10,005 research outputs found
Mind The Gap
We discuss an optimisation criterion for the exact renormalisation group
based on the inverse effective propagator, which displays a gap. We show that a
simple extremisation of the gap stabilises the flow, leading to better
convergence of approximate solutions towards the physical theory. This improves
the reliability of truncations, most relevant for any high precision
computation. These ideas are closely linked to the removal of a spurious scheme
dependence and a minimum sensitivity condition. The issue of predictive power
and a link to the Polchinski RG are discussed as well. We illustrate our
findings by computing critical exponents for the Ising universality class.Comment: 6 pages, Talk presented at 2nd Conference on Exact Renormalization
Group (ERG2000), Rome, Italy, 18-22 Sep 200
Effect of Multiphase Radiation on Coal Combustion in a Pulverized Coal jet Flame
The accurate modeling of coal combustion requires detailed radiative heat transfer models for both gaseous combustion products and solid coal particles. A multiphase Monte Carlo ray tracing (MCRT) radiation solver is developed in this work to simulate a laboratory-scale pulverized coal flame. The MCRT solver considers radiative interactions between coal particles and three major combustion products (CO2, H2O, and CO). A line-by-line spectral database for the gas phase and a size-dependent nongray correlation for the solid phase are employed to account for the nongray effects. The flame structure is significantly altered by considering nongray radiation and the lift-off height of the flame increases by approximately 35%, compared to the simulation without radiation. Radiation is also found to affect the evolution of coal particles considerably as it takes over as the dominant mode of heat transfer for medium-to-large coal particles downstream of the flame. To investigate the respective effects of spectral models for the gas and solid phases, a Planck-mean-based gray gas model and a size-independent gray particle model are applied in a frozen-field analysis of a steady-state snapshot of the flame. The gray gas approximation considerably underestimates the radiative source terms for both the gas phase and the solid phase. The gray coal approximation also leads to under-prediction of the particle emission and absorption. However, the level of under-prediction is not as significant as that resulting from the employment of the gray gas model. Finally, the effect of the spectral property of ash on radiation is also investigated and found to be insignificant for the present target flame
A Fast Integrated Planning and Control Framework for Autonomous Driving via Imitation Learning
For safe and efficient planning and control in autonomous driving, we need a
driving policy which can achieve desirable driving quality in long-term horizon
with guaranteed safety and feasibility. Optimization-based approaches, such as
Model Predictive Control (MPC), can provide such optimal policies, but their
computational complexity is generally unacceptable for real-time
implementation. To address this problem, we propose a fast integrated planning
and control framework that combines learning- and optimization-based approaches
in a two-layer hierarchical structure. The first layer, defined as the "policy
layer", is established by a neural network which learns the long-term optimal
driving policy generated by MPC. The second layer, called the "execution
layer", is a short-term optimization-based controller that tracks the reference
trajecotries given by the "policy layer" with guaranteed short-term safety and
feasibility. Moreover, with efficient and highly-representative features, a
small-size neural network is sufficient in the "policy layer" to handle many
complicated driving scenarios. This renders online imitation learning with
Dataset Aggregation (DAgger) so that the performance of the "policy layer" can
be improved rapidly and continuously online. Several exampled driving scenarios
are demonstrated to verify the effectiveness and efficiency of the proposed
framework
Data-Efficient Reinforcement Learning with Probabilistic Model Predictive Control
Trial-and-error based reinforcement learning (RL) has seen rapid advancements
in recent times, especially with the advent of deep neural networks. However,
the majority of autonomous RL algorithms require a large number of interactions
with the environment. A large number of interactions may be impractical in many
real-world applications, such as robotics, and many practical systems have to
obey limitations in the form of state space or control constraints. To reduce
the number of system interactions while simultaneously handling constraints, we
propose a model-based RL framework based on probabilistic Model Predictive
Control (MPC). In particular, we propose to learn a probabilistic transition
model using Gaussian Processes (GPs) to incorporate model uncertainty into
long-term predictions, thereby, reducing the impact of model errors. We then
use MPC to find a control sequence that minimises the expected long-term cost.
We provide theoretical guarantees for first-order optimality in the GP-based
transition models with deterministic approximate inference for long-term
planning. We demonstrate that our approach does not only achieve
state-of-the-art data efficiency, but also is a principled way for RL in
constrained environments.Comment: Accepted at AISTATS 2018
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