DPM: A deep learning PDE augmentation method (with application to large-eddy simulation) Jonathan B. Freund, Jonathan F. MacArt †, and Justin Sirignano ‡§ November 22, 2019 Abstract Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is embedded in a partial differential equation (PDE) that expresses the known physics and learns to describe the corresponding unknown or unrepresented physics from the data. Crafted as such, the neural network can also provide corrections for erroneously represented physics, such as discretization errors associated with the PDE's numerical solution. Once trained, the deep learning PDE model (DPM) can make out-of-sample predictions for new physical parameters, geometries, and boundary conditions. Estimating the embedded neural network requires optimizing over the entire PDE, which itself is a function of the neural network. Adjoint partial differential equations are used to efficiently calculate the high-dimensional gradient of the objective function with respect to the neural network parameters. A stochastic adjoint method (SAM), similar in spirit to stochastic gradient descent, further accelerates training. The approach is demonstrated and evaluated for turbulence predictions using large-eddy simulation (LES), a filtered version of the Navier-Stokes equation containing unclosed sub-filter-scale terms. High-fidelity direct numerical simulations (DNS) of decaying isotropic turbulence provide the training and testing data. The DPM outperforms the widely-used constant-coefficient and dynamic Smagorinsky models, even for filter sizes so large that these established models become qualitatively incorrect. It also significantly outperforms a priori trained models, which do not account for the full PDE. For comparable accuracy, the overall cost is reduced. Simulations of the DPM are accelerated by efficient GPU implementations of network evaluations. Measures of discretization errors, which are well-known to be consequential in LES, suggest that the ability of the training formulation to correct for these errors Mechanical Science & Engineering and Aerospace Engineering, University of Illinois at Urbana-Champaign, jbfre-und@illinois.edu

Due to limited computational power, performing uncertainty quantification analyses with complex computational models can be a challenging task. This is exacerbated in the context of stochastic simulators, the response of which to a given set of input parameters, rather than being a deterministic value, is a random variable with unknown probability density function (PDF). Of interest in this paper is the construction of a surrogate that can accurately predict this response PDF for any input parameters. We suggest using a flexible distribution family -- the generalized lambda distribution -- to approximate the response PDF. The associated distribution parameters are cast as functions of input parameters and represented by sparse polynomial chaos expansions. To build such a surrogate model, we propose an approach based on a local inference of the response PDF at each point of the experimental design based on replicated model evaluations. Two versions of this framework are proposed and compared on analytical examples and case studies.

GeoSoftware, part of CGG's Geoscience division, has announced that machine learning technology in Python ecosystems will be available in …

Just as power system operators are mastering data analytics to optimize hardware efficiencies, they are discovering how the complexities of artificial intelligence tools can do far more, and how to choose which to use. With deployment of advanced metering infrastructure (AMI) and smart sensor-equipped hardware, system operators are capturing unprecedented levels of data. Cloud computing and massive computational capabilities are allowing data analytics to make these investments pay off for customers. But it may take machine learning (ML) and artificial intelligence (AI) to address new power grid complexities. AI is a form of computer science that would make power system management fully autonomous in real time, researchers and private sector providers of power system services told Utility Dive.

Nobel Prize-winning novelist Anatole France famously opined: "It is human nature to think wisely and act foolishly." As a species, we're innately designed with -- as far as our awareness extends -- the highest, most profound levels of intellect, knowledge, and insight in our vast, infinite universe. But this does not equate to omniscience or absolute precision. Humans are by no stretch of the imagination perfect. We feel pressured, we get stressed, life happens, and we end up making mistakes.

We all likely remember when supply chain visibility changed the game for commodity management. Suddenly, global suppliers had insights into the real-time locations and quantities of their inventory. This type of visibility gave crude oil marketers and traders actionable insights, improved ability to respond to the unexpected, and a leg up on their competition. Early adopters of game-changing technological trends like supply chain visibility often see unprecedented growth in their business. The key is identifying new technology with the potential to usher in a new era of commodity management.

Microsoft (NasdaqGS:MSFT), Baker Hughes Company (NYSE:BKR) and AI software provider C3.ai, have allied to bring enterprise artificial intelligence solutions to the energy industry on Microsoft Azure. According to the press release, the alliance "leverages the significant energy technology expertise of Baker Hughes, C3.ai's proven AI platform and applications, and the Microsoft Azure cloud computing platform" to "streamline the adoption of scalable AI solutions for the energy industry that help promote safety, reliability, and sustainability". "We are witnessing a massive market shift as oil and gas businesses undergo enterprise-level digital transformation to improve efficiencies and increase safety, while simultaneously reducing environmental impact. With Microsoft's global reach and horizontal cloud platform, Baker Hughes's technology domain expertise, and C3.ai's industrial AI capabilities, organizations can rapidly improve core business operations and better serve customers with AI-enabled products and services. This strategic alliance is a complete game-changer for the industry."

The paper argues machine learning can be used in many climate change related areas including energy production, carbon dioxide removal, and solar geoengineering. Penn postdoctoral research fellow David Rolnick co-authored a paper on artificial intelligence's ability to help combat climate change. The paper, titled "Tackling Climate Change with Machine Learning," argues that machine learning can be used in many climate change related areas including energy production, carbon dioxide removal, and solar geoengineering, according to National Geographic. The paper was originally submitted in June and revised earlier this month. In the paper, the researchers wrote that artificial intelligence could help assess damage after disasters, select new materials to use for batteries or carbon capture technology, and reduce food waste.

New York(CNN Business) A secretive startup backed by Bill Gates has achieved a solar breakthrough aimed at saving the planet. Heliogen, a clean energy company that emerged from stealth mode on Tuesday, said it has discovered a way to use artificial intelligence and a field of mirrors to reflect so much sunlight that it generates extreme heat above 1,000 degrees Celsius. Essentially, Heliogen created a solar oven -- one capable of reaching temperatures that are roughly a quarter of what you'd find on the surface of the sun. The breakthrough means that, for the first time, concentrated solar energy can be used to create the extreme heat required to make cement, steel, glass and other industrial processes. In other words, carbon-free sunlight can replace fossil fuels in a heavy carbon-emitting corner of the economy that has been untouched by the clean energy revolution.

New York (CNN Business)A secretive startup backed by Bill Gates has achieved a solar breakthrough aimed at saving the planet. Heliogen, a clean energy company that emerged from stealth mode on Tuesday, said it has discovered a way to use artificial intelligence and a field of mirrors to reflect so much sunlight that it generates extreme heat above 1,000 degrees Celsius. This is an existential issue for your children, for my children and our grandchildren." Essentially, Heliogen created a solar oven -- one capable of reaching temperatures that are roughly a quarter of what you'd find on the surface of the sun. The breakthrough means that, for the first time, concentrated solar energy can be used to create the extreme heat required to make cement, steel, glass and other industrial processes. In other words, carbon-free sunlight can replace fossil fuels in a heavy carbon-emitting corner of the economy that has been untouched by the clean energy revolution. "We are rolling out technology that can beat the price of fossil fuels and also not make the CO2 emissions," Bill Gross, Heliogen's founder and CEO, told CNN Business. Heliogen, which is also backed by billionaire Los Angels Times owner Patrick Soon-Shiong, believes the patented technology will be able to dramatically reduce greenhouse gas emissions from industry. "Bill and the team have truly now harnessed the sun," Soon-Shiong, who also sits on the Heliogen board, told CNN Business. "The potential to humankind is enormous.