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Complex systems' modeling and simulation are powerful ways to investigate a multitude of natural phenomena providing extended knowledge on their structure and behavior. However, enhanced modeling and simulation require integration of…
Data assimilation is uniquely challenging in weather forecasting due to the high dimensionality of the employed models and the nonlinearity of the governing equations. Although current operational schemes are used successfully, our…
Modeling environmental ecosystems is essential for effective resource management, sustainable development, and understanding complex ecological processes. However, traditional methods frequently struggle with the inherent complexity,…
We present a data-driven modeling strategy to overcome improperly modeled dynamics for systems exhibiting complex spatio-temporal behaviors. We propose a Deep Learning framework to resolve the differences between the true dynamics of the…
Model uncertainty quantification is an essential component of effective data assimilation. Model errors associated with sub-grid scale processes are often represented through stochastic parameterizations of the unresolved process. Many…
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…
We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale…
Seismic data processing involves techniques to deal with undesired effects that occur during acquisition and pre-processing. These effects mainly comprise coherent artefacts such as multiples, non-coherent signals such as electrical noise,…
In meteorological and oceanological studies the classical approach for finding the numerical solution of the regional model consists in formulating and solving the Cauchy-Dirichlet problem. The related boundary conditions are obtained by…
Mathematical models are crucial for optimizing and controlling chemical processes, yet they often face significant limitations in terms of computational time, algorithm complexity, and development costs. Hybrid models, which combine…
With the advent of modern data collection and storage technologies, data-driven approaches have been developed for discovering the governing partial differential equations (PDE) of physical problems. However, in the extant works the model…
In modern data science, it is often not enough to obtain only a data-driven model with a good prediction quality. On the contrary, it is more interesting to understand the properties of the model, which parts could be replaced to obtain…
Data assimilation is widely used in many disciplines such as meteorology, oceanography, and robotics to estimate the state of a dynamical system from noisy observations. In this work, we propose a lightweight and general method to perform…
Removing geometrical details from a complex domain is a classical operation in computer aided design. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. However, depending on the…
Development of air pollution models for large regions is a priority for population-based epidemiologic studies. The rapid development of big data information systems and machine learning algorithms have opened new grounds for refinements of…
The generation of initial conditions via accurate data assimilation is crucial for weather forecasting and climate modeling. We propose DiffDA as a denoising diffusion model capable of assimilating atmospheric variables using predicted…
We address data assimilation for linear and nonlinear dynamical systems via the so-called \emph{model reference adaptive system}. Continuing our theoretical developments in \cite{Tram_Kaltenbacher_2021}, we deliver the first practical…
Accurate predictions and representations of plant growth patterns in simulated and controlled environments are important for addressing various challenges in plant phenomics research. This review explores various works on state-of-the-art…
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…