 Okay, can you see my screen? Yes. Okay, so also hi from me. I'm Torben, I'm a PhD student of Giovanni Bussi. And since this is our last presentation of today, I will try to stay on time. Everything I would like to present today will be in the context of machine learning in order to improve RNA force fields. And one motivation when working within this framework is that currently RNA is becoming very popular and becomes a more and more relevant target in therapeutics. And here, accurate methods which can predict or design structures and dynamics of RNA are needed to accelerate progress. However, already for small systems and the predictive capability of current force fields is limited. And therefore in the previous years, the works have been focused on taking advantage of experimental data in order to enforce agreement with experiments. A critical issue here is to take into account errors either in experimental data, or in the forward models used to back calculate the experiments from simulations. And at the same time account for overfitting on the training data set. Among frameworks such as Bayesian inference and also in the refinement and other forms of wisdom which allows to enforce agreement with experiments is maximum entropy. And there are limits in this procedure which are that corrections are not transferable to new unknown systems. Alternative transferable procedures which provide more flexibility regarding this. And they have already been introduced and we are trying to extend them. We are writing this down in like a reweighting problem as such here. We can, we are, we can have like arbitrarily chosen correction functions, and which can be adjusted by Lagrangian multipliers. The multipliers themselves are found by minimizing the square difference between observable averages in the current ensemble and the experimental observables. And then the, the observable averages themselves are computed as can be seen here. Let's note that nonlinearity can be present in observables as well as in the corrections, or at the same time. And I would like to close out my talk today with an outlook going also in this direction of, of nonlinearity. One of the challenges for current RNA standard force fields is the UUCG tetraloupe. And the native confirmation of this motive is stabilized by an intricate hydrogen bond network and this network is not represented correctly currently and consequences of this have been published, as in this example here on the right. And that MD is run on the ribosomal L1 stock RNA segment which contains the UUCG loop highlighted in red in these figures. And this L1 stock RNA is involved in the process of translation by guiding tRNA during the translocation step. And it does this in this native con confirmation, which is characterized by a compact fold with multiple tertiary contacts, and then performing standard MD on this system, these tertiary contacts start degrading immediately, such that after some time, one ends up with a non native elongated conformation, and which is just played basically in this second snapshot. And these issues like native confirmations being populated with less than 1% in some cases have not been solved yet, as even titles of recent publications indicate. Because of this, we, or our group collaborates closely with researchers at the Palacki University in the Czech Republic, we're trying to resolve these problems of RNA misrepresentation within force fields. And in the past, they approached this challenge by running simulations with different settings of corrections on hydrogen bond interactions. And these corrections are switching functions based on the distance and they are shown down here in the corner, and a parameter choice which has evidently improved the agreement of simulations to experimental data are the ones shown next to it. And these these basically favor base base interactions, and this favor all interactions between sugar and phosphate oxygens. However, our collaborators up to now only tried to change a small number of parameters at a, at a time and order to still be able to interpret findings. And the effect of the resulting force field changes to make use of all available 12 free parameters we applied a linear force field fitting protocol to allow for more automatic refinement which additionally removes the human bias and this process of selecting certain interactions for correcting. And to avoid overfitting on this uscg motive we included more systems. We added the GA GA tetraloupe as a representative of the GNRA sequence family, to which a great majority of known RNA tetraloupe structures belong. And also the unstructured da cc system, which as shown here on the right the native confirmations are not, or is not a single structure but in an ensemble of structures, which populate at least two, maybe three, three basins. In this plot which is basically the distance from a form helix. And for all these systems that we see here experimental NMR data are available. And the corresponding observables can be back calculated from the simulations when one is using for example forward models like these here. For the NOEs we have this relationship of signal and distance for the J couplings we have the couplers equations which are the relationship of signal to dihedral angles. And for the tetraloops we have the native confirmation which for which we arbitrarily are choosing the ones with ERMSD smaller 0.7 from the NMR solution structure, which effectively carries a lot of information. So now let me give you a quick outline first I would like to start with the details of the first project in which we are refining existing correction functions in an automatic way by fitting simulations to experimental data. And this hopefully touches on the most relevant steps when applying such protocols like regularization cross validation and final validation. And then I have some slides which are giving the outlook for a closely related project on using artificial neural networks within the correction function, but still aiming at force field matching to experiments. So let's go into the first project details. Previous studies have clearly stated that regularization is necessary when one is facing extensive data sets. And we are testing different regularization functions for comparison. And therefore, and the fitting parameters are no longer just a function of the discrepancy to experiments what is called the cost here. So also depends on the penalties and only one of the penalties I'm listing here is used at a time and the strength of a penalty can be tuned using additional hyper parameter which often is called alpha. And the most common regularization function is a to regularization, which targets the magnitude of the fitting parameters. And also targets them but leads to more sparse results. And this can help to identify, maybe the most relevant parameters. Besides these two, their penalties which keep the statistic efficiency after reweighting high, because usually, and others we heard today multiple times, usually a lot of statistical significance is lost to during reweighting. The the inverse of the of the kish size can be used when a higher number of frames with a significant large weight is desired. The relative, the inverse of the relative kish size can be used to reduce the distance of the weights before and after the fitting and the relative entropy or exponential of this and tries to tries the same but uses the Kulbach Leibler divergence for this. And then there are ways to embed such penalties into a protocol. And I want to show you what is a standard procedure for this. This is called cross validation. And this means to split any data set into subsets and then perform fitting on one subset and validation on the other. And this way an average cross validation error can be obtained. And here we see different ways of splitting the data on the right, which is, which are not necessarily standard protocols. And on the trajectory horizontally where we iteratively leave one of the subsets out for validation while trying training on the remaining. And the other option is to split vertically which can be either either be along systems as it's displayed here or along the observables extracted from each of these simulated systems. And in all these cases is to find the best hyper parameter, which can be found by scanning the error function over a certain range of hyper parameters as I try to show here. And the anatomical shape when overfitting is detected looks like here in this region where we have low hyper parameters which corresponds to almost unregularized fitting where the error function of the cross validation increases again and sometimes this exceeds the reference error of the force field. Ideally, one is able to identify a minimum within this scan, however, and we applied these protocols on the real data set. I have here the the first of four figures that are coming in the sub figure we have the error function for the cross validation on trajectory here evaluated on the training data themselves which is, as you can see increasing here on the exercise the hyper parameter is increasing. And this is by construction and for all regularization terms, except the kish size. There will be a legend. This one is the kish size for all other penalties except this the reference error of the force field is recovered. And the reason for this that the kish size is not reaching there is because our reference force field in this one we don't have uniform weights across all visited confirmations. In this sub figure here, we see the error function evaluated on the validation data, and we can see that there's no significant difference for range of low hyper parameter values, meaning overfitting is not an issue in this case, because the trajectories we are using are sufficiently long. And therefore the parameters are transferable when one is interested in just continuing the simulations on the same system that we were training on. Penalcy is again the training error, however, for the cross validation on observable as you can see in the scheme here. And here, the, okay, here nothing qualitatively changes, and we still have the by construction increasing error function. The interesting penalties this this figure D, which, which shows for the first time qualitative differences, because for each regularization function for each penalty, we can identify a specific hyper parameters which are minimizing the error function. And these hyper parameters and the minima represent the best balance between overfitting and predictiveness. However, because of the different nature of the regularization functions, the value of the the error function in the minima should be compared. And here, in this case the the relative kish size at a hyper parameter of around 18 shows the lowest error. And therefore, we treated it as the optimal regularization and all the following results. What we also did was additionally perform cross validation on systems, which is yet another possible protocol, as I mentioned, and this has the purpose of highlighting the contribution of of each system to the error function and also show advantages of regularization in the parameters which I tried to show in the in the right half of this. And this first row, which I'm showing now, it shows the results when GACC as one of the three systems we are training or validating on in this case GACC is the validation system. Always with a hedge background and also some parameters are shown here on the right here this is the parameter set of the three parameters when no regularization is used so hyper parameter equal to zero. And then also with the regularization where we chose, as I mentioned this relative kish size, and we extracted these parameters from the plot here, where you can identify the same style. So, we see, maybe as one first interpretation of these plots here that the UCG system has the highest error contribution, and it can be among the systems and it can be significantly improved when included in the training. When fitting UCG simultaneously the GA GA system improves with respect to its error function. And this is independent of whether it is included or not, as you can see here now GA GA is the validation set and and still the error function experiences a decrease with decreasing hyper parameter and the GACC tetramer always experiences overfitting whenever you UCG is included in the training set. However, the magnitude of this overfitting is within experimental uncertainty, and also the improvements made on this other system here, much larger. When using UCG as the validation system, its error contribution shows an optimum for all regularization penalties, while both remaining systems can be can be improved. However, the improvements for the left out system in this case are significantly lower than when it is included. And this suggests that the native UCG confirmation is stabilized by interactions which are not present in the other two systems. Then generally the relevance of regularization can be seen also from these plots here when taking a look at the error when no regularization is used, which is in all these plots the pink line. So for the training set, the lowest errors are usually achieved. However, in the cross validation in the validation system, you can see that usually the largest error functions are produced. Interestingly, when no regularization is used, the parameters become extremely large in cases where the GACC system is used in the training. Yes, exactly. All these parameters are large, which means that the best balance between overfitting and predictiveness cannot be guaranteed. However, using regularization penalties, the magnitude of these parameters is reduced while maintaining a low error function. And in general, when regularizing the parameters identified are similar independently of which system is left out from the fitting. And even if we perform a minimization on all the systems at the same time, we can see in the corner down here for the regularization that these 12 free parameters favor and disfavor the respective interactions in a similar manner as the ones above. Maybe a possible interpretation why parameters become very large when GACC is included in the training set is that certain interactions here that are extremely large are only present in the GACC non-native structure and therefore are extremely disfavored. Okay, we decided to use the obtained parameters and validate them by running new simulations on equally challenging TetraMERS, CAEU, UUU and again the Tetraloop UUCG. In this table here, we are showing the CAEI square error, the error function and native populations for the training and testing simulations. And in this table, we can see we report both the direct results of the simulation and the results of reweighting those simulations to the optimal parameters identified by cross-validation and later full minimization of the parameters with the ideal hyperparameter. And then for the validations simulations, we report both the direct results of the simulations and the results predicted by reweighting those simulations back to the starting GHB fixed force field. And the improvements made on error function and native population for all systems can be seen clearly. Exception is this GACC TetraMERS system, however, as I said before, the error remains within the range of experimental uncertainty. For all three validation systems of which CAEU and UUU were not included in the training, decrease in the error function is experienced, which was the goal of adding this rigorous regularization protocol. And in order to also have more technical idea on how these parameters, which ultimately lead to transferable force field corrections were obtained, we can follow these steps in this flow chart here. And after performing simulations, which would be the first step, the observables can be extracted. One among many possibilities to extract ERMSD, J-Couplings and NOE distances would be via BANABAR package for Python in which these forward models are already implemented. If you simply recover angles or distances, you might have to define the forward models yourself, which you could see here. And maybe something important is that not only observables for comparing two experiments are relevant, but also the ones which have to be considered for the correction function. And in this case, the switching function I showed earlier has to be evaluated. But since we added GHB fix as a collective variable to a recent climate version, this can be direct output of simulations now. So among these observables here, we can see GHB fix trajectories and as well and down here, we load experiment data. Yes, you have five minutes left. And then using all bias potentials used in the simulations, in case you're having some, the weights can be obtained by using one. And then you might define a cost function, which takes the free parameters as an input. And then, yeah, we decided here to use CUDA mat, which is for most matrix operations, CUDA mat is an open source software package that provides CUDA based matrix class for Python and it makes it easy to perform those matrix operations on a GPU. And in some cases it can offer significant speed ups compared to NumPy or Matlab. And further, you can see here there are some helper functions which have to be defined like compute new weights or this function here. And these basically allow the correction potentials to cause a change to the weights and the average observables and then you compute the error function basically. And the only thing that's missing then are the regularization penalties. If we choose to regularize we can select the different regularization functions and just select the one you want to apply. And finally, we split the data into training and validation set and then we start to minimize the cost function. And we do this with a loop over a range of hyper parameters. And ideally we store the free parameters at every step so you can recover all the quantities you're interested in. We use sci-pi and which functions for minimizing or maximizing objective functions are provided and we chose BFGS B as a solver which is the limited memory version of the quasi Newton BFGS. The solver allows to identify the set of parameters in the minimum in the end. And now this was everything regarding the first project and since I assume I don't have so much time left I will be quick on this because our interest here is that we want to test the possibility to introduce non-linear corrections in the form of artificial neural networks. And one motivation that I can maybe give is like that there are certain minimization problems where only non-linearity offers sufficient flexibility. And an adenosine nucleoside as you can see here in water it can be a model system for such a scenario. And if you would perform some simulations on this system you can identify interesting free energy landscape which basically consists of four states. And then you could pretend to also possess experimental information about which quadrants are populated and decide that we want to enforce that the experiments by reweighting. And when trying to enforce certain cases like upper left, lower right at the same time then you might realize an analogy to the XOR problem which is then the same as this model system linearly inseparable problem. And then when you perform a linear reweighting you actually unsurprisingly find that the results are not ideal in the attempt of enforcing these two quadrants. So why this non-linearity gives some additional flexibility and with such bias simulations you can actually successfully achieve your goal of enforcing such things. So today we are testing these non-linear protocols and we do this on a larger database of all these systems that you can see up here. For them also in an experiment data available and then what changed with respect to the previous project I spent most of my time on is that correction functions here depend not on hydrogen bond interactions but on the different fields and you can maybe from here see that we decided to use sine and cosine up to multiplicity three. And later on we will compare these fitting attempts to linear fitting procedures as I have introduced. But there will be more definite results coming up shortly and I will just quickly conclude here. The main focus was on the extension of existing force field correction procedures showing that it is possible to train in an automatic fashion correction terms and we saw different forms of regularization functions and different protocols that can be used to perform. Only because you are using such rigorous cross validation you are able to identify 12 or whatever free parameters and an advantage here is also that they are interpretable in this case. And in the end, yeah, I mentioned our interest in understanding if non-linear corrections can be suitable or even better than linear ones. So with this, I'm at the end of this talk and thank you for listening. Thank you very much. Virtual clap for you. Okay, so the floor is open for questions. Please feel free to unmute yourself or post the question in the chat. Yeah, I have a more general question and which is partly philosophical. So if I understand this whole fitting force field correction procedure. You correct for the force field of an underlying force field which still has the same, let's say, the wrong electrostatics. So eventually yes, if there is a mistake there then yes, which is which is very likely because of course one is what's missing from the force field is polarization, for example. So, so what's, yeah, what's the thing I mean I'm not criticizing all I'm asking what's the thinking on this so I guess it depends a lot on what one is interested in in computing. But surely these corrections don't, they don't fix that part of the problem, right. So yeah, just curious to hear what your what your thoughts are on this. I mean I would agree that the very basic problems of force fields will not be changed by this however and what these corrections can do is like. Now, like, as you see in the automatic way and eventually quick adjustable way, make your systems of interest behave more the way you would like to sample them, let's say, and you do it on top of dihedral angles eventually as now in the current attempt that we're trying with nonlinearity as well, you try to apply it on maybe one of the last layers of of what is defined in the force field. So you tweak it in one of the last steps which is has also its advantages, then if you want to go into the really basics, maybe this approach will not help. I mean, it's all a criticism I guess it's a one can one can imagine that this this is a another effective way of correcting for the problems and. I mean for practical the practical implication is that if you want to simulate your sometimes very challenging systems because there's some misrepresentation if you if you just want them to run in a specific way in the in the agreement to the experiment way, then this this is maybe straightforward. This is clearly, I agree. Okay. Questions from the audience. Someone has a question also for material. Welcome to pose it now. Okay, no questions. So if there are no questions, I guess we'll end this session. I just wanted to thank all the speakers again for your contributions. I know it's not officially on the program. The gather dot town session is going to happen and we encourage all the speakers to to make your way after this, as well as the participants, so that you can try. So with that, I think we can close today session. So thank you very much.