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 241 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&thinsp;+&thinsp;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 $\mathit{phonino}$. 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

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

Spectral function of the supersymmetry current

We continue our study of the retarded Green's function of the universal fermionic supersymmetry current ("supercurrent") for the most general class of d=3 N=2 SCFTs with D=10 or D=11 supergravity duals by studying the propagation of the Dirac gravitino in the electrically charged AdS-Reissner-Nordstr\"om black-brane background of N=2 minimal gauged supergravity in D=4. We expand upon results presented in a companion paper, including the absence of a Fermi surface and the appearance of a soft power-law gap at zero temperature. We also present the analytic solution of the gravitino equation in the AdS_2 X R^2 background which arises as the near-horizon limit at zero temperature. In addition we determine the quasinormal mode spectrum.Comment: 65 pages, 6 Figs; version published in journa