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04/28/2023
The Kolmogorov N-width for linear transport: Exact representation and the influence of the data
The Kolmogorov N-width describes the best possible error one can achieve...
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12/29/2022
An Ultra-Weak Space-Time Variational Formulation for the Schrödinger Equation
We present a well-posed ultra-weak space-time variational formulation fo...
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12/16/2022
A certified wavelet-based physics-informed neural network for the solution of parameterized partial differential equations
Physics Informed Neural Networks (PINNs) have frequently been used for t...
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02/25/2022
An ultraweak variational method for parameterized linear differential-algebraic equations
We investigate an ultraweak variational formulation for (parameterized) ...
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07/26/2021
Very Weak Space-Time Variational Formulation for the Wave Equation: Analysis and Efficient Numerical Solution
We introduce a very weak space-time variational formulation for the wave...
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07/09/2021
Linear/Ridge expansions: Enhancing linear approximations by ridge functions
We consider approximations formed by the sum of a linear combination of ...
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10/01/2020
A Space-Time Variational Method for Optimal Control Problems
We consider a space-time variational formulation of a PDE-constrained op...
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12/20/2019