Materials

In most complex physical systems (and to some extent others like financial markets), competing non-linear forces lead to instabilities and organized large scale structures. The overall dynamics are controlled by the large scale structures to a great extent but those large structures cannot be accessed directly as they are the result of the small scale interactions.  In CFD (Computational Fluid Dynamics), we are stuck in the pursuit of conducting even higher resolving simulations to get to the ground truth by modeling all those small scale interactions that lead to the emergent large scale structures. We are creative in coming up with subgrid models to reduce the computational load to resolve absolutely what we have to and have correlations for the unresolved scales. There are other heuristics that we apply to things like turbulence and drag closures, etc. to make the problems computationally tractable.  I have been introduced to Machine Learning by Badri Asokan in 2007 and the objective then was to find low dimensional manifolds, segment them into linear spaces, and map PODs (Proper Orthogonal Decomposition – a derivative of PCA) onto those linear spaces with the objective of developing reduced order models. We made some progress on a toy problem (spouted bed) but the proposal to generalize and further this idea was unfortunately not funded and we never got to develop this further. On the other end of the spectrum, I worked with Stuart Daw and Jack Halow to work on an agent based model in 2003 to simulate bubbling fluidized beds with bubbles with simple interaction rules. As I shared recently, these models run in real time and can predict emerging behavior such as slugging quite well but are limited in their own ways. Any extensions that I tried to do to make them more attuned to data failed.  Having a taste of methods to unravel low dimensional manifolds and also realizing that most systems we are trying to model lie in much lower dimensions than than the millions or now billions of degrees we bring in through CFD, I presented concepts at various venues on how we can use AI/ML to break these vicious dependencies between heterogeneities, tyranny of scales, and curse of ever increasing mesh sizes. Now it is more imperative to revisit as the LLM boom brought us into our laps the neural networks based learning algorithms that give access to low dimensional latent spaces and possibly transfer learning from similar phenomena, hardware co-designed with software for deep learning on large datasets, and plethora of software and data analysis tools available to explore all aspects of heterogeneous structures in complex systems. Presenting a concept without actual data or a proof-of-concept doesn’t catch the attention as I was hoping someone smarter than me will pick it up and pursue those concepts. Traditional CFD codes (including the many I have developed or contributed) are not flexible to try out new concepts and I never could do this on my own till recently without significant investment of my time.  With the advent of LLM tools, it has become easier to try out new ideas and also create a proof-of-concept that one can interact with live to understand and later utilize this understanding to advance methods to model systems with a computational dimensionality that matches the underlying physical dimensionality.  Modeling risers in fluid catalytic crackers (FCCs) turned out to be one of the most difficult problems of great practical relevance emblematic of the topic of this post. Particles in the riser collide and dissipate to form clusters and these clusters with reduced drag drop down to create interesting phenomena like core annulus, create back mixing, high solids concentration at the bottom of the riser, and control the solids holdup and gas-solids contacting. We made tremendous progress on this front with the filtered-drag and EMMS models. One thing I wanted to explore was to reconstruct the large scale structures and use that to modify the drag as based on my experience with modeling a square cross-section circulating fluidized bed (particularly in 2D), the drag reduction from clustering is key to the solids fraction profile along the axis. The interactive website (https://ekta.net/LI/Riser-DHRDM.html) will introduce Dynamic Heterogeneity-Resolving Drag Model (DHRDM) – a dynamic way to detect clusters based on some heuristics that you can play with and that will affect the solids holdup and distribution along the axis. This is a grossly simplified version to play around and develop intuition. There is a lot more work to be done in terms of automating all this by training AI on large datasets where one can identify these structures based on local parameters and use more sophisticated corrections for drag based on the cluster shape. It is exciting that the modern AI tools help us to play around with our ideas – from start to finish, I must have spent around 5-6 hours and most of that time is to get the plots right.