang-Trung Luu

Many applications in computational and experimental fluid mechanics require effective methods for reconstructing the flow fields from limited sensor data. However, this task remains a significant challenge because the measurement operator, which provides the punctual sensor measurement for a given state of the flow field, is often ill-conditioned and non-invertible. This issue impedes the feasibility of identifying the forward map, theoretically the inverse of the measurement operator, for field reconstruction purposes. While data-driven methods are available, their generalizability across different flow conditions (\textit{e.g.,} different Reynold numbers) remains questioned. Moreover, they frequently face the problem of spectral bias, which leads to smooth and blurry reconstructed fields, thereby decreasing the accuracy of reconstruction. We introduce FLRNet, a deep learning method for flow field reconstruction from sparse sensor measurements. FLRNet employs an variational autoencoder with Fourier feature layers and incorporates an extra perceptual loss term during training to learn a rich, low-dimensional latent representation of the flow field. The learned latent representation is then correlated to the sensor measurement using a fully connected (dense) network. We validated the reconstruction capability and the generalizability of FLRNet under various fluid flow conditions and sensor configurations, including different sensor counts and sensor layouts. Numerical experiments show that in all tested scenarios, FLRNet consistently outperformed other baselines, delivering the most accurate reconstructed flow field and being the most robust to noise.