6 papers
Symbolic recovery of PDEs from measurement data
Erion Morina, Philipp Scholl, Martin Holler
Models based on partial differential equations (PDEs) are powerful for describing a wide range of complex phenomena in the natural sciences. Accurately identifying the PDE model, w…
On uniqueness in structured model learning
Martin Holler, Erion Morina
This paper addresses the problem of uniqueness in learning physical laws for systems of partial differential equations (PDEs). Contrary to most existing approaches, it considers a…
Physically consistent model learning for reaction-diffusion systems
Erion Morina, Martin Holler
This paper addresses the problem of learning reaction-diffusion (RD) systems from data while ensuring physical consistency and well-posedness of the learned models. Building on a r…
-approximation with rational functions and rational neural networks
Erion Morina, Martin Holler
We show that suitably regular functions can be approximated in the -norm both with rational functions and rational neural networks, including approximation rates wit…
Exact Parameter Identification in PET Pharmacokinetic Modeling: Extension to the Reversible Two Tissue Compartment Model
Martin Holler, Erion Morina, Georg Schramm
This paper addresses the problem of recovering tracer kinetic parameters from multi-region measurement data in quantitative PET imaging using the reversible two tissue compartment…
On the growth of the parameters of approximating ReLU neural networks
Erion Morina, Martin Holler
This work focuses on the analysis of fully connected feed forward ReLU neural networks as they approximate a given, smooth function. In contrast to conventionally studied universal…