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Errors in the representation of clouds in convection-permitting numerical weather prediction models can be introduced by different sources. These can be the forcing and boundary conditions, the representation of orography, the accuracy of…

Variational data assimilation optimizes for an initial state of a dynamical system such that its evolution fits observational data. The physical model can subsequently be evolved into the future to make predictions. This principle is a…

Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…

Physics-based and first-principles models pervade the engineering and physical sciences, allowing for the ability to model the dynamics of complex systems with a prescribed accuracy. The approximations used in deriving governing equations…

Methods to deal with systematic model errors are an increasingly important component of modern data assimilation systems and their effectiveness has increased in recent years thanks to advances in methodology and the quality and density of…

Fitting a simplifying model with several parameters to real data of complex objects is a highly nontrivial task, but enables the possibility to get insights into the objects physics. Here, we present a method to infer the parameters of the…

Data Assimilation is the process in which we improve the representation of the state of a physical system by combining information coming from a numerical model, real-world observations, and some prior modelling. It is widely used to model…

Model approximations are common practice when estimating structural or quasi-structural models. The paper considers the econometric properties of estimators that utilize projections to reimpose information about the exact model in the form…

Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…

While the formulation of most data assimilation schemes assumes an unbiased observation model error, in real applications, model error with nontrivial biases is unavoidable. A practical example is the error in the radiative transfer model…

Compounding error, where small prediction mistakes accumulate over time, presents a major challenge in learning-based control. For example, this issue often limits the performance of model-based reinforcement learning and imitation…

We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the…

We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is in the form of noisy partial measurements of the past and present state of the dynamical system. Recently there have been several…

Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach…

Dynamical weather and climate prediction models underpin many studies of the Earth system and hold the promise of being able to make robust projections of future climate change based on physical laws. However, simulations from these models…

Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and non-measurable parameters, which have to be…

Data assimilation combines forecasts from a numerical model with observations. Most of the current data assimilation algorithms consider the model and observation error terms as additive Gaussian noise, specified by their covariance…

Every day, weather forecasting centres around the world make use of noisy, incomplete observations of the atmosphere to update their weather forecasts. This process is known as data assimilation, data fusion or state estimation and is best…

Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the…

In meteorology, engineering and computer sciences, data assimilation is routinely employed as the optimal way to combine noisy observations with prior model information for obtaining better estimates of a state, and thus better forecasts,…