Aidata 64 Extreme

Like the extreme value distribution, the generalized extreme value distribution is often used to model the smallest or largest value among a large set of independent, identically distributed random values representing measurements or observations. For example, you might have batches of 1000 washers from a manufacturing process. If you record the size of the largest washer in each batch, the data are known as block maxima (or minima if you record the smallest). You can use the generalized extreme value distribution as a model for those block maxima.

The three cases covered by the generalized extreme value distribution are often referred to as the Types I, II, and III. Each type corresponds to the limiting distribution of block maxima from a different class of underlying distributions. Distributions whose tails decrease exponentially, such as the normal, lead to the Type I. Distributions whose tails decrease as a polynomial, such as Student's t, lead to the Type II. Distributions whose tails are finite, such as the beta, lead to the Type III.

Aidata 64 Extreme

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Although the extreme value distribution is most often used as a model for extreme values, you can also use it as a model for other types of continuous data. For example, extreme value distributions are closely related to the Weibull distribution. If T has a Weibull distribution, then log(T) has a type 1 extreme value distribution.

The function evfit returns the maximum likelihood estimates (MLEs) and confidence intervals for the parameters of the extreme value distribution. The following example shows how to fit some sample data using evfit, including estimates of the mean and variance from the fitted distribution.

Suppose you want to model the size of the smallest washer in each batch of 1000 from a manufacturing process. If you believe that the sizes are independent within and between each batch, you can fit an extreme value distribution to measurements of the minimum diameter from a series of eight experimental batches. The following code returns the MLEs of the distribution parameters as parmhat and the confidence intervals as the columns of parmci.

The extreme value distribution is skewed to the left, and its general shape remains the same for all parameter values. The location parameter, mu, shifts the distribution along the real line, and the scale parameter, sigma, expands or contracts the distribution.

In this article, we introduce an Uber forecasting model that combines historical data and external factors to more precisely predict extreme events, highlighting its new architecture and how it compares to our previous model.

Forecasting for extreme events can be difficult because of their infrequency. To overcome this data deficiency, we decided to train a single, flexible neural network to model data from many cities at once, which greatly improved our accuracy.

Gravitational waves are ripples in spacetime generated by extremely energetic cosmic events, such as the collision of black holes and neutron stars. These waves of undulating spacetime propagate away from these cataclysmic events, traveling unimpeded throughout the universe at the speed of light, carrying unique insights about the astrophysical properties of their sources.

This study shows that combining black hole physics, advances in AI, and extreme scale computing enables the creation of AI models that learn and describe the physics of gravitational waves that describe binary black hole mergers.

We show that AI can infer the astrophysical parameters that determine the properties of the gravitational waves that describe quasi-circular, spinning, non-precessing, binary black hole mergers. This work required the use of extreme scale computing, since AI required tens of millions of modeled waveforms to understand the physics of the problem, and training these AI models required thousands of GPUs in the Summit supercomputer to reduce time-to-insight. Furthermore, we incorporated physics and mathematical principles in the training of AI models to help AI more quickly identify the patterns and features in higher order modes that unveil the physical properties of black hole mergers.

Asad Khan, E.A. Huerta and Prayush Kumar, AI and extreme scale computing to learn and infer the physics of higher order gravitational wave modes of quasi-circular, spinning, non-precessing black hole mergers. Physics Letters B 835, 137505 (2022)

However, extreme weather events such as extended hot and cold spells that can produce deadly heat waves and winter storms are entirely different. They can have dire impacts on public health, the environment, and the economy.

Forecasting the weather patterns that cause extreme weather events is challenging despite decades of efforts and advances in numerical weather prediction (NWP). Modern forecasts use mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Even with the increasing power of today's supercomputers, the forecasting skill of numerical weather models extends to only about six days, although there is some dependence on location, season, and type of weather pattern.

Persistent weather patterns that are often the drivers of extreme events are particularly hard to forecast. Improving the forecast of such events using NWP requires using higher resolution models and running more simulations starting from almost the same weather conditions. The latter is needed to tackle the chaotic nature of the atmosphere, i.e., the famous butterfly effect. However, higher resolution models and more simulations demand enormous computational resources.

Pedram Hassanzadeh, an assistant professor in Mechanical Engineering and Earth, Environmental and Planetary Sciences at Rice University, and his PhD students Ashesh Chattopadhyay and Ebrahim Nabizadeh, recently introduced a data-driven framework that: 1) formulates extreme weather prediction as a pattern recognition problem, and 2) employs state-of-the-art deep learning techniques. Their findings were published in the February 2020 edition of the American Geophysical Union's Journal of Advances in Modeling Earth Systems.

"Generally, the numerical weather models do a good job predicting weather, but they still have some difficulties with extreme weather," Hassanzadeh said. "We're trying to do extreme weather prediction in a very different way."

The results of their demonstration suggest that extreme weather prediction can be done as a pattern recognition problem, particularly enabled by the recent advances in deep learning. In fact, the researchers found that more advanced deep learning methods outperformed simpler techniques, suggesting potential benefits in developing deep learning methods tailored for climate and weather data.

Three types of extreme value distributions are common, each as the limiting case for different types of underlying distributions. For example, the type I extreme value is the limit distribution of the maximum (or minimum) of a block of normally distributed data, as the block size becomes large. In this example, we will illustrate how to fit such data using a single distribution that includes all three types of extreme value distributions as special case, and investigate likelihood-based confidence intervals for quantiles of the fitted distribution.

The Generalized Extreme Value (GEV) distribution unites the type I, type II, and type III extreme value distributions into a single family, to allow a continuous range of possible shapes. It is parameterized with location and scale parameters, mu and sigma, and a shape parameter, k. When k < 0, the GEV is equivalent to the type III extreme value. When k > 0, the GEV is equivalent to the type II. In the limit as k approaches 0, the GEV becomes the type I.

Notice that the 95% confidence interval for k does not include the value zero. The type I extreme value distribution is apparently not a good model for these data. That makes sense, because the underlying distribution for the simulation had much heavier tails than a normal, and the type II extreme value distribution is theoretically the correct one as the block size becomes large.

In Europe, drought is a recurring phenomenon, affecting extended areas and large populations every year. Across the world, millions of people are annually exposed to droughts that seriously affect economic development and the environment. With advancing climate change, droughts are more likely to become more severe and frequent than any other extreme weather hazards. Thus, future impacts are expected to present a major threat for society and the environment. For example, Zimbabwe, Zambia and south Mozambique have been facing a severe drought since the beginning of 2020.

SUMMARY

The DOE SC program in Advanced Scientific Computing Research (ASCR) hereby announces its interest in research applications to explore potentially high-impact approaches in the development and use of randomized algorithms for scientific computing and extreme-scale science.

Extreme-scale science recognizes that disruptive technology changes are occurring across the science applications, algorithms, computer architectures and ecosystems. Recent reports and trends are heralding the convergence of high-performance computing, massive data, and scientific machine learning on increasingly heterogeneous architectures. Furthermore, the concept of programming is evolving thanks to neural networks that can learn from massive amounts of training data (without being explicitly programmed). Significant innovation will be required in the development of good paradigms and approaches for realizing the full potential of randomized algorithms for scientific computing. Proposed research should not focus strictly on a specific science application, but rather on creating the body of knowledge and understanding that will inform future advances in extreme-scale science. Consequently, the funding from this FOA is not intended to incrementally extend current research in the area of the proposed project. It is expected that the proposed projects will significantly benefit from the exploration of innovative ideas or from the development of unconventional approaches. e24fc04721