Article title: “Toward Machine Learning Optimization of Experimental Design”
Authors: MODE Collaboration
In a previous post we wondered if (machine learning) algorithms can replace the entire simulation of detectors and reconstruction of particles. But meanwhile some experimentalists have gone one step further – and wondered if algorithms can design detectors.
Indeed, the MODE collaboration stands for Machine-learning Optimized Design of Experiments and in its first paper promises nothing less than that.
The idea here is that the choice of characteristics that an experiment can have is vast (think number of units, materials, geometry, dimensions and so on), but its ultimate goal can still be described by a single “utility function”. For instance, the precision of the measurement on specific data can be thought of as a utility function.
Then, the whole process that leads to obtaining that function can be decomposed into a number of conceptual blocks: normally there are incoming particles, which move through and interact with detectors, resulting in measurements; from them, the characteristics of the particles are reconstructed; these are eventually analyzed to get relevant useful quantities, the utility function among them. Ultimately, chaining together these blocks creates a pipeline that models the experiment from one end to the other.
Now, another central notion is differentiation or, rather, the ability to be differentiated; if all the components of this model are differentiable, then the gradient of the utility function can be calculated. This leads to the holy grail: finding its extreme values, i.e. optimize the experiment’s design as a function of its numerous components.
Before we see whether the components are indeed differentiable and how the gradient gets calculated, here is an example of this pipeline concept for a muon radiography detector.
Muons are not just the trendy star of particle physics (as of April 2021), but they also find application in scanning closed volumes and revealing details about the objects in them. And yes, the Great Pyramid has been muographed successfully.
In terms of the pipeline described above, a muon radiography device could be modeled in the following way: Muons from cosmic rays are generated in the form of 4-vectors. Those are fed to a fast-simulation of the scanned volume and the detector. The interactions of the particles with the materials and the resulting signals on the electronics are simulated. This output goes into a reconstruction module, which recreates muon tracks. From them, an information-extraction module calculates the density of the scanned material. It can also produce a loss function for the measurement, which here would be the target quantity.
This whole ritual is a standard process in experimental work, although the steps are usually quite separate from one another. In the MODE concept, however, not only are they linked together but also run iteratively. The optimization of the detector design proceeds in steps and in each of them the parameters of the device are changed in the simulation. This affects directly the detector module and indirectly the downstream modules of the pipeline. The loop of modification and validation can be constrained appropriately to keep everything within realistic values, and also to make the most important consideration of all enter the game – that is of course cost and the constraints that it brings along.
As mentioned above, the proposed optimization proceeds in steps by optimizing the parameters along the gradient of the utility function. The most famous incarnation of gradient-based optimization is gradient descent which is customarily used in neural networks. Gradient descent guides the network towards the minimum value of the error that it produces, through the possible “paths” of its parameters.
In the MODE proposal the optimization is achieved through automatic differentiation (AD), the latest word in the calculation of derivatives in computer programs. To shamefully paraphrase Wikipedia, AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations and functions. By applying the chain rule repeatedly to these operations, derivatives can be computed automatically, accurately and efficiently.
Also, something was mentioned above about whether the components of the pipeline are “indeed differentiable”. It turns out that one isn’t. This is the simulation of the processes during the passage of particles through the detector, which is stochastic by nature. However, machine learning can learn how to mimic it, take its place, and provide perfectly fine and differentiable modules. (The brave of heart can follow the link at the end to find out about local generative surrogates.)
This method of designing detectors might sound like a thought experiment on steroids. But the point of MODE is that it’s the realistic way to take full advantage of the current developments in computation. And maybe to feel like we have really entered the third century of particle experiments.
The MODE website: https://mode-collaboration.github.io/
A Beginner’s Guide to Differentiable Programming: https://wiki.pathmind.com/differentiableprogramming
Black-Box Optimization with Local Generative Surrogates: https://arxiv.org/abs/2002.04632