Publications

Sunseri, Isaac P.; Hart, Joseph L.; Alexanderian, Alen A.; van Bloemen Waanders, Bart G.

Abstract not provided.

SIAM Journal on Mathematics of Data Science

Newman, Elizabeth N.; Ruthotto, Lars R.; Hart, Joseph L.; van Bloemen Waanders, Bart G.

Deep neural networks (DNNs) have achieved state-of-the-art performance across a variety of traditional machine learning tasks, e.g., speech recognition, image classification, and segmentation. The ability of DNNs to efficiently approximate high-dimensional functions has also motivated their use in scientific applications, e.g., to solve partial differential equations and to generate surrogate models. In this paper, we consider the supervised training of DNNs, which arises in many of the above applications. We focus on the central problem of optimizing the weights of the given DNN such that it accurately approximates the relation between observed input and target data. Devising effective solvers for this optimization problem is notoriously challenging due to the large number of weights, nonconvexity, data sparsity, and nontrivial choice of hyperparameters. To solve the optimization problem more efficiently, we propose the use of variable projection (VarPro), a method originally designed for separable nonlinear least-squares problems. Our main contribution is the Gauss--Newton VarPro method (GNvpro) that extends the reach of the VarPro idea to nonquadratic objective functions, most notably cross-entropy loss functions arising in classification. These extensions make GNvpro applicable to all training problems that involve a DNN whose last layer is an affine mapping, which is common in many state-of-the-art architectures. In our four numerical experiments from surrogate modeling, segmentation, and classification, GNvpro solves the optimization problem more efficiently than commonly used stochastic gradient descent (SGD) schemes. Finally, GNvpro finds solutions that generalize well, and in all but one example better than well-tuned SGD methods, to unseen data points.

White, Rebekah D.; Jakeman, John D.; van Bloemen Waanders, Bart G.; Kouri, Drew P.; Alexanderian, Alex &.

Abstract not provided.

Morrow, Zachary B.; van Bloemen Waanders, Bart G.; Jakeman, John D.

Abstract not provided.

Hart, Joseph L.; van Bloemen Waanders, Bart G.

Abstract not provided.

Numerical Linear Algebra with Applications

Saibaba, Arvind K.; Hart, Joseph L.; van Bloemen Waanders, Bart G.

The generalized singular value decomposition (GSVD) is a valuable tool that has many applications in computational science. However, computing the GSVD for large-scale problems is challenging. Motivated by applications in hyper-differential sensitivity analysis (HDSA), we propose new randomized algorithms for computing the GSVD which use randomized subspace iteration and weighted QR factorization. Detailed error analysis is given which provides insight into the accuracy of the algorithms and the choice of the algorithmic parameters. We demonstrate the performance of our algorithms on test matrices and a large-scale model problem where HDSA is used to study subsurface flow.

McQuarrie, Shane A.; van Bloemen Waanders, Bart G.

Abstract not provided.

Kapilavai, Dheeraj K.; Roychowdhury, Subhrajit R.; Fu, Yiwei F.; Yu, Lei Y.; van Bloemen Waanders, Bart G.

Abstract not provided.

Reese, William M.; Hart, Joseph L.; van Bloemen Waanders, Bart G.; Perergo, Mauro P.; Jakeman, John D.; Saibaba, Arvind S.

Abstract not provided.

Phillips, Cynthia A.; Chatter, Michelle A.; Eckstein, Jonathan E.; Erturk, Alper E.; El-Kady, I.; Gerbe, Romain G.; Kouri, Drew P.; Loughlin, William L.; Reinke, Charles M.; Rokkam, Rohith R.; Ruzzene, Massimo R.; Sugino, Chris S.; Swanson, Calvin S.; van Bloemen Waanders, Bart G.

ROL-PEBBL is a C++, MPI-based parallel code for mixed-integer PDE-constrained optimization (MIPDECO). In these problems we wish to optimize (control, design, etc.) physical systems, which must obey the laws of physics, when some of the decision variables must take integer values. ROL-PEBBL combines a code to efficiently search over integer choices (PEBBL = Parallel Enumeration Branch-and-Bound Library) and a code for efficient nonlinear optimization, including PDE-constrained optimization (ROL = Rapid Optimization Library). In this report, we summarize the design of ROL-PEBBL and initial applications/results. For an artificial source-inversion problem, finding sources of pollution on a grid from sparse samples, ROL-PEBBLs solution for the nest grid gave the best optimization guarantee for any general solver that gives both a solution and a quality guarantee.

SIAM Journal on Scientific Computing

Glusa, Christian A.; ANTIL, HARBIR; D'Elia, Marta D.; van Bloemen Waanders, Bart G.; Weiss, Chester J.

The purpose of this paper is to study a Helmholtz problem with a spectral fractional Laplacian, instead of the standard Laplacian. Recently, it has been established that such a fractional Helmholtz problem better captures the underlying behavior in geophysical electromagnetics. We establish the well-posedness and regularity of this problem. We introduce a hybrid spectral-finite element approach to discretize it and show well-posedness of the discrete system. In addition, we derive a priori discretization error estimates. Finally, we introduce an efficient solver that scales as well as the best possible solver for the classical integer-order Helmholtz equation. We conclude with several illustrative examples that confirm our theoretical findings.

Proceedings of the IEEE Conference on Decision and Control

Joshi, Girish; Chowdhary, Girish; van Bloemen Waanders, Bart G.

In this paper, we present a Stochastic Deep Neural Network-based Model Reference Adaptive Control. Building on our work "Deep Model Reference Adaptive Control", we extend the controller capability by using Bayesian deep neural networks (DNN) to represent uncertainties and model nonlinearities. Stochastic Deep Model Reference Adaptive Control uses a Lyapunov-based method to adapt the outputlayer weights of the DNN model in real-time, while a data-driven supervised learning algorithm is used to update the inner-layers parameters. This asynchronous network update ensures boundedness and guaranteed tracking performance with a learning-based real-time feedback controller. A Bayesian approach to DNN learning helped avoid over-fitting the data and provide confidence intervals over the predictions. The controller's stochastic nature also ensured "Induced Persistency of excitation,"leading to convergence of the overall system signal.

van Bloemen Waanders, Bart G.; Ober, Curtis C.

Accurate and timely weather predictions are critical to many aspects of society with a profound impact on our economy, general well-being, and national security. In particular, our ability to forecast severe weather systems is necessary to avoid injuries and fatalities, but also important to minimize infrastructure damage and maximize mitigation strategies. The weather community has developed a range of sophisticated numerical models that are executed at various spatial and temporal scales in an attempt to issue global, regional, and local forecasts in pseudo real time. The accuracy however depends on the time period of the forecast, the nonlinearities of the dynamics, and the target spatial resolution. Significant uncertainties plague these predictions including errors in initial conditions, material properties, data, and model approximations. To address these shortcomings, a continuous data collection occurs at an effort level that is even larger than the modeling process. It has been demonstrated that the accuracy of the predictions depends on the quality of the data and is independent to a certain extent on the sophistication of the numerical models. Data assimilation has become one of the more critical steps in the overall weather prediction business and consequently substantial improvements in the quality of the data would have transformational benefits. This paper describes the use of infrasound inversion technology, enabled through exascale computing, that could potentially achieve orders of magnitude improvement in data quality and therefore transform weather predictions with significant impact on many aspects of our society.

van Bloemen Waanders, Bart G.; Hart, Joseph L.

Abstract not provided.

Sunseri, Isaac P.; van Bloemen Waanders, Bart G.; Hart, Joseph L.; Alexandarian, Alen A.

Abstract not provided.

Inverse Problems in Science and Engineering

Seidl, D.T.; van Bloemen Waanders, Bart G.; Wildey, T.M.

We present a formulation to simultaneously invert for a heterogeneous shear modulus field and traction boundary conditions in an incompressible linear elastic plane stress model. Our approach utilizes scalable deterministic methods, including adjoint-based sensitivities and quasi-Newton optimization, to reduce the computational requirements for large-scale inversion with partial differential equation (PDE) constraints. We address the use of regularization for such formulations and explore the use of different types of regularization for the shear modulus and boundary traction. We apply this PDE-constrained optimization algorithm to a synthetic dataset to verify the accuracy in the reconstructed parameters, and to experimental data from a tissue-mimicking ultrasound phantom. In all of these examples, we compare inversion results from full-field and sparse data measurements.

Newman, Elizabeth N.; Ruthotto, Lar R.; Hart, Joseph L.; van Bloemen Waanders, Bart G.; van Bloemen Waanders, Bart G.

Abstract not provided.

van Bloemen Waanders, Bart G.; Littlewood, David J.; Turner, Daniel Z.; Parks, Michael L.

Abstract not provided.

Sunseri, Isaac P.; Hart, Joseph L.; Alexandarian, Alen A.; van Bloemen Waanders, Bart G.

Abstract not provided.

International Journal for Uncertainty Quantification

Hart, Joseph; van Bloemen Waanders, Bart G.; Herzog, Roland

Many problems in engineering and sciences require the solution of large scale optimization constrained by partial differential equations (PDEs). Though PDE-constrained optimization is itself challenging, most applications pose ad-ditional complexity, namely, uncertain parameters in the PDEs. Uncertainty quantification (UQ) is necessary to char-acterize, prioritize, and study the influence of these uncertain parameters. Sensitivity analysis, a classical tool in UQ, is frequently used to study the sensitivity of a model to uncertain parameters. In this article, we introduce “hyperdiffer-ential sensitivity analysis" which considers the sensitivity of the solution of a PDE-constrained optimization problem to uncertain parameters. Our approach is a goal-oriented analysis which may be viewed as a tool to complement other UQ methods in the service of decision making and robust design. We formally define hyperdifferential sensitivity indices and highlight their relationship to the existing optimization and sensitivity analysis literatures. Assuming the presence of low rank structure in the parameter space, computational efficiency is achieved by leveraging a generalized singular value decomposition in conjunction with a randomized solver which converts the computational bottleneck of the algorithm into an embarrassingly parallel loop. Two multiphysics examples, consisting of nonlinear steady state control and transient linear inversion, demonstrate efficient identification of the uncertain parameters which have the greatest influence on the optimal solution.

Solid Freeform Fabrication 2018: Proceedings of the 29th Annual International Solid Freeform Fabrication Symposium - An Additive Manufacturing Conference, SFF 2018

Roach, R.A.; Bishop, Joseph E.; Johnson, Kyle J.; Rodgers, Theron R.; Boyce, B.L.; Swiler, L.; van Bloemen Waanders, Bart G.; Chandross, M.; Kammler, Daniel K.; Balch, Dorian K.; Jared, B.; Martinez, Mario J.; Leathe, Nicholas L.; Ford, K.

Additive Manufacturing (AM) offers the opportunity to transform design, manufacturing, and qualification with its unique capabilities. AM is a disruptive technology, allowing the capability to simultaneously create part and material while tightly controlling and monitoring the manufacturing process at the voxel level, with the inherent flexibility and agility in printing layer-by-layer. AM enables the possibility of measuring critical material and part parameters during manufacturing, thus changing the way we collect data, assess performance, and accept or qualify parts. It provides an opportunity to shift from the current iterative design-build-test qualification paradigm using traditional manufacturing processes to design-by-predictivity where requirements are addressed concurrently and rapidly. The new qualification paradigm driven by AM provides the opportunity to predict performance probabilistically, to optimally control the manufacturing process, and to implement accelerated cycles of learning. Exploiting these capabilities to realize a new uncertainty quantification-driven qualification that is rapid, flexible, and practical is the focus of this paper.

Weiss, Chester J.; Downs, Christine M.; van Bloemen Waanders, Bart G.

Abstract not provided.

Glusa, Christian A.; D'Elia, Marta D.; Antil, Harbir A.; Weiss, Chester J.; van Bloemen Waanders, Bart G.

Abstract not provided.

Weiss, Chester J.; Beskardes, G.D.; van Bloemen Waanders, Bart G.

Motivated by the need for improved forward modeling and inversion capabilities of geophysical response in geologic settings whose fine--scale features demand accountability, this project describes two novel approaches which advance the current state of the art. First is a hierarchical material properties representation for finite element analysis whereby material properties can be perscribed on volumetric elements, in addition to their facets and edges. Hence, thin or fine--scaled features can be economically represented by small numbers of connected edges or facets, rather than 10's of millions of very small volumetric elements. Examples of this approach are drawn from oilfield and near--surface geophysics where, for example, electrostatic response of metallic infastructure or fracture swarms is easily calculable on a laptop computer with an estimated reduction in resource allocation by 4 orders of magnitude over traditional methods. Second is a first-ever solution method for the space--fractional Helmholtz equation in geophysical electromagnetics, accompanied by newly--found magnetotelluric evidence supporting a fractional calculus representation of multi-scale geomaterials. Whereas these two achievements are significant in themselves, a clear understanding the intermediate length scale where these two endmember viewpoints must converge remains unresolved and is a natural direction for future research. Additionally, an explicit mapping from a known multi-scale geomaterial model to its equivalent fractional calculus representation proved beyond the scope of the present research and, similarly, remains fertile ground for future exploration.

Stracuzzi, David J.; Vollmer, Charles V.; Poppeliers, Christian P.; Beskardes, G.D.; Schwering, Paul C.; Cashion, Avery T.; van Bloemen Waanders, Bart G.; Weiss, Chester J.; Matteo, Edward N.; Bettin, Giorgia B.

Abstract not provided.

van Bloemen Waanders, Bart G.

Abstract not provided.

Ridzal, Denis R.; Cyr, Eric C.; van Bloemen Waanders, Bart G.

Abstract not provided.

Roach, R.A.; Jared, Bradley H.; Boyce, Brad B.; Lechman, Jeremy B.; Martinez, Mario A.; Forrest, Eric C.; Taylor, Samantha T.; Dagel, Amber L.; Madison, Jonathan D.; Ivanoff, Thomas I.; Koepke, Joshua R.; Swiler, Laura P.; van Bloemen Waanders, Bart G.; Clark, Brett W.; Rodgers, Theron R.; Johnson, Kyle J.

Abstract not provided.

Computational Mechanics

Salloum, Maher S.; Johnson, Kyle J.; Bishop, Joseph E.; Aytac, Jon M.; Dagel, Daryl D.; van Bloemen Waanders, Bart G.

New manufacturing technologies such as additive manufacturing require research and development to minimize the uncertainties in the produced parts. The research involves experimental measurements and large simulations, which result in huge quantities of data to store and analyze. We address this challenge by alleviating the data storage requirements using lossy data compression. We select wavelet bases as the mathematical tool for compression. Unlike images, additive manufacturing data is often represented on irregular geometries and unstructured meshes. Thus, we use Alpert tree-wavelets as bases for our data compression method. We first analyze different basis functions for the wavelets and find the one that results in maximal compression and miminal error in the reconstructed data. We then devise a new adaptive thresholding method that is data-agnostic and allows a priori estimation of the reconstruction error. Finally, we propose metrics to quantify the global and local errors in the reconstructed data. One of the error metrics addresses the preservation of physical constraints in reconstructed data fields, such as divergence-free stress field in structural simulations. While our compression and decompression method is general, we apply it to both experimental and computational data obtained from measurements and thermal/structural modeling of the sintering of a hollow cylinder from metal powders using a Laser Engineered Net Shape process. The results show that monomials achieve optimal compression performance when used as wavelet bases. The new thresholding method results in compression ratios that are two to seven times larger than the ones obtained with commonly used thresholds. Overall, adaptive Alpert tree-wavelets can achieve compression ratios between one and three orders of magnitude depending on the features in the data that are required to preserve. These results show that Alpert tree-wavelet compression is a viable and promising technique to reduce the size of large data structures found in both experiments and simulations.

Geophysics

Weiss, Chester J.; van Bloemen Waanders, Bart G.

The feasibility of Neumann-series expansion of Maxwell's equations in the electrostatic limit is investigated for potentially rapid and approximate subsurface imaging of geologic features proximal to metallic infrastructure in an oilfield environment. Although generally useful for efficient modeling of mild conductivity perturbations in uncluttered settings, we have raised the question of its suitability for situations such as oilfields, in which metallic artifacts are pervasive and, in some cases, in direct electrical contact with the conductivity perturbation on which the Neumann series is computed. Convergence of the Neumann series and its residual error are computed using the hierarchical finite-element framework for a canonical oilfield model consisting of an L-shaped, steel-cased well, energized by a steady-state electrode, and penetrating a small set of mildly conducting fractures near the heel of the well. For a given node spacing h in the finite-element mesh, we find that the Neumann series is ultimately convergent if the conductivity is small enough - a result consistent with previous presumptions on the necessity of small conductivity perturbations. However, we also determine that the spectral radius of the Neumann series operator grows as approximately 1/h, thus suggesting that in the limit of the continuous problem h→0, the Neumann series is intrinsically divergent for all conductivity perturbations, regardless of their smallness. The hierarchical finite-element methodology itself is critically analyzed and shown to possess the h2 error convergence of traditional linear finite elements, thereby supporting the conclusion of an inescapably divergent Neumann series for this benchmark example. Application of the Neumann series to oilfield problems with metallic clutter should therefore be done with careful consideration to the coupling between infrastructure and geology. The methods used here are demonstrably useful in such circumstances.

van Bloemen Waanders, Bart G.

Abstract not provided.

Hart, Joseph L.; van Bloemen Waanders, Bart G.

Abstract not provided.

Hart, Joseph L.; van Bloemen Waanders, Bart G.

Abstract not provided.

Weiss, Chester J.; van Bloemen Waanders, Bart G.; Beskardes, G.D.

Abstract not provided.

van Bloemen Waanders, Bart G.

Abstract not provided.

Parks, Michael L.; Turner, Daniel Z.; van Bloemen Waanders, Bart G.; Panchadhara, Rohan P.; Gordon, Peter G.

Abstract not provided.

Weiss, Chester J.; Beskardes, G.D.; van Bloemen Waanders, Bart G.

Abstract not provided.

IEEE Sensors Journal

Mazumdar, Anirban; Chen, Yi; van Bloemen Waanders, Bart G.; Brooks, Carlton F.; Kuehl, Michael K.; Nemer, Martin N.

Epoxies and resins can require careful temperature sensing and control in order to monitor and prevent degradation. To sense the temperature inside a mold, it is desirable to utilize a small, wireless sensing element. In this paper, we describe a new architecture for wireless temperature sensing and closed-loop temperature control of exothermic polymers. This architecture is the first to utilize magnetic field estimates of the temperature of permanent magnets within a temperature feedback control loop. We further improve performance and applicability by demonstrating sensing performance at relevant temperatures, incorporating a cure estimator, and implementing a nonlinear temperature controller. This novel architecture enables unique experimental results featuring closed-loop control of an exothermic resin without any physical connection to the inside of the mold. In this paper, we describe each of the unique features of this approach, including magnetic field-based temperature sensing, extended Kalman filtering for cure state estimation, and nonlinear feedback control over time-varying temperature trajectories. We use experimental results to demonstrate how low-cost permanent magnets can provide wireless temperature sensing up to ∼ 90°C. In addition, we use a polymer cure-control testbed to illustrate how internal temperature sensing can provide improved temperature control over both short and long time-scales. This wireless temperature sensing and control architecture holds value for a range of manufacturing applications.

Swiler, Laura P.; van Bloemen Waanders, Bart G.; Jared, Bradley H.; Koepke, Joshua R.; Whetten, Shaun R.; Madison, Jonathan D.; Ivanoff, Thomas I.; Jackson, Olivia D.; Cook, Adam W.; Brown-Shaklee, Harlan J.; Kammler, Daniel K.; Johnson, Kyle J.; Ford, Kurtis R.; Bishop, Joseph E.; Roach, R.A.

This report summarizes the data analysis activities that were performed under the Born Qualified Grand Challenge Project from 2016 - 2018. It is meant to document the characterization of additively manufactured parts and processe s for this project as well as demonstrate and identify further analyses and data science that could be done relating material processes to microstructure to properties to performance.

Littlewood, David J.; van Bloemen Waanders, Bart G.; Hegde, Arun S.; Cook, Adam W.

Abstract not provided.

van Bloemen Waanders, Bart G.; Hart, Joey H.

Abstract not provided.

van Bloemen Waanders, Bart G.

Abstract not provided.

IEEE Transactions on Magnetics

Chen, Yi; Mazumdar, Anirban; Brooks, Carlton F.; van Bloemen Waanders, Bart G.; Bond, Stephen D.; Nemer, Martin N.

Vibration sensing is critical for a variety of applications from structural fatigue monitoring to understanding the modes of airplane wings. In particular, remote sensing techniques are needed for measuring the vibrations of multiple points simultaneously, assessing vibrations inside opaque metal vessels, and sensing through smoke clouds and other optically challenging environments. In this paper, we propose a method which measures high-frequency displacements remotely using changes in the magnetic field generated by permanent magnets. We leverage the unique nature of vibration tracking and use a calibrated local model technique developed specifically to improve the frequency-domain estimation accuracy. The results show that two-dimensional local models surpass the dipole model in tracking high-frequency motions. A theoretical basis for understanding the effects of electronic noise and error due to correlated variables is generated in order to predict the performance of experiments prior to implementation. Simultaneous measurements of up to three independent vibrating components are shown. The relative accuracy of the magnet-based displacement tracking with respect to the video tracking ranges from 40 to 190 μ m when the maximum displacements approach ±5 mm and when sensor-to-magnet distances vary from 25 to 36 mm. Last, vibration sensing inside an opaque metal vessel and mode shape changes due to damage on an aluminum beam are also studied using the wireless permanent-magnet vibration sensing scheme.

Tikare, Veena T.; Abdeljawad, Fadi F.; Silling, Stewart A.; van Bloemen Waanders, Bart G.

Abstract not provided.

Wildey, Timothy M.; Butler, Troy B.; Jakeman, John D.; Seidl, Daniel T.; van Bloemen Waanders, Bart G.

Abstract not provided.

Roach, R.A.; Bishop, Joseph E.; Jared, Bradley H.; Keicher, David M.; Cook, Adam W.; Whetten, Shaun R.; Forrest, Eric C.; Stanford, Joshua S.; Boyce, Brad B.; Johnson, Kyle J.; Rodgers, Theron R.; Ford, Kurtis R.; Martinez, Mario J.; Moser, Daniel M.; van Bloemen Waanders, Bart G.; Chandross, M.; Abdeljawad, Fadi F.; Allen, Kyle M.; Stender, Michael S.; Beghini, Lauren L.; Swiler, Laura P.; Lester, Brian T.; Argibay, Nicolas A.; Brown-Shaklee, Harlan J.; Kustas, Andrew K.; Sugar, Joshua D.; Kammler, Daniel K.; Wilson, Mark A.

Abstract not provided.

El-Kady, I.; Reinke, Charles M.; van Bloemen Waanders, Bart G.; Ridzal, Denis R.; Su, Mehmet F.; Fitzpatrick, David F.; Chilton, Ryan C.

Abstract not provided.

El-Kady, I.; Reinke, Charles M.; van Bloemen Waanders, Bart G.; Ridzal, Denis R.; Su, Mehmet F.; Fitzpatrick, David F.; Chilton, Ryan C.

Abstract not provided.

Reinke, Charles M.; El-Kady, I.; Reinke, Charles M.; van Bloemen Waanders, Bart G.; Ridzal, Denis R.; Su, Mehmet F.; Fitzpatrick, David F.; Chilton, Ryan C.

Abstract not provided.

El-Kady, I.; Reinke, Charles M.; van Bloemen Waanders, Bart G.; Ridzal, Denis R.; Su, Mehmet F.; Fitzpatrick, David F.; Chilton, Ryan C.

Abstract not provided.