58 research outputs found
Rainfall–runoff modelling using Long Short-Term Memory (LSTM) networks
Rainfall–runoff modelling is one of the key
challenges in the field of hydrology. Various approaches exist, ranging from
physically based over conceptual to fully data-driven models. In this paper,
we propose a novel data-driven approach, using the Long Short-Term Memory
(LSTM) network, a special type of recurrent neural network. The advantage of
the LSTM is its ability to learn long-term dependencies between the provided
input and output of the network, which are essential for modelling storage
effects in e.g. catchments with snow influence. We use 241Â catchments of the
freely available CAMELS data set to test our approach and also compare the
results to the well-known Sacramento Soil Moisture Accounting Model (SAC-SMA)
coupled with the Snow-17 snow routine. We also show the potential of the LSTM
as a regional hydrological model in which one model predicts the discharge
for a variety of catchments. In our last experiment, we show the possibility
to transfer process understanding, learned at regional scale, to individual
catchments and thereby increasing model performance when compared to a LSTM
trained only on the data of single catchments. Using this approach, we were
able to achieve better model performance as the SAC-SMA + Snow-17, which
underlines the potential of the LSTM for hydrological modelling applications.</p
Supersymmetric sound in fluids
We consider the hydrodynamics of supersymmetric fluids. Supersymmetry is
broken spontaneously and the low energy spectrum includes a fermionic massless
mode, the . We use two complementary approaches to describe
the system: First, we construct a generating functional from which we derive
the equations of motion of the fluid and of the phonino propagating through the
fluid. We write the form of the leading corrections in the derivative
expansion, and show that the so called diffusion terms in the supercurrent are
in fact not dissipative. Second, we use an effective field theory approach
which utilizes a non-linear realization of supersymmetry to analyze the
interactions between phoninos and phonons, and demonstrate the conservation of
entropy in ideal fluids. We comment on possible phenomenological consequences
for gravitino physics in the early universe.Comment: Modified introduction and discussion of diffusion terms in the
supercurren
Supersymmetric Field-Theoretic Models on a Supermanifold
We propose the extension of some structural aspects that have successfully
been applied in the development of the theory of quantum fields propagating on
a general spacetime manifold so as to include superfield models on a
supermanifold. We only deal with the limited class of supermanifolds which
admit the existence of a smooth body manifold structure. Our considerations are
based on the Catenacci-Reina-Teofillatto-Bryant approach to supermanifolds. In
particular, we show that the class of supermanifolds constructed by
Bonora-Pasti-Tonin satisfies the criterions which guarantee that a
supermanifold admits a Hausdorff body manifold. This construction is the
closest to the physicist's intuitive view of superspace as a manifold with some
anticommuting coordinates, where the odd sector is topologically trivial. The
paper also contains a new construction of superdistributions and useful results
on the wavefront set of such objects. Moreover, a generalization of the
spectral condition is formulated using the notion of the wavefront set of
superdistributions, which is equivalent to the requirement that all of the
component fields satisfy, on the body manifold, a microlocal spectral condition
proposed by Brunetti-Fredenhagen-K\"ohler.Comment: Final version to appear in J.Math.Phy
Quantization of Dirac fields in static spacetime
On a static spacetime, the solutions of the Dirac equation are generated by a
time-independent Hamiltonian. We study this Hamiltonian and characterize the
split into positive and negative energy. We use it to find explicit expressions
for advanced and retarded fundamental solutions and for the propagator.
Finally, we use a fermion Fock space based on the positive/negative energy
split to define a Dirac quantum field operator whose commutator is the
propagator.Comment: LaTex2e, 17 page
Microlocal analysis of quantum fields on curved spacetimes: Analytic wavefront sets and Reeh-Schlieder theorems
We show in this article that the Reeh-Schlieder property holds for states of
quantum fields on real analytic spacetimes if they satisfy an analytic
microlocal spectrum condition. This result holds in the setting of general
quantum field theory, i.e. without assuming the quantum field to obey a
specific equation of motion. Moreover, quasifree states of the Klein-Gordon
field are further investigated in this work and the (analytic) microlocal
spectrum condition is shown to be equivalent to simpler conditions. We also
prove that any quasifree ground- or KMS-state of the Klein-Gordon field on a
stationary real analytic spacetime fulfills the analytic microlocal spectrum
condition.Comment: 31 pages, latex2
NeuralHydrology -- Interpreting LSTMs in Hydrology
Despite the huge success of Long Short-Term Memory networks, their
applications in environmental sciences are scarce. We argue that one reason is
the difficulty to interpret the internals of trained networks. In this study,
we look at the application of LSTMs for rainfall-runoff forecasting, one of the
central tasks in the field of hydrology, in which the river discharge has to be
predicted from meteorological observations. LSTMs are particularly well-suited
for this problem since memory cells can represent dynamic reservoirs and
storages, which are essential components in state-space modelling approaches of
the hydrological system. On basis of two different catchments, one with snow
influence and one without, we demonstrate how the trained model can be analyzed
and interpreted. In the process, we show that the network internally learns to
represent patterns that are consistent with our qualitative understanding of
the hydrological system.Comment: Pre-print of published book chapter. See journal reference and DOI
for more inf
Quantum field theory in static external potentials and Hadamard states
We prove that the ground state for the Dirac equation on Minkowski space in
static, smooth external potentials satisfies the Hadamard condition. We show
that it follows from a condition on the support of the Fourier transform of the
corresponding positive frequency solution. Using a Krein space formalism, we
establish an analogous result in the Klein-Gordon case for a wide class of
smooth potentials. Finally, we investigate overcritical potentials, i.e. which
admit no ground states. It turns out, that numerous Hadamard states can be
constructed by mimicking the construction of ground states, but this leads to a
naturally distinguished one only under more restrictive assumptions on the
potentials.Comment: 30 pages; v2 revised, accepted for publication in Annales Henri
Poincar
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