Computing large deviation prefactors of stochastic dynamical systems based on machine learning

We present a large deviation theory that characterizes the exponential estimate for rare events in stochastic dynamical systems in the limit of weak noise.We aim to consider a next-to-leading-order approximation for more accurate calculation of the mean exit time by computing large deviation prefactors with the aid of machine learning.More specifically,we design a neural network framework to compute quasipotential,most probable paths and prefactors based on the orthogonal decomposition of a vector field.We corroborate the higher effectiveness and accuracy of our algorithm with two toy models.Numerical experiments demonstrate its powerful functionality in exploring the internal mechanism of rare events triggered by weak random fluctuations.

The Approximate Solutions of FPK Equations in High Dimensions for Some Nonlinear Stochastic Dynamic Systems

The probabilistic solutions of the nonlinear stochastic dynamic(NSD)systems with polynomial type of nonlinearity are investigated with the subspace-EPC method.The space of the state variables of large-scale nonlinear stochastic dynamic system excited by white noises is separated into two subspaces.Both sides of the Fokker-Planck-Kolmogorov(FPK)equation corresponding to the NSD system is then integrated over one of the subspaces.The FPK equation for the joint probability density function of the state variables in another subspace is formulated.Therefore,the FPK equation in low dimensions is obtained from the original FPK equation in high dimensions and it makes the problem of obtaining the probabilistic solutions of largescale NSD systems solvable with the exponential polynomial closure method.Examples about the NSD systems with polynomial type of nonlinearity are given to show the effectiveness of the subspace-EPC method in these cases.

Monthly and seasonal streamflow forecasting of large dryland catchments in Brazil

Streamflow forecasting in drylands is challenging.Data are scarce,catchments are highly humanmodified and streamflow exhibits strong nonlinear responses to rainfall.The goal of this study was to evaluate the monthly and seasonal streamflow forecasting in two large catchments in the Jaguaribe River Basin in the Brazilian semi-arid area.We adopted four different lead times:one month ahead for monthly scale and two,three and four months ahead for seasonal scale.The gaps of the historic streamflow series were filled up by using rainfall-runoff modelling.Then,time series model techniques were applied,i.e.,the locally constant,the locally averaged,the k-nearest-neighbours algorithm(k-NN)and the autoregressive(AR)model.The criterion of reliability of the validation results is that the forecast is more skillful than streamflow climatology.Our approach outperformed the streamflow climatology for all monthly streamflows.On average,the former was 25%better than the latter.The seasonal streamflow forecasting(SSF)was also reliable(on average,20%better than the climatology),failing slightly only for the high flow season of one catchment(6%worse than the climatology).Considering an uncertainty envelope(probabilistic forecasting),which was considerably narrower than the data standard deviation,the streamflow forecasting performance increased by about 50%at both scales.The forecast errors were mainly driven by the streamflow intra-seasonality at monthly scale,while they were by the forecast lead time at seasonal scale.The best-fit and worst-fit time series model were the k-NN approach and the AR model,respectively.The rainfall-runoff modelling outputs played an important role in improving streamflow forecasting for one streamgauge that showed 35%of data gaps.The developed data-driven approach is mathematical and computationally very simple,demands few resources to accomplish its operational implementation and is applicable to other dryland watersheds.Our findings may be part of drought forecasting systems and potentially help allocating water months in advance.Moreover,the developed strategy can serve as a baseline for more complex streamflow forecast systems.