% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@INPROCEEDINGS{Westphal:616787,
      author       = {Westphal, Alexander},
      title        = {{F}rom testing cosmological inflation models to solving
                      {PDE}s - d{NN}solve: an efficient {NN}-based {PDE} solver},
      school       = {DESY Hamburg},
      reportid     = {PUBDB-2024-06541},
      year         = {2024},
      abstract     = {Neural Networks (NNs) can be used to solve Ordinary and
                      Partial Differential Equations (ODEs and PDEs) by redefining
                      the question as an optimization problem. The objective
                      function to be optimized is the sum of the squares of the
                      PDE to be solved and of the initial/boundary conditions. A
                      feed forward NN is trained to minimise this loss function
                      evaluated on a set of collocation points sampled from the
                      domain where the problem is defined. A compact and smooth
                      solution, that only depends on the weights of the trained
                      NN, is then obtained. This approach is often referred to as
                      PINN, from Physics Informed Neural Network. Despite the
                      success of the PINN approach in solving various classes of
                      PDEs, an implementation of this idea that is capable of
                      solving a large class of ODEs and PDEs with good accuracy
                      and without the need to finely tune the hyperparameters of
                      the network, is not available yet. In this paper, we
                      introduce a new implementation of this concept - called
                      dNNsolve - that makes use of dual Neural Networks with
                      different activation functions to solve ODEs/PDEs. We show
                      that dNNsolve is capable of solving a broad range of
                      ODEs/PDEs in 1, 2 and 3 spacetime dimensions, without the
                      need of hyperparameter fine-tuning.},
      month         = {Jul},
      date          = {2024-07-01},
      organization  = {FH SciComp Workshop, Hamburg
                       (Germany), 1 Jul 2024 - 2 Jul 2024},
      subtyp        = {Invited},
      cin          = {T},
      cid          = {I:(DE-H253)T-20120731},
      pnm          = {611 - Fundamental Particles and Forces (POF4-611) / DFG
                      project G:(GEPRIS)390833306 - EXC 2121: Quantum Universe
                      (390833306)},
      pid          = {G:(DE-HGF)POF4-611 / G:(GEPRIS)390833306},
      experiment   = {EXP:(DE-MLZ)NOSPEC-20140101},
      typ          = {PUB:(DE-HGF)6},
      url          = {https://bib-pubdb1.desy.de/record/616787},
}