Artificial Intelligence, Modeling and Simulation

Question

Artificial Intelligence (AI) and its subsets i.e. Deep Learning (DL), Machine Learning (ML) etc. are becoming more and more ubiquitous in engineering, technology and science. Modeling and Simulation (M&S) is no exception. I am currently engaging in a project with the objective of exploiting the synergy put forward by AI and M&S in order to propose more efficient models and results.

I understand there are various publications on this topic although I see two limitations with the publications I encountered so far: 1. The publications on AI + M&S are very application exclusive, e.g. application of DL in reservoir modeling, application of ML in fluid dynamics. 2. The application of AI in M&S usually focuses on a specific level in system hierarchy (by system hierarchy I would like to address different levels in M&S). For instance I see there are papers discussing the use of DL in analyzing the results of a simulation in order to optimize the input of the same simulation (it falls in the context of sensitivity analysis).

So bottom line is I don't see any comprehensive work on the use of AI in M&S as a whole, let's say having models that can learn how to produce new improved models using the existing models. That is to say suggesting intelligent tools capable of learning how to perform simulation solely by some input data.

Am I missing something? Did I not look careful enough to find such publications?

Answer 1

So bottom line is I don't see any comprehensive work on the use of AI in M&S as a whole, let's say having models that can learn how to produce new improved models using the existing models.

There's definitely some work out there on this. This is the field of scientific machine learning. Currently there's three major paths that I'd break it into:

1. Neural networks outside of the simulation. This is commonly referred to as physics-informed neural networks, where neural networks represent the solution to some kind of model, usually a differential equation, and then this neural network is utilized as a form of data-driven object that is regularized against scientific models. This is one of the new classic papers on the topic. Software along these lines includes DeepXDE and NeuralNetDiffEq.jl.
2. Neural networks inside of the simulation. Essentially, you can augment your simulation with universal approximators to learn the missing parts of your models directly from data. This has been my work, and the preprint is Universal Differential Equations for Scientific Machine Learning. Software along these lines is DiffEqFlux.jl.
3. Data-driven equation discovery techniques. Instead of having a simulation, these methods are trying to find the simulation to use, like Koopman dynamic mode decomposition (DMD) and sparse identification of dynamical systems (SInDy). SInDy is somewhat related to classical AI techniques and can be mixed with things like dictionary learning, or can be mixed with neural networks as is shown in the universal differential equations paper and in this paper on nonlinear basis discovery.