While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter estimation. To overcome the challenges, we introduce a strongly regularized posterior by normalizing the likelihood and by imposing physical constraints through priors of the parameters and states. We investigate joint parameter-state estimation by the regularized posterior in a physically motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate reconstruction. The high-dimensional posterior is sampled by a particle Gibbs sampler that combines MCMC with an optimal particle filter exploiting the structure of the SEBM. In tests using either Gaussian or uniform priors based on the physical range of parameters, the regularized posteriors overcome the ill-posedness and lead to samples within physical ranges, quantifying the uncertainty in estimation. Due to the ill-posedness and the regularization, the posterior of parameters presents a relatively large uncertainty, and consequently, the maximum of the posterior, which is the minimizer in a variational approach, can have a large variation. In contrast, the posterior of states generally concentrates near the truth, substantially filtering out observation noise and reducing uncertainty in the unconstrained SEBM.
Over recent years heterogeneous systems have become more prevalent across HPC systems, with over 100 supercomputers in the TOP500 incorporating GPUs or other accelerators. These hardware platforms have different performance characteristics and optimization requirements. In order to make the most of multiple accelerators a developer has to provide implementations of their algorithms tuned for each device. Hardware vendors provide libraries targeting their devices specifically, which provide good performance but frequently have different API designs, hampering portability. The SYCL programming model allows users to write heterogeneous programs using completely standard C++, and so developers have access to the power of C++ templates when developing compute kernels. In this paper we show that by writing highly parameterized kernels for matrix multiplies and convolutions we achieve performance competitive with vendor implementations across different architectures. Furthermore, tuning for new devices amounts to choosing the combinations of kernel parameters that perform best on the hardware.
Deep Learning is applied to energy markets to predict extreme loads observed in energy grids. Forecasting energy loads and prices is challenging due to sharp peaks and troughs that arise due to supply and demand fluctuations from intraday system constraints. We propose deep spatio-temporal models and extreme value theory (EVT) to capture theses effects and in particular the tail behavior of load spikes. Deep LSTM architectures with ReLU and $\tanh$ activation functions can model trends and temporal dependencies while EVT captures highly volatile load spikes above a pre-specified threshold. To illustrate our methodology, we use hourly price and demand data from 4719 nodes of the PJM interconnection, and we construct a deep predictor. We show that DL-EVT outperforms traditional Fourier time series methods, both in-and out-of-sample, by capturing the observed nonlinearities in prices. Finally, we conclude with directions for future research.
Although there have been extensive studies on transmit beamforming in multi-input single-output (MISO) multicell networks, achieving optimal sum-rate with limited channel state information (CSI) is still a challenge even with a single user per cell. A novel cooperative downlink multicell MISO beamforming scheme is proposed with highly limited information exchange among the base stations (BSs) to maximize the sum-rate. In the proposed scheme, each BS can design its beamforming vector with only local CSI based on limited information exchange on CSI. Unlike previous studies, the proposed beamforming design is non-iterative and does not require any vector or matrix feedback but requires only quantized scalar information. The proposed scheme closely achieves the optimal sum-rate bound in almost all signal-to-noise ratio regime based on non-iterative optimization with lower amount of information exchange than existing schemes, which is justified by numerical simulations.
Thermal preferences vary from person to person and may change over time. The objective of this paper is to sequentially pose intelligent queries to occupants in order to optimally learn the room temperatures which maximize their satisfaction. Our central hypothesis is that an occupant's preference relation over room temperatures can be described using a scalar function of these temperatures, which we call the "occupant's thermal utility function". Information about an occupant's preference over room temperatures is available to us through their response to thermal preference queries : "prefer warmer," "prefer cooler" and "satisfied" which we interpret as statements about the derivative of their utility function, i.e. the utility function is "increasing", "decreasing" and "constant" respectively. We model this hidden utility function using a Gaussian process with a built-in unimodality constraint, i.e., the utility function has a unique maximum, and we train this model using Bayesian inference. This permits an expected improvement based selection of next preference query to pose to the occupant, which takes into account both exploration (sampling from areas of high uncertainty) and exploitation (sampling from areas which are likely to offer an improvement over current best observation). We use this framework to sequentially design experiments and illustrate its benefits by showing that it requires drastically fewer observations to learn the maximally preferred room temperature values as compared to other methods. This framework is an important step towards the development of intelligent HVAC systems which would be able to respond to individual occupants' personalized thermal comfort needs. In order to encourage the use of our PE framework and ensure reproducibility in results, we publish an implementation of our work named GPPrefElicit as an open-source package in the Python language .
We present a full implementation of the parareal algorithm---an integration technique to solve differential equations in parallel---in the Julia programming language for a fully general, first-order, initial-value problem. We provide a brief overview of Julia---a concurrent programming language for scientific computing. Our implementation of the parareal algorithm accepts both coarse and fine integrators as functional arguments. We use Euler's method and another Runge-Kutta integration technique as the integrators in our experiments. We also present a simulation of the algorithm for purposes of pedagogy and as a tool for investigating the performance of the algorithm.