I. OK, so I hope by the end of my talk, you will have an appreciation of the complexity of the sorts of experiments that we do.
I will also try and give you an idea of why these experiments are well suited to machine learning techniques.
And I will aim to do this by giving you an overview of some experiments that have already been optimised using machine learning methods.
So firstly, the question I want to address is why should we be interested in these experiments?
Why should we take the time to develop these kind of quantum mechanical experiments, the kinds of experiments that I will be looking at,
experiments done at the very low temperature limit where the thermal energy of the systems are comparable to the sort of
quantisation of the energy levels of the systems so that my system can be very accurately described by quantum mechanics.
There are essentially three reasons which you may be interested in building these experiments.
The first one I indicate by this clock here, which is that these are very low temperature experiments,
can give very accurate measurements of things such as time.
So, for example, this image here is a illustration of the atomic clock.
Atomic clocks based on strong team are currently one of the most accurate time measurements that we can make,
and it's equivalent to sort of knowing the age of the universe to the nearest second in terms of the precision that we can get.
Another reason which is quite often in the news these days, is that these kinds of experiments can be used as ways of doing quantum computing.
So the image that I show here is an ion trap from David Lucas's group here in the Department of Physics.
And in that small region here. So we have kind of these metal electrodes here which have an oscillating electric field of to them.
And in the centre,
you can see this single ion that is held and you can manipulate the states this ion using lasers to perform your quantum computation experiments.
And the final reasons are effectively illustrated here by this microscope are the kind of blue skies research questions that we might have.
So how can we basically perform experiments that will help inform our understanding of of the universe or physical systems?
So this comes broadly into the category of quantum simulation. So the idea is that we have some Hamiltonian that we seek to understand.
So say, for example, a Hamiltonian for superconductivity. And what we can try and do is build an experimental system which will have that Hamiltonian.
And then we can we can turn a sort of experimental parameters to adjust that Hamiltonian and see how the system behaves.
We might want to do this because some Hamiltonians are interesting, but not necessarily solvable with our with our numerical methods.
So instead, we can build a machine to sort of directly simulate that Hamiltonian itself.
And that's very much the area of research that I will be talking about.
So to give you an idea of what a kind of typical quantum simulation experiment will look like,
this is a cad schematic of our experiment in the in the basement downstairs.
So these experiments tend to start with a stage of laser cooling on which is illustrated in this area here,
where we will capture some atoms from thermal vapour and cooled them down to about 100 micron kelvin using laser cooling methods.
Once we've captured our vapour,
we will then transport through this differential pumping section of this vacuum system to an ultra high vacuum region, and you can see this.
So this glass cell here is sort of blown up on the right, and you can see various coils around this.
So what we are ultimately doing is applying various magnetic fields and laser fields to manipulate our atoms,
to make them experience different potentials and so simulate different Hamiltonians and therefore simulate different systems.
If our experiment works well, we will basically produce a Bose-Einstein condensate,
which is where we have macroscopic occupation of the ground state of our system.
The metric that we use normally for sort of actually exploring the state of the
system is we release the atoms and they fall on the time of flight and expand.
And we can basically take a picture using a sort of standard imaging camera and
image the distribution of atoms after they have had this ballistic expansion.
And what you see here in this picture is such an image that this is a real space image.
You can see that there is a sort of bimodal distribution in that I have this kind of faint background, which is a kind of Gaussian distribution.
So effectively, this is the atoms that remain in this sort of thermal state.
And then this large sort of dense core is effectively the atoms in the in the ground.
The system deploys Arnstein condensate.
The point I would like to make is that these experiments are very complicated, so I'll show you what our typical sequence looks like.
So this is basically in time series so long the x axis, I have time.
And then on the y axis, I have various parameters that I need to control my experiment.
So, for example, these are analogue voltages that choreograph the various parts of the experiment.
These are digital shots as things used to sort of toggling the laser beams or applying different pulses to the atoms.
You can see there is a lot of complexity going along. And the point I would like to make is that this is a very vast parameter space.
So if we want to find a way of optimising our experiment, this becomes very laborious to search for it.
But because it is a very difficult thing to orchestrate, I should say this is about a minute long,
by the way, to actually produce this, this cloud of atoms, because this requires very precise timings.
Most of these systems are already computer controlled,
and that gives a really nice advantage when you want to then use machine learning to control these experiments.
Because normally these experiments are already parameterised in a way that you can take
a machine learning package and connect it and immediately start testing to see results.
So in the first part of my talk,
I'm going to talk about using machine learning to optimise these experiments and specifically I'm going to look at how we produce ultracold gases.
So first, let's ask kind of what are the advantages of machine learning that we expect we will be able to use to improve our experiment?
So firstly, I would like to say that during the learning process,
our machine learning actually acquires a sort of intuitive understanding of the experiment.
So this is kind of like how a Ph.D. student will tend to perform an experiment.
It will sit in the laboratory and it will turn knobs. And although you may have an idea of of what will happen if you turn a knob.
Sometimes the experiments don't actually always work that way,
and there are quite often sort of tricks that well will be needed to to get things to work.
And sometimes things can occur that are slightly unexpected.
And so that's why this other point, the fact that the machine learning has no a priori model of the experiment can also be an advantage.
So whereas we, as physicists, will tend to sit down and write out a physical model of our system and then use that physical model to
try and develop a kind of theoretical ramp or sequence of parameters that we think will perform best.
Sometimes that doesn't work, and it can be good to have effectively no prior knowledge.
So reasons that might not work is, for example, because our model is incomplete.
We have failed to account for some imperfection in the apparatus or our calibrations may be incorrect.
Another important thing about the machine learning is is that they are patient,
and that means that machine learning will happily sit down and optimise this for six hours straight,
which, you know, most humans will get bored after 15 minutes, basically.
So that allows you to very rigorously explore the parameter space without distraction.
And the last point is, I would like to say that I wouldn't say so.
There was a question about whether or not machine learning algorithms will achieve a DPhil.
I would like to think of it as this machine learning algorithm approach actually sort of frees us to think about other problems.
So before we use machine learning in our laboratory,
we would tend to spend maybe sort of 10 hours of a 12 hour day getting the experiment to work nicely and then only two hours on the science.
But now what we can actually do is we can leave it running overnight. The experiment can tune itself up.
And then when we come in in the morning, the experiment is ready and waiting to to be used.
So in the context of producing ultracold quantum gases, I'm going to talk about two workhorse techniques today,
which are sort of broadly used in many of these experiments. And I'll talk about the optimisation of each of them.
So the first is evaporative cooling, which work lot, which works largely in the same way that a cup of coffee cools down.
And the second is laser cooling, which you may be familiar with, but I'll attempt to describe both of these.
So the first thing with evaporative cooling is that if I imagine that I have a collection of atoms in a trap,
I will have a distribution of energies that those atoms can take.
So this is, for example, the max volts and distribution.
You have the velocity along the x axis and the probability of having that velocity along the y axis.
The point that is important here is that there is a high energy tail to this distribution in evaporative cooling.
What I want to do is I want to find a way to remove atoms from my system in a way
that they will take away energy from that system in the most efficient way possible.
So if I can find a way to remove the highest energy atoms, by definition, I will reduce the average energy of the remaining atoms.
And then once I allow those atoms to collide and referrals, I will produce another distribution, which is characterised by a lot of temperature.
So I lose atoms. But what I gain is an increase in the face space density, which is a measure of sort of how cold and dense this sample is.
So just to sort of show this quickly, I have here a simulation of some atoms trapped inside a harmonic trap.
You can see them sort of jostling around at the centre. So when these atoms are shown and grey is basically when they've collided,
so you can see there are many collisions happening at the centre and you'll see that
the atoms which have ice energy tend to sort of fly out to the very edges of the trap.
So what this sphere around the outside is is effectively a surface where if an atom reaches that surface, it will be removed from the trap.
So if you watch, what happens is, as I would use this surface,
I'm basically lowering the potential energy that an atom has to have for it to to escape from the trap.
And in doing so, I will only remove the highest energy atoms if I keep slowly decreasing this.
Then basically, my remaining atoms are thermals and I reduce the temperature.
But a key point here is that there is a sort of timescale involved in this,
which is set by the rate at which these collisions occur because if I make my cut too quickly.
So just to refresh this, if I go far too quickly, then basically I will remove atoms before they can reach thermals,
and I will end up basically losing many, many atoms without efficiently reducing the temperature of the system.
I'm going to talk about a work that was done in by a group in Australia.
It's this paper here by Wigley and co-authors, which was published in Scientific Reports.
And it effectively describes how this how they used Gaussian process to perform an optimisation of their evaporative cooling ramps.
So in their experimental setup, they basically use dipole traps to confine the atoms.
So the actual confinement I showed in the simulation was sort of a harmonic trap.
The way that they achieve that harmonic trapping is by shining in laser beams, which are right to choose from the atomic transition.
And in doing so, they shift the energy levels of the atoms by an amount which is proportional to the intensity of the laser.
So what that means is that at the centre of the beam, the shift is much greater than at the edges of the beam.
There is no shift, so it will produce a sort of potential well, which can confine the atoms.
What they can then do, basically, is by reducing the intensity of their laser beams over time,
they reduce the depth of that potential well, so they reduce the amount of energy required for an atom to escape from the trap.
And that's that's effectively the same as reducing that, that the radius of that grace sphere that I showed in the simulation.
The measure that they use to sort of I mean, if you want to optimise,
you would like ideally to have a way of determining that you're actually improving the system in the first place.
So the way that they measure the performance of their system is, as I said,
to release the atoms and allow them to expand in a kind of ballistic expansion so that hot clouds.
So these are again real space images if they release atoms of hot cloud or expand very quickly for the same time of flight.
And you will see this kind of very broad distribution here, whereas a cold cloud will remain very,
very cold and dense because they if the thermal energy such that the velocity distribution of this cloud is is narrow.
There optimisation process looks like this, so when you use machine learning for optimisation,
what you typically are doing is building a model of the system that you want to optimise, where the model is effectively your kind of learnt process.
So they use a Gaussian process, which I won't have time to go into the details of,
but effectively what they are assuming is that there is some function.
Which would you describe the response of the system given some input parameters x, which are effectively your sort of experimental settings?
So say, for example, how quickly you reduce the intensities of the laser beams and it would it would produce some cost from some value,
which this cost function here is the measure of how well the experiment performs.
What they assume is that you have some, some function, which has possibly some stochastic variation on it as well.
And by basically sort of having this feedback loop where they they feed in parameters to the experiment, they receive the result from the experiment,
which they analyse to determine the cost,
and they then use that to improve their fitting of the model to effectively better learn how to approximate the experiment.
And then they use that to to seek optimisation of the experiment.
And one important thing I would like to say about the Gaussian process is that it has.
There was a question earlier in the previous session about a lot of these machine
learning is looked like black boxes and they tell you how something works, but don't necessarily give you any other intuition as to it.
One thing that's nice about the Gaussian process is that it has the concept of a sort of characteristic length scale for each of the parameter,
which is a measure of how much I expect the cost function to change if I change one of those parameters.
And that's illustrated here in this diagram.
So imagine that I had this this one dimensional access x and I have this this cost function, which is a function of that parameter.
Then these red, green and blue lines are effectively different faiths, assuming different characteristic length scales.
So if I seem a very long characteristic length scale for these black data points here, then this would be the sort of best fit that I would have.
Whereas if I assumed that the process would actually vary more quickly as a function of X,
I would be allowed to have this, this sort of green function here.
And so part of the optimisation process is also about learning about what the length scales that describe this experimental process.
So it gives you a measure of how sensitive your experiment is to different parameters.
I'd like to say that, so they basically perform this optimisation over this effective curtain so you can see different stages of
their cooling process and they find so they benchmark the sort of downstream process against this Nelda need,
which is a sort of kind of very dumb local sort of gradient descent type algorithm,
which is effectively trying to find the optimum configuration by only ever looking at the sort of last few data points.
Whereas the Gaussian process is taking the entire set that it's learnt so far and is attempting to find best parameters based on those.
And you see that this fast convergence of the Gaussian process. So the reason they both are converging at the same rates here is because basically
they need to provide some training data for the Gaussian process to get started. And they use the analogy made for generating that, that trading set.
And then afterwards, you see that gathering process converges much, much faster.
So they are able to produce a very cold, dense cloud only after a very few evaluations.
I should say that these are very small datasets compared to the kind of datasets that we've seen so far in the talks.
I mentioned that these typical experiments take on the order of 30 seconds to a minute to perform.
And if you want to actually have time to do your experiments as well as your optimisation,
that means that you only ever have a small number of evaluations to look at. So one kind of nice result,
wiggly and co-authors show is that effectively what you can use your Gaussian process
for is to eliminate parameters which are less important for optimising your system.
So this blue line here shows effectively a kind of Gaussian process optimisation using seven parameters.
And then what they did is they looked at the characteristic length scales that the
machine learner determined for those seven parameters and removed the parameter,
which was the least sensitive. So effectively this, they said the outcome of the evaporation doesn't matter at all about the seventh parameter.
So let's not bother optimising it. And then they get a much faster optimisation when they on the six remaining parameters.
And that will be important Lightroom.
I'd like to say that we here in Oxford have kind of benchmark this Gaussian process algorithm against other approaches for these types of experiments.
So this we sort of generate training datasets using a differential evolution algorithm,
which is a sort of genetic algorithm approach to effectively sort of taking different combinations
of parameters and selecting features from the parameters which have performed well so far.
This very fast blue line here, you can see, is the performance of the calcium process.
And then this darker blue line is the performance of a neural network.
So the neural network ultimately produces a slightly better solution for us, but it takes longer to converge.
And part of the reason is that it requires a larger number of datasets to train.
And as I say, we only are typically dealing with sort of 80 datasets for our experiment, which would be, you know, just over an hour of running.
Another nice thing I can say is that you might think they're looking at that
original parameter suite that I had in the in the one of the earlier slides.
They are very complicated experiments, so you might think these optimisations will only work if I can already provide them with a starting point.
But what we actually do here is we start with entirely randomised parameters.
So this is the first image that we produce, which has absolutely nothing in it whatsoever.
So another thing is very nice about this is in principle you could build an
experimental apparatus only knowing that your your apparatus could in principle
make a cloud of cold atoms and then allow the algorithm to take it from there and ultimately reproduce these very nice Bose-Einstein condensates.
I'll talk about the next method of cooling, but I wanted to mention which is laser cooling,
so I'm not sure how many of you are familiar with laser cooling. It might seem slightly counterintuitive,
but a laser can cool something down because obviously lasers are typically associated with sort of heating things up,
cutting things in half, etc. in the movies.
So one of the nice things obviously about lasers is that they are a stream of photons and photons each carry momentum.
What this means is that if an atom interacts with a laser beam, so here I have my vote on streaming in from the left hand side.
If my atom absorbs these photons to get into some excited state,
it will effectively absorb these full momentum kicks from the left hand side when it then emits.
Eventually, my hands and will relax back down to the ground state. It'll limit the photons back out, but in a random direction.
So if I take the sum of of this process, these emission will have a sort of mean momentum of zero,
whereas these four well will provide a momentum kick from one side.
So the sum of this process will be to exert a force on the outer.
So in principle, what I want to do to do laser cooling is I want to have it so that my atom will
always absorb photons from a laser beam coming opposite to its direction of travel.
If I can do that, I can arrange it so that my force applied to the atom will always act to slow the atom down.
The way we do this in the lab is we we send two counts propagating beams in from either
side like this and my atom is here moving with some velocity in a certain direction.
Now what you should remember is that Atoms responds to very narrow band ranges of radiation.
So if the optical frequencies that matter will respond to defined by the
electronic transmissions that can occur within within the shells with an atom. What this means is that if I write detuned, my two laser beams.
My answer will initially see those if my team is stationary, it would be far detuned from those two transitions when my team starts moving.
It will see one of the lasers as blue shifted and it will say the other is red shifted. So I will basically break the symmetry of that system.
My answer will more rapidly radiate photons from the laser that it is travelling
into the direction of which is effectively shifted into resonance with it.
And in doing so, the atom will feel a force that pushes against the direction of motion.
So this is the kind of principle of of laser cooling.
I did this small picture of an ambulance down in the bottom right because you will identify this fact to this effect as the Doppler shift,
which is the same reason why an ambulance siren changes pitch as it comes towards you and then drives away.
This is exactly the same trick that we are performing with the atoms, but we're performing it with optical radiation.
If you want to make a trap, I also need some position dependents for my forces.
And the way that that's done in the laboratories, you apply a magnetic field.
So by applying a magnetic field because of the same, in effect, my optical frequencies with my transitions will now gain a spatial dependence,
and that allows me to to set up a potential where I can trap atoms at some well-defined point.
And this so in this image here in the bottom right, this is an image taken from our lab, which is laser cooling of strontium.
And you can see this bright speck in the middle is a large number of strontium atoms,
which have been collected from an oven cooled and are now held by these.
You can see in the background this bright blue laser. So how can optimisation of laser cooling be done?
Well, so this was shown by Tranter and co-authors in this Nature Communications paper.
This flow diagram, I'll sort of break it down because it looks quite complicated at first.
Essentially, it is the same sort of idea as the previous optimisation and that we want to model some process.
We set up a machine learner which will learn what that process is, and then we will we will effectively feedback parameters into that experiment,
learn how the experiment behaved given those parameters, and use that to improve our knowledge of the machine learning.
So the system that they have up here in the top left is a magnetar optical trap of rubidium.
They have a very sort of elongated cigar shaped a cloud of atoms.
And so the way they measure how many atoms they've laser cooled and how cold intensities is, they send a laser beam in along the axis.
So that's this here, and that laser beam will be absorbed more if there are more atoms in the track.
And so they basically measure a voltage on a photodiode,
which becomes a measure of sort of how cold and dense this cloud is to perform well to model this behaviour.
They use stochastic artificial neural networks.
So we saw in the earlier example how machine learning is don't necessarily always fit to data properly and in attempts to get around.
This is to use three different machine liners, which are each initialised with different random parameters.
So this is a kind of machine learning. By consensus, we attempt to train three different learners if one of them gets stuck.
Hopefully, the other two will have figured out what's going on and help to help to correct for that.
And then the other thing which isn't drawn on the diagrams,
they also use a genetic algorithm to generate a sort of fourth data point each time they run.
So they use these. These four different is the three neural networks and the one differential evolution to basically model this process.
They generate a series of ramps, so they have three control parameters, which are effectively the D tuning of the cooling laser beams,
50 tuning of a pump, a laser beam which is used to basically keep atoms in this cooling transition.
Because what I didn't mention in the previous slide is that your atoms can be promoted to an excited state.
And what you want to have to have your laser cooling work is that they fall
back into the same state they were initially in so that you can cycle them.
But what actually can happen is obviously there are other electronic states and atoms will fall out into the dark states eventually.
So you use this great Panopto sort of out the atoms back into the cooling transition.
And then the last parameter they have is the coil current.
And what they want to do is basically sort of perform a sequence where they can kind of compress this to get the coldest and to sample.
And so what they do is they separate their parameters into twenty one time bins, and that gives sixty three parameters for them to to optimise.
So I'll show you what they uh. Let me just check something.
Yeah, I show you what their convergence looks like effectively, so they start by well,
these blue dots are effectively an optimisation using differential evolution, so attempting to model the process using a genetic algorithm.
And these red dots show the faster convergence that they're sort of stochastic neural network produces.
So what this is showing is that in a lower number of runs, they can more efficiently understand what the process is and then optimise it.
And then over on the right here, we have absorption images showing what they're called dense cloud to look like,
and they show this against what the sort of best students in the lab could achieve.
So they basically showing that the machine learner in only a sort of few hours
is able to outperform a student which has been working on the experiment for, you know, a few years, basically.
And this is one of the kind of wackier things, and I mentioned at the start that one of the advantages that you have with machine
learning is the fact that they don't have an a priori understanding of the system.
So obviously, as physicists, one of the things we do is we come up with very simple toy models to describe systems.
But the problem is is that those toy models can often be flawed on the left.
Here we see the sort of best optimised human parameters that kind of sensible.
You see that this rate bumper d tuning sort of decreases linearly over time.
We keep one parameter constant and then the coil current is sort of ramped up.
But if you actually look at what the best parameters the machine a learner produces, they look completely different.
I mean, this is kind of the sort of equivalent of a sort of unhuman chess move.
This is not something that the expert, the researchers sort of expected when they first ran this.
They still are in the paper. They were not necessarily even sure how to explain why this was optimum.
Apart from the fact that it was, but what they believe may be happening is that there is a sort of dynamics happening where the models are.
So you're sort of at Magneto optical trap, which is what you're using to confine the atoms,
is sort of releasing the atoms, allowing them to sort of adiabatic, expand and cool and then sort of recapturing them.
So it's effectively sort of learnt a new technique which which the the experimentalists were not using beforehand to show that well,
they show that these parameters are effectively stable and don't change from day to day.
And they plop sort of these parameters versus kind of other sort of less optimal runs over here.
One thing is that you'll notice that the parameters sort of rail very strongly.
So for example, in this part here you can see this coil currently sort of basically turning off and on very quickly.
They suggest that. So if you look at this kind of cost landscape as a function of the coil current for this optimal solution,
they basically show that it seems like in principle,
you may even want to actually extend the ranges of these parameters beyond what their experiment was able to do.
I'd like to say that, so we've sort of looked at optimising two separate stages that what we've done here in Oxford as well is applied,
applied these techniques to optimise a full experimental suite. But obviously we do have a very large number of parameters.
So in order to optimise our sort of entire experiment, we have to be selective about the parameters that we choose to optimise.
And in order to do this, we basically use the Gaussian process to understand which parameters our experiment is most sensitive to.
So these two plots on the right hand side show show for the laser cooling and for the evaporative cooling,
what the kind of length scales are for the most important parameters as a function of running so effectively as the learner learns.
These are what it thinks are sort of how sensitive various parameters are.
And ultimately, what we use this to do is extract which parameters are the most sensitive parameters for each of these cooling stages.
Once we know what the most sensitive parameters are,
we can fix all of the other parameters and perform a complete optimisation over the whole sequence,
but only considering the most sensitive parameters. To put this into context again.
So we have a human optimisation, which is effectively the the best of the Ph.D. students can do.
And then this is the sort of final optimisation, including all of the different stages.
So without going into the details it from the colour map, you can see this one is colder and denser.
Basically, this is a much better experiment.
Another very nice thing that you can do once you have set this up is that what may constitute an optimum experiment is very situationally dependent.
So so far, I've said that it is optimum to have very cold, dense clouds.
And it often is because being cold and dense sets quantity called the chemical potential,
which then becomes important in determining which times of your Hamiltonian are important.
But depending on what you actually want to use, the experiment for, you may find other metrics which are significant.
So for example, in this, we change the cost function to basically say give us the largest number of atoms at a temperature of one microcap.
And so the cost function looks like this. As you increase the number, the cost function goes lower and lower,
and you can effectively see all of these cost functions are centred on this, this one, like a Kelvin.
And this this will basically produce a larger cloud.
This line will produce you'll find a sequence which will generate the largest cloud of atoms at exactly the temperature we've asked for.
Other optimisations which are useful include things like asking the question What is the fastest time I can actually create a proton stone condensate?
And so say, for example, that may be useful.
If I'm aligning some optics around my experiment, I want to be able to adjust the lens and then take a picture.
But I don't necessarily want to wait around for one minute in between leaving the lens each time,
because that quickly becomes tedious, so we can basically use this to cut down sequence times as well.
I would like to now talk about a slightly different use of machine learning in the laboratory,
so we've looked at how machine learning can be used to improve the performance of an experiment.
But what if I had a device which has a certain fixed performance or instead what I'm doing is trying to find out how I can best evaluate that device?
So I want to. The question becomes how can I extract the most information possible in the smallest number of measurements?
And so this is the this is the device into question.
This is a quantum dot. This is done by a group of Andrew bricks here in Oxford.
The kind of measurements that they want to take is effectively the conductance of this device as a function of different gait voltages.
So we see we have a number of different voltages which we can apply to our chip and that will change the conductance of this of this device.
This is a kind of 2D parameter scan of the space we're interested in.
So say, for example, we take a gate voltage and a biased voltage.
You'll notice that there are some features that you can immediately see in this image.
So, for example, we have a very large band in the middle where there is basically no current flowing.
So if I wanted to take accurate, if I wanted to make a very efficient characterisation of the device,
it probably wouldn't be sensible to take many measurements in this region.
Instead, what you would want to do is take measurements around these areas where there's sort of a lot of things happening, basically.
So the so I should say I'm sorry, the reference has been lost because the slide has resized to these four by three ratio.
But this paper was led by Natalie IRAs. Yeah, I mean, I guess you have the exact reference and huge quantum information.
Yes, in future quantum information, this was last year, wasn't it? Yeah.
So what they are trying to do is, is, as I say, characterise these devices efficiently.
The way that they do this is they they first perform an initial scan over a device, so they perform a very rough scan.
And then the question is, if I have this eight by eight scan of my parameter space,
how can I then choose my variables to my remaining measurements to take to learn this device as best as I can?
So. The way that they do this is they train a machine learning to predict what the device should look like based on a map given like this.
And this machine learning will produce various different candidate devices.
So effectively, I say the eight by eight scan looks like this. The machine learning generates all this random distribution of what the full
device scan might look like and then what you can look for is you can look for.
Well, where do these pictures actually disagree?
Where are the parts where my machine learner is sort of saying, I don't really know what is happening on the device at this point,
and that produces this map here, which is effectively a sort of map of where the uncertainties lie in this parameter space.
And so from this map, you can effectively extract what is the measurement that will give us the moat,
which will effectively reduce our uncertainties about how about this device?
So they call this the sort of information gain. And so by looking at this map, you can then say, Well,
let's take the points in this map where the information going is going to be greatest, measure those.
And in doing so, you can you can reduce your uncertainties. So this is sort of showing, for example, some different reconstructions.
So if I had this partial scan of the parameter space here and I looked at what the
various machine learning generated solutions would look like along this line,
here you see all these like different grey wavy suggestions as to how the response may vary.
Obviously, over here, all these different grey, wavy suggestions converge, so there's very little point taking a measurement here.
But here they're very, very different. So there would be a lot of benefit to some measuring at that particular point.
One thing they do to show that this algorithm works very well is they basically make the observation.
So going back to this one, they make the observation that this information gain map looks kind of like the gradient of this function.
So as I said, this flat region in the centre where not a lot is happening.
That also obviously has a very flat gradient.
So you're kind of saying your your function, your output doesn't really depend on the parameters in that region,
whereas along these parts where we want to measure, we have large gradients.
So they define this gradient, which is effectively a measure of of of the slope of the function at different points.
And they define an information content as if I take the measurements that I've made so far.
If I measure the gradients of those points and then compare that back to the sort of total amount of gradient in the image,
given that when the scan is complete, I can basically determine how much information have I extracted so far from the device.
A linear sort of standard raster scan will basically decrease linearly like this,
so I'm effectively sort of randomly sometimes picking up a thought which has a large change,
you know, a large gradient and therefore a lot of information given.
And sometimes I end up sampling a very flat region, so it just decreases linearly.
The optimal solution? So if I had a device that was fully characterised,
I know that the measurements I should have made is effectively to arrange those
points by the amount of gradient in each point and just measure accordingly.
That would give me this Green Line here. This is effectively the sort of measurement sorted by the great end at each point.
And what they show is that each machine learner basically very closely approximates this Green Line.
So what they're saying is this machine learning is very good at identifying the points
that it should sample in order to best improve our understanding of the device.
So sort of conclude the talk.
I hope I go back to my slide at the start, which is effectively the sort of advantages the machine learning will will give us as experimentalists.
I've given you an example of, well, in this sort of optimisations,
I've given an example about how it's useful sometimes to have an unbiased mind with no kind of prior AI model of how these systems work.
I've also shown how the learn can pick up an intuitive understanding. So we saw that in the in the work where they optimise the laser cooling stage,
the machine learning or ended up finding effectively an entirely new way to
do the laser cooling that the experimentalists hadn't thought of beforehand.
And that's just because the machine learning gains are sort of intuition as to how the system will respond.
And I guess the the other point that I would like to emphasise is this last one about the fact that having machine
learning methods in our laboratories basically frees us up as experimentalists to think about the bigger picture.
We're not necessarily getting bogged down in terms of getting the experiment running well.
We can turn up in the morning with an experiment that has been optimised overnight and get straight down to doing the physics.
So thank you very much for listening and.