Accelerating amorphous polymer electrolyte screening by learning to reduce errors in molecular dynamics simulated properties

Polymer electrolytes are promising candidates for the next generation lithium-ion battery technology. Large scale screening of polymer electrolytes is hindered by the significant cost of molecular dynamics (MD) simulation in amorphous systems: the amorphous structure of polymers requires multiple, repeated sampling to reduce noise and the slow relaxation requires long simulation time for convergence. Here, we accelerate the screening with a multi-task graph neural network that learns from a large amount of noisy, unconverged, short MD data and a small number of converged, long MD data. We achieve accurate predictions of 4 different converged properties and screen a space of 6247 polymers that is orders of magnitude larger than previous computational studies. Further, we extract several design principles for polymer electrolytes and provide an open dataset for the community. Our approach could be applicable to a broad class of material discovery problems that involve the simulation of complex, amorphous materials.

where ✏ follows a normal distribution with zero bias N (0, ⌘). Here, we assume that ✏ is not a function of G, i.e. di↵erent polymers have the same random error independent of their structure. This assumption is approximately correct based on the di↵erences in conductivity of the same polymer between two independent MD simulations in the log scale (Fig. 2).
To estimate the true prediction error of our model, we write our graph neural network model as a deterministic function g that predicts polymer property based on their structure G, y = g(G). (2) Note that we use di↵erent labels for the predicted property y and the MD simulated property t.
Under these assumptions, the mean squared error between ML predictions and MD simulated properties, i.e. apparent prediction error, is, Note that in the last step we use the fact that EG [✏] = 0.
The mean squared error between two independent MD simulations for the same polymer is, Therefore, the mean squared error between ML predictions and the true target property, i.e. true prediction error, is, Based on our predictions on 86 testing data, MSE(y, t) = 0.0173 and MSE(t 1 , t 2 ) = 0.0274. Therefore, the true prediction error MSE(y, f (G)) = 0.0036. In comparison, the random error ⌘ 2 ⇡ EG [✏ 2 ] = 0.0137. Remember that random errors can be reduced by running multiple MD simulations on the same polymers and computing the mean of target properties. Since ⌘ n = ⌘/ p n, we estimate our ML prediction accuracy is approximately the accuracy of running 3.8 ⇡ 4 MD simulations for each polymer. We note that uncertainty of this estimation is likely high due to the small size of test data and the relatively strong assumption that the random noise is Gassuian.

Supplementary Note 2: random forest model
Since our dataset is relatively small, we develop a simpler random forest (RF) model to compare its performance with our GNN model in both random and systematic error reductions. We use the Morgan fingerprint to featurize the molecular structure of the polymers and then build a RF regression model using scikit-learn to predict the properties. For the multi-task model, we use a first RF to predict the 5 ns MD properties, and then concatenate the predicted values with the Morgan fingerprint as the input features to train a second RF model. This model has a similar architecture with our multi-task GNN model but is fully composed of random forests. We also experimented a model that uses a linear model to replace the second RF, but it su↵ers from numerical instability so we do not report the results here.

Supplementary Note 3: reason for choosing the simulation time
We choose 5 ns as the simulation time of our short MD simulation because we need to run 5 ns MD prior to sample and relax equilibrium structure of the amorphous polymers.
A shorter simulation time than 5 ns does not save total simulation time because the 5 ns MD needed for relaxation cannot be reduced. We choose 50 ns as the simulation time of our long MD simulation because we empirically find that 50 ns is enough to achieve good agreement with experiments. To apply our approach to other systems, the short and long

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