[D] AI4PDEs, SciML, Foundational Models: Where are we going?

I’m no ML expert, but a master’s student working on computational mechanics, PDEs and some deep learning for these topics.

I have been following some groups, papers and trends and it is still unclear what is the exact direction in which AI4PDEs and scientific ML is going into.

Recent works show reinforcement learning for fluid dynamics, neural operators applied to irregular domains via transformers, GNNs or PointNet, nice works on diffusion or flow matching for inverse problems with physical constraints, and of course protein ans drug discovery tasks.

Robotics folks also are using physics environments for policy learning, which based on my limited knowledge, also include some aspects of scientific machine learning. Of course due to ODEs/PDEs, the field also naturally extends to control theory and chaotic systems.

Very recently some groups also published foundational models for PDEs. In robotics, major work on foundation VLA-type models is also going on.

Some simulation software providers have also included ML or AI surrogates in their workflows. Agents that can automate complex simulation workflows, ML models that can learn from an existing DoE, and geometric deep learning is applied to iterate designs efficiently on irregular domains.

My question: The research still seems scattered and I am unable to notice any trend. Is this true? Or am I missing a major trend that is picking up in research labs.

For e.g. LLMs have had some noticeable trends: initially starting with prompt engineering, then reasoning and logical capabilities, now key focus on agentic systems and so on.

Another question I have is: Is robot learning also aiming to include some aspects of scientific ML, possibly to reduce the sim-to-real gap?

I’d like to know opinions and observations from folks interested in these areas.

Thank you for the discussion.