As artificial intelligence tools continue to evolve and improve their performance on more and more general tasks, scientists struggle to make the best use of them. 
The problem is not incompetence - in fact, at least in my field of study (high-energy physics) most of us have grown rather well educated on the use and development of tailored machine learning algorithms. The problem is rather that our problems are enormously complex. Long gone are the years when we started to apply with success deep neural networks to classification and regression problems of data analysis: those were easy tasks. The bar now is set much higher - optimize the design of instruments we use for our scientific research. 

Designing a detector for a particle collider is a mindbogglingly hard task, as it involves choosing between tens of thousands of different parameters, continuous and discrete (e.g., materials). But today's AI tools can start to pull that off, too. Of course, we must start with more modest tasks, to try our hand and show the world that it can be done.

In this spirit, we published on the arXiv today a study that shows how a diffusion model can be used in an end-to-end optimization task involving a calorimeter, tasked with the precise measurement of the energy of photons and charged pions. The idea is to define the basic "envelope" of the feature space: a maximum cost for the materials, a fixed number of different layers of absorbers and active scintillation mediums, and a choice of different absorbing and active materials. Within this envelope, the machine should work its way to learning what is the best arrangement that fulfils cost constraints and improves as much as possible the overall resolution to the studied incident particles.

I have no stamina to describe here the complex algorithm we (but mostly Jan Kieseler and Kylian Schmidt, the main authors, with a significant contribution of my student Andrea de Vita) put together. It relies on a software framework that allows interfacing with a high-fidelity simulator (Geant4) which provides the data on which we base the learning of a surrogate model, which is differentiable and can thus be part of a gradient descent optimization loop. You can find more detail in the paper here.

Instead, here i will just showcase the results, in the form of a graph (see below) that shows the evolution of the considered composition and geometry of the calorimeter sandwich, as a function of the epochs of training the system. You can see that we start from a very bad design, with insufficient containment and bad resolution overall, and the system learns that the detector must be thicker, spend more money on lead tungstate, especially at the start of the shower where photons must be measured well, and reduce the initial "preradiator' on the front face (at the bottom in the graph). Polystyrene is instead used to measure the longer hadronic shower development, after an absorbing layer that allows for hadron shower multiplication.



I think the above is a great demonstration that these AI tools are capable of finding optimized designs that we know and use since a long time - which implies that if tested on harder problems they may eventually outperform our design ideas. That is the long-term goal we have set to ourselves. 

In the meantime, it is fun to also try to see if a large language model can do something similar. I thus prepared a question for ChatGPT4 and observed his reasoning. It does really well, as its guess of how to design the instrument is not far off the mark! Are really LLMs "an off ramp" in the highway to AGI, as LeCun claims? I tend to doubt it.

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My question to ChatGPT4:
Hi, let us try an exercise. I want to design a calorimeter that measures with high resolution the energy of photons and hadrons. We can assume we only need to decide the width of a few layers of different materials, and their composition. So, say we use as a metric the resolution to a 50% mixture of photons and charged pions. Say we have money for up to 50cm of lead tungstate, while polystirene costs a tenth of that; and that we can use either iron or lead for absorbing sheets. Assume we want two absorbing layers and two active layers. How would you choose the composition and width of these layers? Can you make an educated guess?

Its answer:

Great exercise! Let's break this down systematically and make an educated guess.

Step 1: Understanding Our Goal

We want to design a calorimeter that provides high-resolution energy measurements for both photons and hadrons (charged pions). This means we need to balance:

  • Electromagnetic shower containment (for photons, mainly through pair production and bremsstrahlung).
  • Hadronic shower containment (for charged pions, which involve nuclear interactions).
  • Energy resolution, which depends on the sampling fraction and fluctuations in shower development.

Given that we have constraints on material cost and thickness, we need to optimize the composition and thickness of each layer.

Step 2: Material Selection

We have the following materials available:

  • Lead Tungstate (PbWO₄): A dense, fast scintillator with a small Molière radius, used in electromagnetic calorimeters (ECAL).
  • Polystyrene (PS): A cheaper scintillator, commonly used in sampling calorimeters (e.g., SPACAL or TILECAL designs).
  • Iron (Fe) or Lead (Pb): These act as absorbers, with lead being denser (better for EM showers) and iron being more suitable for hadronic interactions.

Step 3: Structuring the Layers

We assume we have two absorbing layers and two active layers, so a sandwich structure like this:

  1. First Absorber (for EM showers)
  2. First Active Layer (for detecting EM showers)
  3. Second Absorber (for hadronic showers)
  4. Second Active Layer (for detecting hadronic showers)

Electromagnetic Shower Considerations

  • PbWO₄ has a radiation length X0≈0.89X_0 \approx 0.89 cm and is excellent for electromagnetic calorimetry.
  • Lead (Pb) has a radiation length X0≈0.56X_0 \approx 0.56 cm, making it a good alternative absorber for EM showers.
  • A fine sampling fraction improves resolution, so we should aim for a relatively thin first absorber.

Hadronic Shower Considerations

  • The interaction length (λI\lambda_I) of Pb is 1.7 cm, while Fe has 1.76 cm, making them similar for hadronic showers.
  • The second absorber should be thicker to fully develop the hadronic shower.

Step 4: Proposed Design&Thickness Allocation

We have 50 cm of budget for PbWO₄ but should balance it with polystyrene. Given that polystyrene is much cheaper, we can allocate more thickness to it.

Design Choice:

  1. First Absorber (Pb or PbWO₄): 5 cm of PbWO₄ (to initiate EM showers).
  2. First Active Layer (PbWO₄ or PS): 10 cm of PbWO₄ (to accurately sample EM showers).
  3. Second Absorber (Fe or Pb): 20 cm of Fe (to develop hadronic showers effectively).
  4. Second Active Layer (PS): 15 cm of polystyrene (for efficient hadron detection).

Rationale for This Choice

  • Good EM energy resolution: Using PbWO₄ in the first layers ensures precise measurement of photon showers.
  • Hadronic shower containment: Fe as the second absorber ensures deep penetration and full shower development.
  • Balancing cost: Using polystyrene in the last layer reduces costs while still providing a good sampling fraction.

This setup should give a well-balanced combined electromagnetic and hadronic resolution, making it suitable for a 50% photon and pion mix.