**Deep Ritz Method**

We propose a deep learning based method, the Deep Ritz Method, for numerically solving variational problems, particularly the ones that arise from partial differential equations. The Deep Ritz method is naturally nonlinear, naturally adaptive and has the potential to work in rather high dimensions. The framework is quite simple and fits well with the stochastic gradient descent method used in deep learning. We illustrate the method on several problems including some eigenvalue problems. … **Hindcasting**

In oceanography and meteorology, backtesting is also known as hindcasting: a hindcast is a way of testing a mathematical model; known or closely estimated inputs for past events are entered into the model to see how well the output matches the known results. Hindcasting usually refers to a numerical model integration of a historical period where no observations have been assimilated. This distinguishes a hindcast run from a reanalysis. Oceanographic observations of salinity and temperature as well as observations of surface wave parameters such as the significant wave height are much scarcer than meteorological observations, making hindcasting more common in oceanography than in meteorology. Also, since surface waves represent a forced system where the wind is the only generating force, wave hindcasting is often considered adequate for generating a reasonable representation of the wave climate with little need for a full reanalysis. Hindcasting is also used in hydrology for model stream flows. … **Continuous Skip-gram (Skip-gram)**

The training objective of the Skip-gram model is to find word representations that are useful for predicting the surrounding words in a sentence or a document. More formally, given a sequence of training words w1,w2,w3, … ,wT , the objective of the Skip-gram model is to maximize the average log probability, where c is the size of the training context (which can be a function of the center word wt). Larger c results in more training examples and thus can lead to a higher accuracy, at the expense of the 2 training time.

http://…/1301.3781.pdf …

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**08**
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Oct 2017

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