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Inverse design – generation and optimization with respect to target properties

Inverse design aims at guided exploration of chemical compound space. This means suitable molecules or materials shall be obtained starting from desired target properties, e.g. designing a drug that treats a certain disease or a catalyst that supports a certain chemical reaction. Instead of evaluating a large set of randomly obtained candidates, this is achieved by either optimizing a given structure or by generating new ones that are highly likely to exhibit the target property.

As an example for the first case, differentiable models such as the deep neural network architectures SchNet and SchNOrb cannot only be used to accelerate the evaluation of candidates but also for inverse design. Since they predict molecular properties from atomic positions and types, they allow direct optimization of evaluated geometries by following the gradient of the model’s property prediction with respect to the input.

On the other hand, the generative SchNet (G-SchNet) is an auto-regressive generative neural network architecture that can build new molecules from scratch. In contrast to most generative models for molecules, it does not use abstractions such as molecular graphs or string representations but works with actual 3-dimensional structures, respecting their local and global symmetries by design. This allows to bias generation towards complex quantum chemical properties. G-SchNet learns a probability distribution over molecular geometries from a training data set and then samples unseen, valid molecules by placing one atom after another in 3-dimensional space. A scheme of one atom placement step can be found in in the figure above (a). It also shows a few examples of unseen molecules generated with G-SchNet (b) and how the distributions of different quantum chemical target properties can be shifted by biasing generation (c).

Scheme of an atom placement step with G-SchNet. 1. The model extracts atom-wise features from the positions and types of already placed atoms (where one of them is focused). 2. A distribution over the type of the next atom is predicted and the next type is sampled from it 3. Given the next type, distributions over distances between the new atom and every already placed atom are predicted. 4. The distances of candidate positions on a fine grid around the focused atom are evaluated using the predicted distributions. The new position is sampled from the resulting distribution over 3d positions.
Examples of unseen molecules generated with G-SchNet after training on QM9 (left). The orange shadows show the closest actual equilibrium configuration found by relaxing the generated structures with DFT-simulations (as depicted on the right-hand side). The root-mean-square deviation between atom positions before and after relaxation is given for the examples.
Distribution of properties for training molecules (blue), molecules generated with unbiased G-SchNet (purple), and molecules generated with a biased G-SchNet (green) where generation was biased towards small values for the HOMO-LUMO gap and large values for isotropic polarizability, dipole moment, and electronic spatial extent.

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