Track Session Program - All times EST

Note: This track will run three times on Day 1, and twice on Day 2

DAY 1
Monday, December 14

11:00 AM - 12:30 PM: Track Session 1

Talk Title: A data-driven exterior calculus: exact treatment of physics in SciML

Abstract: In the last couple years, it has been well-established that enforcing physical invariances plays a critical role in successfully applying ML tools to science and engineering applications with relatively small available data. Such "physics-informed" approaches generally impose physics by penalty, incorporating physical principles by adding regularizers to the loss, and therefore only preserve structure to within optimization error. We generalize techniques from structure-preserving discretization of PDE to enforce physics strongly, using the topology offered by graph neural networks as a surrogate for the mesh topology supporting traditional discrete exterior calculus structures. As a result, data-driven models are exactly conservative, provide stability guarantees, and handle the non-trivial null-spaces critical to obtaining predictive models in electromagnetics.

Talk Title: Hierarchical Deep-Learning Neural Networks (HiDeNN) for Science and Engineering Simulations and Design: A Proposed AI Framework for Science and Engineering Software

Abstract: Challenges encountered in the application of artificial intelligence (AI) methods to computational science and engineering can be divided into three categories: (1) mechanistically known problems with incomplete models, (2) purely data-driven problems with lack of mechanistic knowledge, and (3) computationally expensive problems. We propose a general AI framework named Hierarchical Deep-learning Neural Network (HiDeNN) for physics-based simulation, discovery, and design optimization. HiDeNN has the capability to combine computational simulation results such as the Integrated Computational Materials Engineering (ICME) with data-driven models to address data-scarcity for the aforementioned challenges. 

The general framework and essential components of HiDeNN as an AI framework are first presented which leads to the demystification of mathematical preliminaries. The process of augmentation of traditional finite element method (FEM) and beyond (e.g., iso-geometric analysis and meshfree methods) with HiDeNN can lead to more accurate solutions. Next, we will show how the HiDeNN framework can be extended to include our developing reduced order methods (e.g., proper generalized decomposition (PGD) and self-consistent clustering analysis (SCA) methods) to increase the flexibility, accuracy, and performance of the proposed HiDeNN AI software system. This is demonstrated by some representative problems, including additive manufacturing, mechanics of materials science, biomedical engineering, fracture and fatigue predictions, design optimization and uncertainty quantification. The outlook of HiDeNN will be discussed, with particular focus on how HiDeNN can be incorporated within proprietary and other commercial software platforms. 

Talk Title: Digital Image-based experimental mechanics to understand materials response under extreme conditions  

Abstract: Understanding the failure mechanisms of materials at extreme conditions is essential and, at the same time, challenging. There have been different approaches proposed over the years to study materials response in extremely aggressive environments, such as high pressure and ultrahigh temperature. With the advent of high-speed imaging systems and computer processing power, one can study the failure mechanisms at such a high event by carefully analyzing the digital images taken during testing.  We used a digital image-based approach to study the fundamental deformation and failure mechanism of materials at different time and length scales and a range of temperatures. Our recent work in progress on the deformation of cellular material under dynamic loading, strain rate effect on grain level deformation of polycrystalline metals, and multiscale failure mechanisms in PBX will be presented. The challenge and opportunity will be discussed. 

12:30 PM - 2:00 PM: Track Session 2

Talk Title: Deep Adversarial Priors for Physics-Driven Bayesian Inference

Abstract: Generative adversarial networks (GANs) have found multiple applications in the solution of inverse problems in science and engineering. These applications are driven by the ability of these networks to learn complex distributions and map the original feature space to a low-dimensional latent space. In this talk we consider the use of GANs as priors in physics-driven Bayesian inference problems. Within this approach the posterior distribution is learnt by mapping the problem to the latent space of the GAN and then using an HMC sampler for efficient sampling. We apply this approach to solving linear and nonlinear inverse problems, including an example with experimental data acquired from an application in biophysical imaging. Furthermore, we analyze the weak convergence of the approximate priort o the true prior and elucidate its dependence on the capacity of the network and the number of training samples.

Authors: Dhruv Patel, Deep Ray, Harisankar Ramaswamy, and Assad A Oberai
The support of ARO grant W911NF2010050 is acknowledged.

Lab: CD3: Computation and Data Driven Discovery Group, Viterbi School of Engineering, USC

Talk Title: A Layer-Parallel Approach for Training Deep Neural Networks

Abstract: Deep neural networks are a powerful machine learning tool with the capacity to “learn” complex nonlinear relationships described by large data sets. Despite their success training these models remains a challenging and computationally intensive undertaking. In this talk we will present a new layer-parallel training algorithm that exploits a multigrid scheme to accelerate both forward and backward propagation. Introducing a parallel decomposition between layers requires inexact propagation of the neural network. The multigrid method used in this approach stiches these subdomains together with sufficient accuracy to ensure rapid convergence. We demonstrate an order of magnitude wall-clock time speedup over the serial approach, opening a new avenue for parallelism that is complementary to existing approaches. Results for this talk can be found in [1,2].

[1] S. Guenther, L. Ruthotto, J. B. Schroder, E. C. Cyr, N. R. Gauger, Layer-Parallel Training of Deep Residual Neural Networks, SIMODs, Vol. 2 (1), 2020.

[2] E. C. Cyr, S. Guenther, J. B. Schroder, Multilevel Initialization for Layer-Parallel Deep Neural Network Training, arXiv preprint arXiv:1912.08974, 2019.

Authors: Eric C. Cyr, Stefanie Guenther, Lars Ruthotto, Jacob B. Schroder, Nico R. Gauger

Talk Title: Reinforcement Learning for Combinatorial Control of Partial Differential Equations

Abstract: Deep reinforcement learning techniques have demonstrated state-of-the-art performance on board games, which can be represented as sequential combinatorial control problems. Many current, long-standing challenges in engineering are approximately governed by partial differential equation models (e.g., diffusion, electromagnetism, elasticity, options pricing) and can be reduced to combinatorial control problems. We present an algorithm framework that combines a generalized k-opt heuristic with recent advances in deep reinforcement learning. Across various combinatorial optimal control problems for fields governed by the parabolic and hyperbolic partial differential equations, our method identifies significantly higher quality solutions than current leading methods in comparable time spans. Our results demonstrate the efficacy of deep reinforcement learning as a method for partial differential equation-based optimal control problems with combinatorial constraints and illustrate the potential of deep reinforcement learning to breathe new life into classical heuristic methods.

Authors: Gradey Wang, Adrian Lew, Eric Darve

2:30 PM - 4:00 PM: Track Session 3

Talk Title: Benchmark datasets for mechanical metamodels

Abstract: Metamodels, or models of models, map defined model inputs to defined model outputs. When metamodels are constructed to be computationally cheap, they are an invaluable tool for applications ranging from topology optimization, to uncertainty quantification, to real-time prediction, to multi-scale simulation. By nature, a given metamodel will be tailored to a specific dataset. However, the most pragmatic metamodel type and structure will often be general to larger classes of problems. At present, the most pragmatic metamodel selection for dealing with mechanical data — specifically simulations of heterogenous materials — has not been thoroughly explored. Drawing inspiration from the benchmark datasets available to the computer vision research community, we introduce a benchmark data set (Mechanical MNIST https://open.bu.edu/handle/2144/39371) for constructing metamodels of heterogeneous material undergoing large deformation. We then show two examples of problems that we have explored thus far with this dataset. First: decreasing the cost of generating training data through transfer learning. Second: generating a training dataset with a limited description of the heterogeneous material of interest. Looking forward, we anticipate that disseminating benchmark datasets will enable the broader community of researchers to develop improved metamodeling techniques for capturing the behavior of spatially heterogeneous materials that will surpass the baseline performance that we show here.

Talk Title: Deep Autoencoders for Physics-Constrained Digital Twins for Musculoskeletal Systems

Abstract: Digital Twins (DT), with their origin in aircraft engine designs, have been extended to healthcare in recent years. DT for musculoskeletal (MSK) systems can be used to provide early detection of muscle function and performance loss due to injuries and diseases, and to test possible solutions virtually before implementing actual changes or procedures. The backbone of the proposed MSK DT is the physics-constrained pixel-based data-driven computational framework driven by high-dimensional material data, image data, and sensor data at cellular, component, and whole-body scales. This study introduces autoencoder-based deep manifold learning for data dimension reduction, which extracts a low-dimensional representation (embedding) of high-dimensional data, and provides noise filtering with enhanced extrapolation generalization. A local convexity-preserving scheme based on Shepard interpolation is also introduced for enhanced efficiency and stability over the locally convex data-driven computing framework [1, 2]. In this study, data-driven modeling of biological tissues using magnetic resonance imaging (MRI), diffusion tensor imaging (DTI), and stress-strain data is demonstrated. The future work in connecting the predicted muscle mechanical properties to the multi-body dynamics MSK DT by solving inverse dynamics using deep neural networks will also be highlighted.

Authors: J. S. Chen¹, Xiaolong He, Qizhi He, and Karan Taneja

Talk Title: The Meta-Modeling of a Plasticity Modeler: A Level Set Approach

Abstract: This talk will provide an overview of a meta-modeling framework that builds interpretable macroscopic surrogate elasto-plasticity models inferred from sub-scale direct numerical simulations (DNS) or experimental data. By recasting the yield function as a signed distance function, we generalize all possible hardening rules as a Hamilton-Jacobi problem. The geometrical interpretation of Helmholtz energy functionals enables us to examine and enforce convexity, frame indifference, and thermodynamic consistency and therefore overcome the technical barrier of black-box neural network models. A graph convolutional neural network is used to deduce low-dimensional descriptors that encode the evolutional of particle topology under path-dependent deformation and are used to replace internal variables. A non-cooperative game is used to train AI agents in a reinforcement learning framework to validate and disprove the constitutive laws and generate the data that improves both the robustness and accuracy of the material laws.

DAY 2
Tuesday, December 15

12:30 PM - 2:00 PM: Track Session 6

Talk Title: Probabilistic Learning on Manifolds (PLoM)

Abstract: An overview is presented of recent developments related to extracting constraints from data, and representing them algorithmically for inference and decision.

Two of the outstanding challenges in computational science and engineering are to characterize modeling errors and to integrate high-fidelity simulations into design optimization. The first of these is a modeling challenge, while the second is numerical challenge. Typically, most of the effort in both tasks goes towards satisfying, with high accuracy, known and intuited constraints. In most cases, these are too many constraints!

Conversely, and while ML algorithms typically provide efficient characterizations of input-output maps, they are awkward at satisfying algebraic or differential constraints. This is exacerbated when the constraints are themselves in error (such as the case with mdoel error).

We tackle both challenges by considering them to be associated with the manner in which the constraints are represented, and the quantities being constrained by them. We thus discover intrinsic relationships between observables. We construct, estimate, and sample from a joint density function of these observables. We demonstrate how statistical conditioning can serve as a highly efficient surrogate for design optimization.

In the proposed framework, the challenges of numerical discretization and ML calibration are replaced by the challenge of selecting suitable observables. We rely on the DMAP formalism to localize observables in lower dimensional spans, and we rely on projected MCMC to generate statistical samples required by the joint density functions and associated conditional regressors.

We demonstrate the above machinery of probabilistic physics-informed learning on a selection of problems from science and engineering.

Talk Title: Bayesian System Identification: Accounting for Model Error for Improved Robustness to Sparse and Noisy Data

Abstract: We consider the problem of reconstructing dynamical systems through indirect and sparse observation. Central to any such learning and system identification problem is the selection of an objective function that measures the quality of a dynamical system fit to data. By and large, a least squares-based objective function that seeks to minimize the sum of the squared deviations of the model from the data is seen as the default choice. Instead, we advocate for a different objective that is derived from probabilistic principles that coherently accounts for both model error in the form of process noise and for measurement data. We show that this objective is robust to a wider range of conditions of noisy and/or sparse data and can outperform the most common existing methods of system identification, sometimes by several orders of magnitude. We also prove that many of the existing approaches, e.g., DMD or sparse identification, can be derived through limiting assumptions in our probabilistic model. We show numerous examples of improved performance on both PDE and ODE systems. We also show how to adapt the approach to Hamiltonian systems and to learn systems from input-output data. In each case, we demonstrate that, even with a capable model approximation space, the learning objective must be carefully designed to encourage proper identification of the dynamical system.

Talk Title: Structures as Sensors: Physics-guided Model Transfer for Indirectly Monitoring Humans across Multiple Structures

Abstract: Smart structures are designed to sense, understand, and respond to various needs of human users. However, traditional monitoring approaches using dedicated sensors often result in dense sensing systems that are difficult to install and maintain in large-scale structures. This talk introduces “structures as sensors” approach that utilizes the structure itself as a sensing medium to indirectly infer occupant information. For example, we can infer occupant identity, location, and walking pattern through their activity induced building floor vibrations. This approach enables non-intrusive monitoring while significantly reducing the number and type of sensors needed to be installed and maintained. Challenges lie, however, in creating robust inference models for analyzing convoluted noisy structural response data collected from multiple structures (e.g., building responses due to human activities, HVAC systems, and outside traffic). To this end, we developed physics-guided data analytics approaches that combine statistical signal processing and machine learning with physical principles. Specifically, I will present a model transfer approach for occupant tracking and characterization across multiple structures. Our system is deployed in real-world testbeds, including eldercare centers, pig farms, and campus buildings.

4:00 PM - 5:30 PM: Track Session 8

Talk Title: Bioinspired Materials by Design using AI

Abstract: Nature produces a variety of materials with many functions, often out of simple and abundant materials, and at low energy. Such systems - examples of which include silk, bone, nacre or diatoms - provide broad inspiration for engineering. Here we explore the translation of biological composites to engineering applications, using a variety of tools including molecular modeling, AI and machine learning, and experimental synthesis and characterization. We review a series of studies focused on the mechanical behavior of materials, especially fracture, and how these phenomena can be modeled using a combination of molecular dynamics and machine learning. We also present various case studies of material optimization using genetic algorithms, applied to 3D printed composites, protein design, and a translation of protein folding to music and back.

Talk Title: Optimal Sequential Bayesian Design of Experiments Using Reinforcement Learning with Policy Gradient

Abstract: Experiments are indispensable for learning and developing models in engineering and science. When experiments are expensive, a careful design of these limited data-acquisition opportunities can be immensely beneficial. Optimal experimental design, while leveraging the predictive capabilities of a simulation model, provides a rigorous framework to systematically quantify and maximize the value of experiments and their data. We focus on designing a finite sequence of experiments, seeking fully optimal design policies that (a) adapt to newly collected data during the sequence (i.e. feedback) and (b) anticipate future changes (i.e. lookahead). We cast this sequential decision-making problem in a Bayesian setting with information-based utilities, and solve it numerically via policy gradient methods. In particular, we directly parameterize the policies and value functions by neural networks—thus adopting an actor-critic approach—and improve them using gradient estimates produced from simulated design and observation sequences. The overall method is demonstrated on an algebraic benchmark and a sensor placement application in a convection-diffusion field. The results provide insights on the benefits of feedback and lookahead, and computational advantages compared to previous numerical approaches based on approximate dynamical programming.

Authors: Wanggang Shen, University of Michigan, United States, wgshen@umich.edu; and Xun Huan, University of Michigan, United States, xhuan@umich.edu

Talk Title: A Graph Theoretic Framework for Representation, Exploration, Analysis and Reduced Order Modelling on Computed States of Physical Systems

Abstract: A graph theoretic view is taken for a range of phenomena in continuum physics in order to develop representations that will allow analysis of large scale, high-fidelity solutions to these problems. Of interest are phenomena whose description leads to partial differential equations, with solutions being obtained by computation. The motivation is to gain insight that may otherwise be difficult to attain because of the high dimensionality of computed solutions. We consider graph theoretic representations that are made possible by low-dimensional states defined on the systems. These states are typically functionals of the high-dimensional solutions, and therefore retain important aspects of the high-fidelity information present in the original, computed solutions.  Our approach is rooted in regarding each state as a vertex on a graph and identifying edges via processes that are induced either by numerical solution strategies, or by the physics. Correspondences are drawn between the sampling of stationary states, or the time evolution of dynamic phenomena, and the analytic machinery of graph theory. A collection of computations is examined in this framework and new insights to them are presented through the analytic techniques made possible by the graph theoretic representation. Additionally, we present a rigorous framework for reduced order modelling based on these graphs.

Authors: M. Duschenes, X. Zhang, G.H. Teichert and K. Garikipati

Participating Speakers & Track Chairs

Research Submissions

Submission Deadline: October 15, 2020
Acceptance Decision: November 1, 2020
Video Deadline: December 1, 2020
Poster Presentations & Event Date: December 14-15, 2020 (see the full program here)

The Mechanical Engineering, Engineering Mechanics, and Civil Engineering track will collect abstracts and posters, which should be received by the submission deadline. Following review, by December 1, 2020 we will ask you to create short video explanation by the lead author(s), to the conference website.