Advances in Information Theory, Data Assimilation and Stochastics for Dynamical Systems

Dear Colleagues,

Accurate and robust dynamical predictions of nonlinear, multi-scale and/or high-dimensional dynamical systems are invariably crucial in many theoretical and operational settings. Despite the widespread use and many successes of physics-informed neural networks, the fundamental problem of sensitivity to the initial condition in the dynamical prediction of complex dynamics cannot be overcome using any dynamical model alone. The need for data assimilation in dynamic predictions has been recognised long ago. However, it has proven difficult to derive DA techniques for nonlinear dynamics that would be capable of providing reliable estimates of the state and error statistics/uncertainty quantification beyond idealised bounds regarding the asymptotic accuracy of point estimates. For example, currently available methods that can operate in high dimension (e.g. the Ensemble Kalman filter or 3DVar/4DVar) are based on ad-hoc approximations and provide only point estimates for the state and no meaningful error statistics. State estimation based on the dynamical model and partial noisy stream of observations is always associated with loss of information about the true state. Importantly, stochastic filtering/data assimilation can be viewed as a problem that is ‘dual’ to the coding problem in information theory, where one can modify the properties of a DA algorithm (noisy channel) given the input signal, as opposed to devising an encoder of the signal for a given noisy channel.  It turns out that this duality provides fascinating systematic links between stochastic filtering/data assimilation and information theory/information geometry, where rate-distortion theory and reduced-order stochastic modelling contribute to the improved theoretical understanding and development of novel DA techniques.   

This Special Issue on "Advances in Information Theory, Data Assimilation and Stochastics for Dynamical Systems" will serve as a locus for gathering recent theoretical developments and applications on the interface between these three topical themes. We invite both theory- and application-focused research articles, as well as a small number of review style works, to make this Special Issue a relatively self-contained and timely contribution to this rapidly evolving subject.  

Dr. Michal Branicki
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• stochastic filtering
• stochastic control
• data assimilation
• information theory and information geometry
• reduced-order modelling
• stochastic parameterisations
• rate-distortion theory