Physics Informed Recurrent Neural Networks for Seismic Response Evaluation of Nonlinear Systems

Dynamic response evaluation in structural engineering is the process of determining the response of a structure, such as member forces, node displacements, etc when subjected to dynamic loads such as earthquakes, wind, or impact. This is an important aspect of structural analysis, as it enables engineers to assess structural performance under extreme loading conditions and make informed decisions about the design and safety of the structure. Conventional methods for dynamic response evaluation involve numerical simulations using finite element analysis (FEA), where the structure is modeled using finite elements, and the equations of motion are solved numerically. Although effective, this approach can be computationally intensive and may not be suitable for real-time applications. To address these limitations, recent advancements in machine learning, specifically artificial neural networks, have been applied to dynamic response evaluation in structural engineering. These techniques leverage large data sets and sophisticated algorithms to learn the complex relationship between inputs and outputs, making them ideal for such problems. In this paper, a novel approach is proposed for evaluating the dynamic response of multi-degree-of-freedom (MDOF) systems using physics-informed recurrent neural networks. The focus of this paper is to evaluate the seismic (earthquake) response of nonlinear structures. The predicted response will be compared to state-of-the-art methods such as FEA to assess the efficacy of the physics-informed RNN model

From multiscale modeling to metamodeling of geomechanics problems

In numerical simulations of geomechanics problems, a grand challenge consists of overcoming the difficulties in making accurate and robust predictions by revealing the true mechanisms in particle interactions, fluid flow inside pore spaces, and hydromechanical coupling effect between the solid and fluid constituents, from microscale to mesoscale, and to macroscale. While simulation tools incorporating subscale physics can provide detailed insights and accurate material properties to macroscale simulations via computational homogenizations, these numerical simulations are often too computational demanding to be directly used across multiple scales. Recent breakthroughs of Artificial Intelligence (AI) via machine learning have great potential to overcome these barriers, as evidenced by their great success in many applications such as image recognition, natural language processing, and strategy exploration in games. The AI can achieve super-human performance level in a large number of applications, and accomplish tasks that were thought to be not feasible due to the limitations of human and previous computer algorithms. Yet, machine learning approaches can also suffer from overfitting, lack of interpretability, and lack of reliability. Thus the application of machine learning into generation of accurate and reliable surrogate constitutive models for geomaterials with multiscale and multiphysics is not trivial. For this purpose, we propose to establish an integrated modeling process for automatic designing, training, validating, and falsifying of constitutive models, or "metamodeling". This dissertation focuses on our efforts in laying down step-by-step the necessary theoretical and technical foundations for the multiscale metamodeling framework. The first step is to develop multiscale hydromechanical homogenization frameworks for both bulk granular materials and granular interfaces, with their behaviors homogenized from subscale microstructural simulations. For efficient simulations of field-scale geomechanics problems across more than two scales, we develop a hybrid data-driven method designed to capture the multiscale hydro-mechanical coupling effect of porous media with pores of various different sizes. By using sub-scale simulations to generate database to train material models, an offline homogenization procedure is used to replace the up-scaling procedure to generate path-dependent cohesive laws for localized physical discontinuities at both grain and specimen scales. To enable AI in taking over the trial-and-error tasks in the constitutive modeling process, we introduce a novel “metamodeling” framework that employs both graph theory and deep reinforcement learning (DRL) to generate accurate, physics compatible and interpretable surrogate machine learning models. The process of writing constitutive models is simplified as a sequence of forming graph edges with the goal of maximizing the model score (a function of accuracy, robustness and forward prediction quality). By using neural networks to estimate policies and state values, the computer agent is able to efficiently self-improve the constitutive models generated through self-playing. To overcome the obstacle of limited information in geomechanics, we improve the efficiency in utilization of experimental data by a multi-agent cooperative metamodeling framework to provide guidance on database generation and constitutive modeling at the same time. The modeler agent in the framework focuses on evaluating all modeling options (from domain experts’ knowledge or machine learning) in a directed multigraph of elasto-plasticity theory, and finding the optimal path that links the source of the directed graph (e.g., strain history) to the target (e.g., stress). Meanwhile, the data agent focuses on collecting data from real or virtual experiments, interacts with the modeler agent sequentially and generates the database for model calibration to optimize the prediction accuracy. Finally, we design a non-cooperative meta-modeling framework that focuses on automatically developing strategies that simultaneously generate experimental data to calibrate model parameters and explore weakness of a known constitutive model until the strengths and weaknesses of the constitutive law on the application range can be identified through competition. These tasks are enabled by a zero-sum reward system of the metamodeling game and robust adversarial reinforcement learning techniques

Prediction of Nonlinear Drift Demands for Buildings with Recurrent Neural Networks

Application of deep learning algorithms to the problems of structural engineering is an emerging research field. Inthis study, a deep learning algorithm, namely recurrent neural network (RNN), is applied to tackle a problemrelated to the assessment of reinforced concrete buildings. Inter-storey drift ratio profile of a structure is a quiteimportant parameter while conducting assessment procedures. In general, procedures require a series of timeconsuming nonlinear dynamic analysis. In this study, an extensive RNN is trained to tackle these problems andprovide a simple tool for assessment. Aim of the study is to predict the non-linear drift demand along the heightof a structure by employing RNN for a given stiffness profile along the height, strength reduction coefficient, massdensity on a floor, number of storeys. In order to train the network, a large number of nonlinear time historyanalyses are conducted for synthetically created building models. It is shown that RNN is able to accurately predictnonlinear drift demand profile of a structure along height without conducting tedious time history analyses.Therefore, the trained RNN can serve as a drift demand estimation tool, significantly shortening the assessmentprocedure

Nonlinear proper orthogonal decomposition for convection-dominated flows

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research under Award Number DE-SC0019290. O.S. gratefully acknowledges the Early Career Research Program (ECRP) support of the U.S. Department of Energy. O.S. also gratefully acknowledges the financial support of the National Science Foundation under Award No. DMS-2012255. T.I. acknowledges support through National Science Foundation Grant No. DMS-2012253.acceptedVersio

Physics-informed Deep Super-resolution for Spatiotemporal Data

High-fidelity simulation of complex physical systems is exorbitantly expensive and inaccessible across spatiotemporal scales. Recently, there has been an increasing interest in leveraging deep learning to augment scientific data based on the coarse-grained simulations, which is of cheap computational expense and retains satisfactory solution accuracy. However, the major existing work focuses on data-driven approaches which rely on rich training datasets and lack sufficient physical constraints. To this end, we propose a novel and efficient spatiotemporal super-resolution framework via physics-informed learning, inspired by the independence between temporal and spatial derivatives in partial differential equations (PDEs). The general principle is to leverage the temporal interpolation for flow estimation, and then introduce convolutional-recurrent neural networks for learning temporal refinement. Furthermore, we employ the stacked residual blocks with wide activation and sub-pixel layers with pixelshuffle for spatial reconstruction, where feature extraction is conducted in a low-resolution latent space. Moreover, we consider hard imposition of boundary conditions in the network to improve reconstruction accuracy. Results demonstrate the superior effectiveness and efficiency of the proposed method compared with baseline algorithms through extensive numerical experiments