The paper proposes a physics-informed neural network (PINN) architecture that uses the complex exponential function as an activation, producing sine and cosine outputs. Compared to standard sine-activated multilayer perceptrons, this design yields markedly better temperature reconstructions from sparse velocity data in cubic Rayleigh-Bénard convection, while keeping per‑step computational cost similar. The authors attribute the gains to the network’s ability to propagate both sine and cosine components, allowing each neuron in the next layer to adjust the phase of the latent periodic signals.
By Michael Mommert, Marie-Christine Volk, Christian Bauer
This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations. Such systems, found in applications like turbidity currents and thermal convection, feature strong nonlinear coupling and multiscale behavior that make high-fidelity simulations computationally expensive.
The paper introduces an end‑to‑end equivariant surrogate model for three‑dimensional Rayleigh‑Bénard convection, combining an equivariant convolutional autoencoder with an equivariant convolutional LSTM that employs $G$‑steerable kernels. The architecture exploits $D_4$‑steerable kernels in vertically stacked layers and partial kernel sharing in the vertical direction to respect the system’s E(2) equivariance in the horizontal plane while handling broken translational symmetry vertically. Experiments show notable improvements in sample and parameter efficiency and better scaling to more complex dynamics.
By Fynn Fromme, Hans Harder, Christine Allen-Blanchette, Sebastian Peitz
arXiv:2606. 19562v1 Announce Type: new Abstract: This chapter reviews recent advances in Scientific Machine Learning (SciML) for modeling coupled fluid flow and transport phenomena governed by the incompressible Navier-Stokes and scalar transport equations.
By Gabriel F. Barros, R\^omulo M. Silva, Alvaro L. G. A. Coutinho
arXiv:2609.36216v1 Announce Type: new
Abstract: Neural operators are typically trained in a supervised fashion, which requires a dataset to be generated with a classical solver. Training them physics...
By Shizheng Wen, Siddhartha Mishra, Marius Zeinhofer
arXiv:2604.06433v2 Announce Type: replace-cross
Abstract: The impact of wave-induced forcing on the mean water level and nearshore currents is typically modeled through excess momentum fluxes, also k...
By Shukai Cai, Sourav Dutta, Mark Loveland, Eirik Valseth, Peter Rivera-Casillas, Corey Trahan, Clint Dawson