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Acceleration and Enhancement of High-fidelity PDE Solvers through Machine Learning

David Del Rey Fernandez, NASA-Langley

Romit Maulik, Argonne National Laboratory

Machine learning (ML) methods and in particular deep learning via  artificial neural networks have generated significant interest in the scientific community over the last few years.  Increasingly, ML techniques are being applied across abroad spectrum of scientific and engineering fields.  In the context of numerically solving partial differential equations (PDEs), there is growing interest in applying ML techniques across the solver software stack.  One area where ML may be transformational is related to the efficient utilization of production-level solvers.  The latter depends on the careful choice of numerous parameters, for example  for  time  marching,  added  dissipation,  physical  models  (e.g.,  turbulence models), and in the associated solvers for linear and nonlinear systems of equations.  The efficient deployment of such software then depends in part on accumulated engineering expertise to select appropriate parameter values.  Automating the selection of these tunable parameters is potentially well suited for ML algorithms.  Similarly, ML can be used to accelerate numerous aspects of the solution process, for example in predicting a refined mesh in an h/p-refinement process, or a suitable numerical initial condition that can enhance the solver process.  Moreover, ML can also provide surrogates for computationally intensive tasks such as error estimation and uncertainty quantification.Therefore, the purpose of this mini-symposium is to bring together a broad spectrum of researchers interested in the application of ML techniques to accelerating high-fidelity PDE solvers as well as enhancing the resulting outputs.Possible  topics  of  interest  include  (but  are  not  limited  to)  ML  for  to:  mesh adaptation,  error  estimation,  nonlinear  solvers,  system  optimization,  inverse problems, and surrogate modelling.