Replacing Automatic Differentiation by Sobolev Cubatures fastens Physics Informed Neural Nets and strengthens their Approximation Power. - Juan Esteban Suarez Cardona; Michael Hecht (CoRR, 2022)

Learning Partial Differential Equations by Spectral Approximates of General Sobolev Spaces. - Juan Esteban Suarez Cardona; Phil-Alexander Hofmann; Michael Hecht (CoRR, 2023)

Polynomial differentiation decreases the training time complexity of physics-informed neural networks and strengthens their approximation power. - Juan Esteban Suarez Cardona; Michael Hecht (Mach. Learn. Sci. Technol., 2023)

Hybrid Surrogate Models: Circumventing Gibbs Phenomenon for Partial Differential Equations with Finite Shock-Type Discontinuities. - Juan Esteban Suarez Cardona; Shashank Reddy; Michael Hecht (CoRR, 2024)

Negative order sobolev cubatures: preconditioners of partial differential equation learning tasks circumventing numerical stiffness. - Juan Esteban Suarez Cardona; Phil-Alexander Hofmann; Michael Hecht (Mach. Learn. Sci. Technol., 2024)

Ensuring Topological Data-Structure Preservation under Autoencoder Compression Due to Latent Space Regularization in Gauss-Legendre Nodes. - Chethan Krishnamurthy Ramanaik; Anna Willmann; Juan Esteban Suarez Cardona; Pia Hanfeld; Nico Hoffmann; Michael Hecht (Axioms, 2024)