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Large-scale simulation of shallow water waves with computation only on small staggered patches
J. E. Bunder, J. Divahar, Ioannis G. Kevrekidis +2
The multiscale patch scheme is built from given small micro-scale simulations of complicated physical processes to empower large macro-scale simulations. By coupling small patches…
Partial observations and conservation laws: Grey-box modeling in biotechnology and optogenetics
Robert J. Lovelett, Jose L Avalos, Ioannis G. Kevrekidis
Developing accurate dynamical system models from physical insight or data can be impeded when only partial observations of the system state are available. Here, we combine conserva…
Coarse-scale PDEs from fine-scale observations via machine learning
Seungjoon Lee, Mahdi Kooshkbaghi, Konstantinos Spiliotis +2
Complex spatiotemporal dynamics of physicochemical processes are often modeled at a microscopic level (through e.g. atomistic, agent-based or lattice models) based on first princip…
A geometric approach to the transport of discontinuous densities
Caroline Moosmüller, Felix Dietrich, Ioannis G. Kevrekidis
Different observations of a relation between inputs ("sources") and outputs ("targets") are often reported in terms of histograms (discretizations of the source and the target dens…
On Learning Hamiltonian Systems from Data
Tom Bertalan, Felix Dietrich, Igor Mezić +1
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on re…
On the Koopman operator of algorithms
Felix Dietrich, Thomas N. Thiem, Ioannis G. Kevrekidis
A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, acce…