Abstract:  In this thesis, we try to find a probabilistic Koopman-based representation for dynamical systems. Therefore we apply the framework of [Pan et al 2019], where the author successfully found such representation as a residual improvement of the powerful Dynamic Mode Decomposition technique.… [read more]

Abstract: Accurate modeling of physical systems is of great importance to engineers. In this thesis, we construct novel machine learning models based on the Neural ODE approach in Chen et al. (2018) and compare them to existing architectures. The evaluation is performed on multiple physical systems,… [read more]

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More details here Github repository here [read more]

Abstract: Inverse problems are ubiquitous in the engineering domain and often rely on computationally expensive forward models. For applications with societal or economical impact it is of major importance to quantify the uncertainties associated with the simulation results. A Bayesian formulation… [read more]

Our group will participate in this year's SIAM Uncertainty Quantification Conference (UQ18) with four papers on: - Beyond Black-boxes in Model-based Bayesian Inverse Problems - A Bayesian Coarse-graining Approach to the Solution of Stochastic Partial Differential Equations - Incorporating… [read more]

Prof. Zabaras was hosted by our group from 2014-2017 as TUM-IAS Hans Fischer Senior Fellow. [read more]

The title of the talk was "Physics-conversant machine learning: from molecular dynamics to stochastic PDEs". More details can be found here. [read more]

More details can be found here [read more]

Abstract: Fine-scale models based on high-dimensional differential equations (DEs) are available for many systems in science and engineering. In many cases, research focuses on effects which occur on a coarser scale instead of the fine one described by the DEs. As it is usually not feasible to… [read more]