The evolution of many dynamical systems is governed by nonlinear partial differential equations (PDEs), whose solution, in a simulation framework, requires vast amounts of computational resources.

We present a novel method that combines a hyper-network solver with a Fourier Neural Operator architecture. Our method treats time and space separately and as a result, it successfully propagates initial conditions in continuous time steps by employing the general composition properties of the partial differential operators. Supervision is provided at a specific time point. We test our method on various time evolution PDEs, including nonlinear fluid flows in one, two, or three spatial dimensions.

The results show that the new method improves the learning accuracy at the time of the supervision point, and can interpolate the solutions to any intermediate time.

In the figure we see the velocity vector fields, and the corresponding vorticity of the two-dimensional Burgers equation. Shock waves are being formed in the final state and marked by the zoom- ins.

AI has the potential to revolutionize scientific research. Indeed, collaborations between data-scientists and researchers across the TAU campus have already resulted in unique AI-driven discoveries.

The aim of this project was to devise a comprehensive methodology for using deep-learning within all aspects of scientific and engineering research (e.g., simulations, inverse models, and interpretability).

The resulting methods will be applied to research at TAU.

Our research focuses on using deep neural networks to detect exoplanets. Exoplanets are planets that our solar planets and there is a great interest to find such planets, especially ones that will be similar to our planet.

The problem is that current tools allow finding only very large planets.

In our research, we develop deep learning techniques for the purpose of being able to detect smaller planets.