Nonlocal models in computational Science and Engineering: treatment of interfaces in heterogeneous materials and media, image processing, and model learning.
01/10/2020
In this second talk I will address in details some of the challenges and applications mentioned in the first talk. Specifically, I will describe two techniques to tackle the unresolved treatment of nonlocal interfaces in the simulation of heterogeneous material and media. The first technique is based on the minimization of an energy principle and yields a well-posed and physically consistent nonlocal interface problem; the second is based on a new fractional model for anomalous diffusion with increased variability.
Then, I will describe a technique for optimal image denoising using nonlocal operators as filters. The optimal imaging problem is formulated as a bilevel optimization problem where the control variables are the denoising parameters. Several numerical results on benchmark images illustrate the applicability and improved accuracy of our approach.
If time allows, I will also present two recently developed machine-learning techniques for nonlocal model identification. These techniques are physics-informed, data-driven, tools that allow us to reconstruct model parameters from sparse observations. I will also show one- and two-dimensional numerical tests that illustrate robustness and accuracy of our approaches
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New Large Constellations of Low Earth Orbit Satellites - Astronomy and Space Debris Challenges
23/09/2020
Over the next decade plans have been advanced for 100,000 new satellites in Low Earth Orbit (LEO, altitude less than 2000 km). This will increase the total number of objects in this orbital regime by at least a factor of 5, including active satellites and debris larger than 10 cm. I'll review why these constellations of satellites are planned, why so many are needed, and what the basic design parameters of a satellite constellation are. The first of these constellations have been launched: SpaceX Starlink satellites and OneWeb satellites. For the appearance of the night sky to the unaided eye and ground and space based optical astronomy, the night sky will never be the same. These new satellites could be brighter than most of the objects in orbit today, producing contamination by satellite streaks in astronomical images. The growing spatial density of objects in LEO leads to an increased risk of collision between objects in LEO and the increase in the space debris population.
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Nonlocal models in computational science and engineering: theory and challenges
21/09/2020
Nonlocal models such as peridynamics and fractional equations can capture effects that classical partial differential equations fail to capture. These effects include multiscale behavior, discontinuities in the solutions such as cracks, and anomalous behavior such as super- and sub-diffusion. For this reason, they provide an improved predictive capability for a large class of engineering and scientific applications including fracture mechanics, subsurface flow, turbulence, and image processing, to mention a few.
However, the improved accuracy of nonlocal formulations comes at the price of modeling and computational challenges that may hinder the usability of these models. Challenges include the nontrivial prescription of nonlocal boundary conditions, the unresolved treatment of nonlocal interfaces, the identification of model parameters, often sparse and subject to noise, and the incredibly high computational cost.
In this talk I will first introduce nonlocal models and describe a recently developed nonlocal calculus for their analysis. Then, I will discuss simulation challenges and describe in detail how we are addressing some of them at Sandia National Labs.
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Multifidelity Strategies in Uncertainty Quantification: an overview on some recent trends in sampling based approaches
18/09/2020
In the last decades, the advancements in the areas of computer hardware/architectures and scientific computing algorithms enabled engineers and scientists to more rapidly study and design complex systems by heavily relaying on numerical simulations. The increased need for predictive numerical simulations exacerbated the requirement for an accurate quantification of the errors of the numerical simulations beyond the more classical algorithmic verification activities. As a consequence, Uncertainty Quantification (UQ) has been introduced as a task that allows for a formal characterization and propagation of the physical and numerical uncertainty through computational codes in order to obtain statistics of the system's response. Despite the recent efforts and successes in advancing the UQ algorithms’ efficiency, the simultaneous combination of a large number of uncertainty parameters (which often correlates to the complexity of the numerical/physical assumptions) and the lack of regularity of the system's response still represents a formidable challenge for UQ. One of the possible ways of circumventing these difficulties is to rely on sampling-based approaches which are generally robust, easy to implement and they possess a rate of convergence which is independent from the number of parameters. However, for many years the extreme computational cost of these methods prevented their widespread use for UQ in the context of high-fidelity simulations. More recently several multilevel/multifidelity Monte Carlo strategies have been proposed to decrease the Monte Carlo cost without penalizing its accuracy. Several different versions of multifidelity methods exist, but they all share the main idea: whenever a set/cloud/sequence of system realizations with varying accuracy can be obtained, it is often more efficient to fuse data coming from all of them instead of relying to the higher-fidelity model only. In this talk we summarize our recent efforts in investigating novel ways of increasing the efficiency of these multifidelity approaches. We will provide several theoretical and numerical results and we will discuss a collection of numerical examples ranging from simple analytical/verification test cases to more complex and realistic engineering systems.
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The COVID-19 epidemic in Italy --- a modeling perspective (or What I did in the 2 Months Quarantine)
16/09/2020
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Combustion Engines Are Not Dead Yet: Future of Power and Transportation
14/09/2020
Despite the widespread perception about battery-electric and fuel-cell vehicles as future transportation, there are many reasons to believe that “all electric vehicles” scenario is not only unrealistic but also undesirable. The presentation will attempt to present an objective assessment of the future transportation portfolio and the role of advanced internal combustion engines running on conventional and alternative fuels. In particular, objective well-to-wheel life cycle assessment for various competing vehicle technologies will be presented, through which it will become clear that advanced high efficiency internal combustion engines running on carbon-neutral liquid fuels are the most feasible future direction for transportation at scale. Overviews will be given on relevant ongoing research activities and their opportunities and challenges will be addressed.
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Development of reduced-order models based on dimensionality reduction, classification and regression for reacting flow applications.
10/09/2020
In this second part, the reduced representations are used to derive reduced-order models, in combination to typical ML-based tasks such as classification and regression. Examples of applications of these ROM are provided in the context of Large Eddy Simulations of turbulent reacting flows, as well as for the development of digital twins of combustion assets.
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Simple Flows Using a Second Order Theory of Fluids
09/09/2020
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Dimensionality reduction and feature extraction from high-fidelity combustion data
07/09/2020
The use of machine learning algorithms to predict the behaviors of complex systems is booming. However, the key for an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and computer models, to embody in them all the prior knowledge and physical constraints that can enhance their performances, and to improve them based on the feedback coming for the validation experiments. In other words, we need to adapt the scientific method to bring machine learning into the picture and make the best use of the massive amount of data we have produced thanks to the advances in numerical computing.
The webinars review some of the open opportunities for the application of data-driven, reduced-order modelling to combustion systems. In particular, the first webinar focuses on dimensionality reduction in the context of reacting flow applications. Different approaches (based on modal decomposition, neural networks, kernel methods, ...) are presented and compared, based on their ability to identify low-dimensional manifold and provide relevant features.
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Physics-Informed Neural Networks for Optimal Control
03/09/2020
Physics-Informed Neural Networks (PINN) refer to recently defined a class of machine learning algorithms where the learning process for both regression and classification tasks is constrained to satisfy differential equations derived by the straightforward application of known physical laws. Indeed, Deep Neural Networks (DNN) have been successfully employed to solve a variety of ODEs and PDEs arising in fluid mechanics, quantum mechanics, just to mention a few. Optimal control problems, i.e. finding a feasible control that minimize a cost functional while satisfying physical, state and control constraints, are generally difficult to solve and one may nned to resort to specialized numerical methods. The application of Pontryagin minimum principle generates a complex two-point boundary value problem that is very sensitive to the initial guess (“curse of complexity”). The application of dynamic programming principles generate a high-dimensional PDE named Hamilton-Jacobi-Bellman (“Curse of Dimensionality”). In this talk we show the PINN can be employed to solve optimal control problems by tackling their solution using deep and/or shallow NNs. We show that such methods can be coupled with the Theory of Functional Connections (TFC, by Mortari et al.) to create numerical frameworks that generate efficient and accurate solutions with potential for real-time applications.
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