161,191 research outputs found
Order 10 4 speedup in global linear instability analysis using matrix formation
A unified solution framework is presented for one-, two- or three-dimensional complex non-symmetric eigenvalue problems, respectively governing linear modal instability of incompressible fluid flows in rectangular domains having two, one or no homogeneous spatial directions. The solution algorithm is based on subspace iteration in which the spatial discretization matrix is formed, stored and inverted serially. Results delivered by spectral collocation based on the Chebyshev-Gauss-Lobatto (CGL) points and a suite of high-order finite-difference methods comprising the previously employed for this type of work Dispersion-Relation-Preserving (DRP) and Padé finite-difference schemes, as well as the Summationby- parts (SBP) and the new high-order finite-difference scheme of order q (FD-q) have been compared from the point of view of accuracy and efficiency in standard validation cases of temporal local and BiGlobal linear instability. The FD-q method has been found to significantly outperform all other finite difference schemes in solving classic linear local, BiGlobal, and TriGlobal eigenvalue problems, as regards both memory and CPU time requirements. Results shown in the present study disprove the paradigm that spectral methods are superior to finite difference methods in terms of computational cost, at equal accuracy, FD-q spatial discretization delivering a speedup of ð (10 4). Consequently, accurate solutions of the three-dimensional (TriGlobal) eigenvalue problems may be solved on typical desktop computers with modest computational effort
Recommended from our members
Algorithms for First-order Sparse Reinforcement Learning
This thesis presents a general framework for first-order temporal difference learning algorithms with an in-depth theoretical analysis. The main contribution of the thesis is the development and design of a family of first-order regularized temporal-difference (TD) algorithms using stochastic approximation and stochastic optimization. To scale up TD algorithms to large-scale problems, we use first-order optimization to explore regularized TD methods using linear value function approximation. Previous regularized TD methods often use matrix inversion, which requires cubic time and quadratic memory complexity. We propose two algorithms, sparse-Q and RO-TD, for on-policy and off-policy learning, respectively. These two algorithms exhibit linear computational complexity per-step, and their asymptotic convergence guarantee and error bound analysis are given using stochastic optimization and stochastic approximation. The second major contribution of the thesis is the establishment of a unified general framework for stochastic-gradient-based temporal-difference learning algorithms that use proximal gradient methods. The primal-dual saddle-point formulation is introduced, and state-of-the-art stochastic gradient solvers, such as mirror descent and extragradient are used to design several novel RL algorithms. Theoretical analysis is given, including regularization, acceleration analysis and finite-sample analysis, along with detailed empirical experiments to demonstrate the effectiveness of the proposed algorithms
Learning Representations in Model-Free Hierarchical Reinforcement Learning
Common approaches to Reinforcement Learning (RL) are seriously challenged by
large-scale applications involving huge state spaces and sparse delayed reward
feedback. Hierarchical Reinforcement Learning (HRL) methods attempt to address
this scalability issue by learning action selection policies at multiple levels
of temporal abstraction. Abstraction can be had by identifying a relatively
small set of states that are likely to be useful as subgoals, in concert with
the learning of corresponding skill policies to achieve those subgoals. Many
approaches to subgoal discovery in HRL depend on the analysis of a model of the
environment, but the need to learn such a model introduces its own problems of
scale. Once subgoals are identified, skills may be learned through intrinsic
motivation, introducing an internal reward signal marking subgoal attainment.
In this paper, we present a novel model-free method for subgoal discovery using
incremental unsupervised learning over a small memory of the most recent
experiences (trajectories) of the agent. When combined with an intrinsic
motivation learning mechanism, this method learns both subgoals and skills,
based on experiences in the environment. Thus, we offer an original approach to
HRL that does not require the acquisition of a model of the environment,
suitable for large-scale applications. We demonstrate the efficiency of our
method on two RL problems with sparse delayed feedback: a variant of the rooms
environment and the first screen of the ATARI 2600 Montezuma's Revenge game
An Integrated Multi-Time-Scale Modeling for Solar Irradiance Forecasting Using Deep Learning
For short-term solar irradiance forecasting, the traditional point
forecasting methods are rendered less useful due to the non-stationary
characteristic of solar power. The amount of operating reserves required to
maintain reliable operation of the electric grid rises due to the variability
of solar energy. The higher the uncertainty in the generation, the greater the
operating-reserve requirements, which translates to an increased cost of
operation. In this research work, we propose a unified architecture for
multi-time-scale predictions for intra-day solar irradiance forecasting using
recurrent neural networks (RNN) and long-short-term memory networks (LSTMs).
This paper also lays out a framework for extending this modeling approach to
intra-hour forecasting horizons thus, making it a multi-time-horizon
forecasting approach, capable of predicting intra-hour as well as intra-day
solar irradiance. We develop an end-to-end pipeline to effectuate the proposed
architecture. The performance of the prediction model is tested and validated
by the methodical implementation. The robustness of the approach is
demonstrated with case studies conducted for geographically scattered sites
across the United States. The predictions demonstrate that our proposed unified
architecture-based approach is effective for multi-time-scale solar forecasts
and achieves a lower root-mean-square prediction error when benchmarked against
the best-performing methods documented in the literature that use separate
models for each time-scale during the day. Our proposed method results in a
71.5% reduction in the mean RMSE averaged across all the test sites compared to
the ML-based best-performing method reported in the literature. Additionally,
the proposed method enables multi-time-horizon forecasts with real-time inputs,
which have a significant potential for practical industry applications in the
evolving grid.Comment: 19 pages, 12 figures, 3 tables, under review for journal submissio
- …