In 1797, at the dawn of the industrial age, Goethe wrote "The Sorcerer's Apprentice," a poem about a magician in training who, through his arrogance and half-baked powers, unleashes a chain of events that he could not control.

Azeem Azhar is a strategist, product entrepreneur, and analyst living in London. He is the curator of the weekly newsletter Exponential View, from which the following is adapted. This is the first year I am presenting predictions for the coming year. I've received some incredibly helpful comments from readers via Twitter. This has encouraged me to stick my head above the parapet.

In this paper, we present an initial attempt to learn evolution PDEs from data. Inspired by the latest development of neural network designs in deep learning, we propose a new feed-forward deep network, called PDE-Net, to fulfill two objectives at the same time: to accurately predict dynamics of complex systems and to uncover the underlying hidden PDE models. The basic idea of the proposed PDE-Net is to learn differential operators by learning convolution kernels (filters), and apply neural networks or other machine learning methods to approximate the unknown nonlinear responses. Comparing with existing approaches, which either assume the form of the nonlinear response is known or fix certain finite difference approximations of differential operators, our approach has the most flexibility by learning both differential operators and the nonlinear responses. A special feature of the proposed PDE-Net is that all filters are properly constrained, which enables us to easily identify the governing PDE models while still maintaining the expressive and predictive power of the network. These constrains are carefully designed by fully exploiting the relation between the orders of differential operators and the orders of sum rules of filters (an important concept originated from wavelet theory). We also discuss relations of the PDE-Net with some existing networks in computer vision such as Network-In-Network (NIN) and Residual Neural Network (ResNet). Numerical experiments show that the PDE-Net has the potential to uncover the hidden PDE of the observed dynamics, and predict the dynamical behavior for a relatively long time, even in a noisy environment.

Wind energy is a clean resource, and one that is growing worldwide, since it is the most efficient renewable energy source [1,2].

A shortage of charging points and strain on energy supplies are now the main stumbling blocks to the rise of driverless electric cars, according to the UK boss of insurer Axa. Amanda Blanc said a lack of rapid charging bays and pressure on the National Grid have overtaken questions about accident liability as the biggest barriers to autonomous vehicles entering the transport mainstream. Blanc, a Tesla driver, said personal experience pointed to problems lying ahead for driverless electric vehicles. There are around 125,000 plug-in electric cars in the UK and 14,000 chargers - 2,620 of them being rapid chargers that can give a car an 80% charge in 30 minutes. Shell has just opened its first charging points for electric vehicles at 10 filling stations, mostly in London and the south-east.

President Donald Trump has signed into law a $1.5 trillion tax overhaul package. Trump touted the size of the tax cut, declaring to reporters in the Oval Office before he signed it Friday that'the numbers will speak.'

Meteorologists can now reliably tell us if it is going to rain tomorrow, but wouldn't dream of forecasting rain a year from now. Similarly, scientists find it much easier to predict what the world will look like in the next decade rather than in a century. This is because the technology of tomorrow relies on the science of today – it is only after we have understood a certain concept that we can think about how to put it to use. A famous example is Michael Faraday's research into electricity and magnetism in the 1830s. It was only decades later that others saw how to use this new knowledge to build electric motors and power generators, inventions that transformed our world.

Artificial intelligence (AI) has continued to gain prominence in 2017 as one of the biggest upcoming technologies. It is beginning to have more of an influence on companies' strategies and is predicted to drive significant change for organisations. Check out the latest findings on how the hype around artificial intelligence could be sowing damaging confusion. Also, read a number of case studies on how enterprises are using AI to help reach business goals around the world. You forgot to provide an Email Address.

Long Short-Term Memory (LSTM) is a popular approach to boosting the ability of Recurrent Neural Networks to store longer term temporal information. The capacity of an LSTM network can be increased by widening and adding layers. However, usually the former introduces additional parameters, while the latter increases the runtime. As an alternative we propose the Tensorized LSTM in which the hidden states are represented by tensors and updated via a cross-layer convolution. By increasing the tensor size, the network can be widened efficiently without additional parameters since the parameters are shared across different locations in the tensor; by delaying the output, the network can be deepened implicitly with little additional runtime since deep computations for each timestep are merged into temporal computations of the sequence. Experiments conducted on five challenging sequence learning tasks show the potential of the proposed model.

Maximum A posteriori Probability (MAP) inference in graphical models amounts to solving a graph-structured combinatorial optimization problem. Popular inference algorithms such as belief propagation (BP) and generalized belief propagation (GBP) are intimately related to linear programming (LP) relaxation within the Sherali-Adams hierarchy. Despite the popularity of these algorithms, it is well understood that the Sum-of-Squares (SOS) hierarchy based on semidefinite programming (SDP) can provide superior guarantees. Unfortunately, SOS relaxations for a graph with $n$ vertices require solving an SDP with $n^{\Theta(d)}$ variables where $d$ is the degree in the hierarchy. In practice, for $d\ge 4$, this approach does not scale beyond a few tens of variables. In this paper, we propose binary SDP relaxations for MAP inference using the SOS hierarchy with two innovations focused on computational efficiency. Firstly, in analogy to BP and its variants, we only introduce decision variables corresponding to contiguous regions in the graphical model. Secondly, we solve the resulting SDP using a non-convex Burer-Monteiro style method, and develop a sequential rounding procedure. We demonstrate that the resulting algorithm can solve problems with tens of thousands of variables within minutes, and outperforms BP and GBP on practical problems such as image denoising and Ising spin glasses. Finally, for specific graph types, we establish a sufficient condition for the tightness of the proposed partial SOS relaxation.