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Domain decomposition architectures and Gauss-Newton training for physics-informed neural networks
Alexander Heinlein, Taniya Kapoor
Approximating the solutions of boundary value problems governed by partial differential equations with neural networks is challenging, largely due to the difficult training process…
Resolving Extreme Data Scarcity by Explicit Physics Integration: An Application to Groundwater Heat Transport
Julia Pelzer, Corné Verburg, Alexander Heinlein +1
Real-world flow applications in complex scientific and engineering domains, such as geosciences, challenge classical simulation methods due to large spatial domains, high spatio-te…
Numerical study on hyper parameter settings for neural network approximation to partial differential equations
Hee Jun Yang, Alexander Heinlein, Hyea Hyun Kim
Approximate solutions of partial differential equations (PDEs) obtained by neural networks are highly affected by hyper parameter settings. For instance, the model training strongl…