Related papers: Recovering the parameters underlying the Lorenz-96…

The contemporary scientific landscape is characterized by a "curse of dimensionality," where our capacity to collect high-dimensional network data frequently outstrips our ability to computationally simulate or intuitively comprehend the…

Reconstructing network dynamics from data is crucial for predicting the changes in the dynamics of complex systems such as neuron networks; however, previous research has shown that the reconstruction is possible under strong constraints…

The problem of reconstructing nonlinear and complex dynamical systems from measured data or time series is central to many scientific disciplines including physical, biological, computer, and social sciences, as well as engineering and…

Risk management in many environmental settings requires an understanding of the mechanisms that drive extreme events. Useful metrics for quantifying such risk are extreme quantiles of response variables conditioned on predictor variables…

Numerical weather forecasting using high-resolution physical models often requires extensive computational resources on supercomputers, which diminishes their wide usage in most real-life applications. As a remedy, applying deep learning…

Reliable probability estimation is of crucial importance in many real-world applications where there is inherent (aleatoric) uncertainty. Probability-estimation models are trained on observed outcomes (e.g. whether it has rained or not, or…

In this work, we investigate the fundamental trade-off regarding accuracy and parameter efficiency in the parameterization of neural network weights using predictor networks. We present a surprising finding that, when recovering the…

Deep learning algorithms are growing in popularity in the field of exoplanetary science due to their ability to model highly non-linear relations and solve interesting problems in a data-driven manner. Several works have attempted to…

We study prediction-assimilation systems, which have become routine in meteorology and oceanography and are rapidly spreading to other areas of the geosciences and of continuum physics. The long-term, nonlinear stability of such a system…

Due to computational constraints, running global climate models (GCMs) for many years requires a lower spatial grid resolution (${\gtrsim}50$ km) than is optimal for accurately resolving important physical processes. Such processes are…

Atmospheric processes involve both space and time. This is why human analysis of atmospheric imagery can often extract more information from animated loops of image sequences than from individual images. Automating such an analysis requires…

Deep learning algorithms have recently shown to be a successful tool in estimating parameters of statistical models for which simulation is easy, but likelihood computation is challenging. But the success of these approaches depends on…

We address the issue of how to identify the equations of a largely unknown chaotic system from knowledge about its state evolution. The technique can be applied to the estimation of parameters that drift slowly with time. To accomplish…

Predicting chaotic dynamical systems is critical in many scientific fields, such as weather forecasting, but challenging due to the characteristic sensitive dependence on initial conditions. Traditional modeling approaches require extensive…

Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…

We present a new approach for predictive modeling and its uncertainty quantification for mechanical systems, where coarse-grained models such as constitutive relations are derived directly from observation data. We explore the use of a…

Accurately quantifying air-sea fluxes is important for understanding air-sea interactions and improving coupled weather and climate systems. This study introduces a probabilistic framework to represent the highly variable nature of air-sea…

Computer models, aiming at simulating a complex real system, are often calibrated in the light of data to improve performance. Standard calibration methods assume that the optimal values of calibration parameters are invariant to the model…

Constructing efficient and accurate parameterizations of sub-grid scale processes is a central area of interest in the numerical modelling of geophysical fluids. Using a modified version of the two-level Lorenz '96 model, we present here a…

Neural networks can emulate nonlinear physical systems with high accuracy, yet they may produce physically-inconsistent results when violating fundamental constraints. Here, we introduce a systematic way of enforcing nonlinear analytic…