This project will be the first of its kind to use artificial intelligence and machine learning to improve the resilience of the grid,

High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number of financial assets in a portfolio. Moreover, such PDEs are often fully nonlinear due to the need to incorporate certain nonlinear phenomena in the model such as default risks, transaction costs, volatility uncertainty (Knightian uncertainty), or trading constraints in the model. Such high-dimensional fully nonlinear PDEs are exceedingly difficult to solve as the computational effort for standard approximation methods grows exponentially with the dimension. In this work we propose a new method for solving high-dimensional fully nonlinear second-order PDEs. Our method can in particular be used to sample from high-dimensional nonlinear expectations. The method is based on (i) a connection between fully nonlinear second-order PDEs and second-order backward stochastic differential equations (2BSDEs), (ii) a merged formulation of the PDE and the 2BSDE problem, (iii) a temporal forward discretization of the 2BSDE and a spatial approximation via deep neural nets, and (iv) a stochastic gradient descent-type optimization procedure. Numerical results obtained using ${\rm T{\small ENSOR}F{\small LOW}}$ in ${\rm P{\small YTHON}}$ illustrate the efficiency and the accuracy of the method in the cases of a $100$-dimensional Black-Scholes-Barenblatt equation, a $100$-dimensional Hamilton-Jacobi-Bellman equation, and a nonlinear expectation of a $ 100 $-dimensional $ G $-Brownian motion.

Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works have proposed a probabilistic approach able to infer the number of significant components. To this purpose, this paper introduces a Bayesian nonparametric principal component analysis (BNP-PCA). The proposed model projects observations onto a random orthogonal basis which is assigned a prior distribution defined on the Stiefel manifold. The prior on factor scores involves an Indian buffet process to model the uncertainty related to the number of components. The parameters of interest as well as the nuisance parameters are finally inferred within a fully Bayesian framework via Monte Carlo sampling. A study of the (in-)consistence of the marginal maximum a posteriori estimator of the latent dimension is carried out. A new estimator of the subspace dimension is proposed. Moreover, for sake of statistical significance, a Kolmogorov-Smirnov test based on the posterior distribution of the principal components is used to refine this estimate. The behaviour of the algorithm is first studied on various synthetic examples. Finally, the proposed BNP dimension reduction approach is shown to be easily yet efficiently coupled with clustering or latent factor models within a unique framework.

Deep Reinforcement Learning is a branch of Artificial Intelligence that allows machines to learn control and to take actions. Asset Management and Optimization are the natural application of DRL due to its ability to capture complex dependencies and choose optimal actions in real time. Our current energy transition to distributed generation drastically increases the number of actions available, with the optimal action changing throughout the day. Resolving the Operator's Dilemma in the environment with a lot of volatile variables (such as electricity price and energy consumption) is hard. The deterministic set of rules and abstract models used today to guide operations can account for such changes, but they cannot guarantee optimal performance.

Steven Hawking recently commented that artificial intelligence (AI) would be "either the best thing or the worst thing ever to happen to humanity". He was referring to the opportunity that AI offers to improve mankind's situation, set alongside the risks that it also presents. These same competing possibilities apply no less when AI is considered in the context of smart cities and the planet's growing urbanization. With smart cities, though, this is not just some abstract balance: there is a genuine choice of path to be made as smart cities and AI evolve together. This article explores the choice.

Christine Hertzog is the founder and Managing Director of the Smart Grid Library and SGL Partners, delivering consulting and information services about Smart Grid and Smart Infrastructure technologies, services, and solutions. Her firm provides pragmatic guidance to global vendors, governmental entities, and utilities covering a broad range of needs such as strategic corporate and market insights and design and deployment of prosumer-centric utility operations. Christine is the author of the Smart Grid Dictionary that defines the jargon, acronyms, and terminology about technologies, international standards, and organizations associated with the Smart Grid and Smart Infrastructure. She is co-author of The Smart Grid Consumer Focus Strategy, which identifies consumer/utility challenges and methods to ensure successful prosumer operations and interactions. She writes a syndicated blog about Smart Grid and Smart Infrastructure topics and serves as an advisor to Smart Grid companies, industry associations, and publications.

Curie Labs, an energy analytics startup, uses sensors, cloud computation, controllers and AI to cut power consumption in large facilities by 25 percent. Last Diwali, Saurabh Vij and Abhinav Saksena were appalled to see the levels of pollution recorded in Delhi and the country at large. The duo are friends from IIT Delhi. Abhinav comes from a core technical background while Saurabh had earlier founded a startup GTI Labs. Discussing the pollution problem, they soon realised that one unit of power consumption leads to close to 0.5 kilogram of carbon emissions.

We consider the exploration/exploitation problem in reinforcement learning. For exploitation, it is well known that the Bellman equation connects the value at any time-step to the expected value at subsequent time-steps. In this paper we consider a similar uncertainty Bellman equation (UBE), which connects the uncertainty at any time-step to the expected uncertainties at subsequent time-steps, thereby extending the potential exploratory benefit of a policy beyond individual time-steps. We prove that the unique fixed point of the UBE yields an upper bound on the variance of the estimated value of any fixed policy. This bound can be much tighter than traditional count-based bonuses that compound standard deviation rather than variance. Importantly, and unlike several existing approaches to optimism, this method scales naturally to large systems with complex generalization. Substituting our UBE-exploration strategy for $\epsilon$-greedy improves DQN performance on 51 out of 57 games in the Atari suite.

We present a technique for efficiently synthesizing images of atmospheric clouds using a combination of Monte Carlo integration and neural networks. The intricacies of Lorenz-Mie scattering and the high albedo of cloud-forming aerosols make rendering of clouds---e.g. the characteristic silverlining and the "whiteness" of the inner body---challenging for methods based solely on Monte Carlo integration or diffusion theory. We approach the problem differently. Instead of simulating all light transport during rendering, we pre-learn the spatial and directional distribution of radiant flux from tens of cloud exemplars. To render a new scene, we sample visible points of the cloud and, for each, extract a hierarchical 3D descriptor of the cloud geometry with respect to the shading location and the light source. The descriptor is input to a deep neural network that predicts the radiance function for each shading configuration. We make the key observation that progressively feeding the hierarchical descriptor into the network enhances the network's ability to learn faster and predict with high accuracy while using few coefficients. We also employ a block design with residual connections to further improve performance. A GPU implementation of our method synthesizes images of clouds that are nearly indistinguishable from the reference solution within seconds interactively. Our method thus represents a viable solution for applications such as cloud design and, thanks to its temporal stability, also for high-quality production of animated content.

We demonstrate a DNA robot that performs a nanomechanical task substantially more sophisticated than previous work. We developed a simple algorithm and three modular building blocks for a DNA robot that performs autonomous cargo sorting. The robot explores a two-dimensional testing ground on the surface of DNA origami, picks up multiple cargos of two types that are initially at unordered locations, and delivers each type to a specified destination until all cargo molecules are sorted into two distinct piles. The robot is designed to perform a random walk without any energy supply. Exploiting this feature, a single robot can repeatedly sort multiple cargos.