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Absolutely not. Certainly, if you believe this to be the case, you can go make a $1 billion selling this software to the oil industry since full wave inversion
by kxyvr 10y ago
Absolutely not. Certainly, if you believe this to be the case, you can go make a $1 billion selling this software to the oil industry since full wave inversion for seismic imaging problems, one example of an inverse problem, is still an open and very difficult problem.
ML and inverse problems solve two completely different problems. Really, ML should be called more accurately empirical modeling since we're creating a generic model from empirical data. In inverse problems, we choose an underlying model and then fit this model to our data. The difference between the two is that empirical models use generic models whereas inverse problems typically use models based on physical laws like continuum mechanics. Because of this, we often don't care about the end model in an inverse problem, but the variables that parameterize it because they have physical meaning. Generally, in ML, the parameters don't have physical meaning. The similarity between the two is that we're using an optimization engine to match some kind of model to our data.
To reiterate, in an inverse problem, the variables we solve for typically have a physical meaning. For example, in full wave inversion, we often model the problem using the elastic equations and we solve for the tensor that relates stress and strain. This is a 6x6 symmetric matrix (21 variables) at every point in a 3-D mesh. Side note, these meshes are large, so the resulting optimization problem has millions if not billions of variables. This matrix represents the material at that location. In this context, we don't need the end model with all these parameters plugged in. We're just going to look at the material directly because it tells us where stuff like where the oil is. In the context of the optimization, we will run the simulation, but, really, we don't need a simulator when we're done.
Now, in ML, imagine we did something simple like a multilayer perceptron. Yes, there are more complicated models, but it doesn't matter in this context. What is the physical meaning of the weight matrix and offsets? Saying it's the neurons in the brain is a lie. What if we're modeling acoustic data? Now, if we're just interested in creating a box that maps inputs to outputs, it doesn't matter. However, going back to the seismic world, mapping inputs to outputs just means mapping acoustic sources to travel times. No one cares about this. We want to know the rocks in the ground.
As such, ML and inverse problems use some similar machinery. Specifically, they both use optimization tools. However, they're used in very different places. Presentations like the one in the article are important because solving inverse problems at scale is really, really hard.
- deleted 10y ago[deleted]