Water and sediment temperature dynamics in shallow tidal environments: The role of the heat flux at the sediment-water interface

Pivato, Mattia; Carniello, Luca; Gardner, J.; Silvestri, S.; Marani, Marco

doi:10.1016/j.advwatres.2018.01.009

Cited by 27 publications

(34 citation statements)

References 37 publications

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“…[34,35] first derive analytical expression of the energy gradient as infinite tensor networks, and then contract these networks approximately to obtain approximated gradient. Thus, the two approaches perform differentiate the approximation and approximate the derivative respectively [44]. Other than the general recommendation of Ref.…”

Section: Discussionmentioning

confidence: 99%

“…The performance of automatic differentiation has a general theoretical guarantee, which does not exceed the algorithmic complexity of the original program [41,42]. Automatic differentiation is the computational engine of modern deep learning applications [43,44]. Moreover, automatic differentiation also finds applications in quantum optimal control [45] and quantum chemistry calculations such as computing forces [46] and optimizing basis parameters [47].…”

Section: A Automatic Differentiationmentioning

confidence: 99%

“…These frameworks allow one to differentiate through function calls, control flows, loops and many other computation instructions. Building on these infrastructures, differentiable programming is emerging as a new programming paradigm that emphasizes assembling differentiable components and learning the whole program via end-toend optimization [44]. Letting machines deal with automatic differentiation mechanically has greatly reduced laborious human efforts and reallocated human attention to design more sophisticated and creative deep learning algorithms.…”

Section: A Automatic Differentiationmentioning

confidence: 99%

“…One can compute the objective function and the gradient in a single forward pass without storing any intermediate results. However, the forward mode automatic differentiation is not favorable for computation graphs whose input dimension is much larger than the output dimension [44]. Therefore, the majority of deep learning work employs the reverse mode automatic differentiation.…”

Section: A Automatic Differentiationmentioning

confidence: 99%

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Differentiable Programming Tensor Networks

et al. 2019

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Differentiable programming is a fresh programming paradigm which composes parameterized algorithmic components and trains them using automatic differentiation. The concept emerges from deep learning but is not only limited to training neural networks. We present theory and practice of programming tensor network algorithms in a fully differentiable way. By formulating the tensor network algorithm as a computation graph, one can compute higher order derivatives of the program accurately and efficiently using automatic differentiation. We present essential techniques to differentiate through the tensor networks contraction algorithms, including numerical stable differentiation for tensor decompositions and efficient backpropagation through fixed point iterations. As a demonstration, we compute the specific heat of the Ising model directly by taking the second order derivative of the free energy obtained in the tensor renormalization group calculation. Next, we perform gradient based variational optimization of infinite projected entangled pair states for quantum antiferromagnetic Heisenberg model and obtain start-of-the-art variational energy and magnetization with moderate efforts. Differentiable programming removes laborious human efforts in deriving and implementing analytical gradients for tensor network programs, which opens the door to more innovations in tensor network algorithms and applications. * wanglei@iphy.ac.cn † txiang@iphy.ac.cn This fact has limited broad adoption of the gradient based optimization of tensor network states to more complex systems. Alternative approaches, such as computing the gradient using numerical derivative has limited accuracy and efficiency, therefore only applies to cases with few variational parameters [36,37]. While deriving the gradient manually using the chain rule is only manageable for purposely designed simple tensor network structures [38].Differentiable programming provides an elegant and efficient solution to these problems by composing the whole tensor network program in a fully differentiable manner. In this paper, we present essential automatic differentiation techniques which compute (higher order) derivatives of tensor network programs efficiently to numeric precision. This progress opens the door to gradient-based (and even Hessian-based) optimization of tensor network states in a general setting. Moreover, computing (higher order) gradients of the output of a tensor network algorithm offer a straightforward approach to compute physical quantities such as the specific heat and magnetic susceptibilities. The differentiable programming approach is agnostic to the detailed lattice geometry, Hamiltonian, and tensor network contraction schemes. Therefore, the approach is general enough to support a wide class of tensor network applications.We will focus on applications which involve two dimensional infinite tensor networks where the differentiable programming techniques offer significant benefits compared to the conventional approaches. We show that after solving m...

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Section: Discussionmentioning

confidence: 99%

Section: A Automatic Differentiationmentioning

confidence: 99%

Section: A Automatic Differentiationmentioning

confidence: 99%

Section: A Automatic Differentiationmentioning

confidence: 99%

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Differentiable Programming Tensor Networks

et al. 2019

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“…(3) we have exploited the reversibility of the coordinate transformation. Interestingly, the momentum transformation has the form of a vector-Jacobian product, which is commonly implemented for the reverse mode automatic differentiation [45]. This is intuitively understandable since the momentum is covariant under the coordinate transformation.…”

Section: Neural Point Transformationsmentioning

confidence: 99%

Neural Canonical Transformation with Symplectic Flows

Dong

Zhang

et al. 2020

Phys. Rev. X

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Canonical transformation plays a fundamental role in simplifying and solving classical Hamiltonian systems. We construct flexible and powerful canonical transformations as generative models using symplectic neural networks. The model transforms physical variables towards a latent representation with an independent harmonic oscillator Hamiltonian. Correspondingly, the phase space density of the physical system flows towards a factorized Gaussian distribution in the latent space. Since the canonical transformation preserves the Hamiltonian evolution, the model captures nonlinear collective modes in the learned latent representation. We present an efficient implementation of symplectic neural coordinate transformations and two ways to train the model. The variational free energy calculation is based on the analytical form of physical Hamiltonian. While the phase space density estimation only requires samples in the coordinate space for separable Hamiltonians. We demonstrate appealing features of neural canonical transformation using toy problems including two-dimensional ring potential and harmonic chain. Finally, we apply the approach to real-world problems such as identifying slow collective modes in alanine dipeptide and conceptual compression of the MNIST dataset. arXiv:1910.00024v2 [cond-mat.stat-mech]

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On the feedback between water turbidity and microphytobenthos growth in shallow tidal environments

Pivato

Carniello

Moro

et al. 2019

Earth Surf Processes Landf

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Shallow tidal environments (e.g. bays, estuaries, lagoons) represent one of the most productive ecosystems in the world, and they are threatened by current climate change and increasing human pressure. Monitoring the bio‐morphodynamic evolution of these environments is therefore a crucial task that requires a detailed and holistic scrutiny. The present study aims to investigate the temperature of the water–sediment continuum, its effect on the related microphytobenthos (MPB) growth and the related bio‐stabilization of the bed sediment surface under different water depth and water turbidity conditions. We investigated the vertical energy transfer and the temperature dynamics by applying a 1‐D model to a shallow coastal lagoon. Our results show that the water temperature does not substantially change under different turbidity conditions, whereas the sediment temperature exhibits important changes. Two major factors driving the MPB photosynthetic growth are the sediment surface temperature and the light availability at the sediment bed, which can both be computed using the vertical energy transfer model. We observed that, in general, clear water conditions better promote MPB growth over the entire year. The limiting factor for the photosynthetic process is usually the light availability at the bottom, which increases under clear water conditions. As MPB provides a bio‐stabilizing effect on the bed sediments by producing a biofilm on the sediment surface that reduces sediment resuspension, our results suggest a positive feedback between MPB growth and water column turbidity. Furthermore, MPB growth and the related sediment bio‐stabilization are clearly affected by the seasonal variation of surface sediment temperature and light availability. This seasonal variation of MPB growth rate and surface sediment bio‐stabilization must be considered when studying the long‐term morphodynamic evolution of tidal environments. © 2018 John Wiley & Sons Ltd.

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Water and sediment temperature dynamics in shallow tidal environments: The role of the heat flux at the sediment-water interface

Cited by 27 publications

References 37 publications

Differentiable Programming Tensor Networks

Differentiable Programming Tensor Networks

Neural Canonical Transformation with Symplectic Flows

On the feedback between water turbidity and microphytobenthos growth in shallow tidal environments

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