Abstract The sensitivity of urban canopy air temperature ( ) to anthropogenic heat flux ( ) is known to vary with space and time, but the key factors controlling such spatiotemporal variabilities remain elusive. To quantify the contributions of different physical processes to the magnitude and variability of (where represents a change), we develop a forcing-feedback framework based on the energy budget of air within the urban canopy layer and apply it to diagnosing simulated by the Community Land Model Urban over the contiguous United States (CONUS). In summer, the median is around 0.01 over the CONUS. Besides the direct effect of on , there are important feedbacks through changes in the surface temperature, the atmosphere–canopy air heat conductance ( ), and the surface–canopy air heat conductance. The positive and negative feedbacks nearly cancel each other out and is mostly controlled by the direct effect in summer. In winter, becomes stronger, with the median value increased by about 20% due to weakened negative feedback associated with . The spatial and temporal (both seasonal and diurnal) variability of as well as the nonlinear response of to are strongly related to the variability of , highlighting the importance of correctly parameterizing convective heat transfer in urban canopy models.
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Infinite neural network quantum states: entanglement and training dynamics
Abstract We study infinite limits of neural network quantum states ( -NNQS), which exhibit representation power through ensemble statistics, and also tractable gradient descent dynamics. Ensemble averages of entanglement entropies are expressed in terms of neural network correlators, and architectures that exhibit volume-law entanglement are presented. The analytic calculations of entanglement entropy bound are tractable because the ensemble statistics are simplified in the Gaussian process limit. A general framework is developed for studying the gradient descent dynamics of neural network quantum states (NNQS), using a quantum state neural tangent kernel (QS-NTK). For -NNQS the training dynamics is simplified, since the QS-NTK becomes deterministic and constant. An analytic solution is derived for quantum state supervised learning, which allows an -NNQS to recover any target wavefunction. Numerical experiments on finite and infinite NNQS in the transverse field Ising model and Fermi Hubbard model demonstrate excellent agreement with theory. -NNQS opens up new opportunities for studying entanglement and training dynamics in other physics applications, such as in finding ground states.
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- Award ID(s):
- 2019786
- PAR ID:
- 10488631
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Machine Learning: Science and Technology
- Volume:
- 4
- Issue:
- 2
- ISSN:
- 2632-2153
- Page Range / eLocation ID:
- 025038
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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