Ranking Pareto optimal solutions based on projection free energy

Ryo Tamura, Kei Terayama, Masato Sumita, and Koji Tsuda (2023)
Highlighted by Jan Jensen

Figure 1 from the paper. (c) APS 2023. Reproduced under the CC-BY license.

One of the main challenges in multi-objective optimisation is how to weigh the different objectives to get the desired results. Pareto optimisation can in principle solve this problem, but of you get too many solutions you have to select a subset for testing, which basically involves (manually) weighing the importance of each objective.

This paper proposes a new way to select the potentially most interesting candidates. The idea is basically to identify the most "novel" candidates to maximise the chances of finding "interesting" properties, They do this by identifying points on the Pareto front with the lowest "density of states" for each objective, i.e. points with few examples in property space.

The method is presented as a post hoc selection method, but could also be used as a search criteria to help focus the search on these areas of property spaces. 

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Accelerated dinuclear palladium catalyst identification through unsupervised machine learning

Julian A. Hueffel, Theresa Sperger, Ignacio Funes-Ardoiz, Jas S. Ward, Kari Rissanen, Franziska Schoenebeck (2021)
Highlighted by Jan Jensen

Figure 1 from the paper. (c) 2021 the authors.

I've been meaning to highlight this paper for years but forgot. However, in the last week k-means clustering came up twice in two completely unrelated contexts, which reminded me of this beautiful paper where the authors managed to use ML to make successful predictions based only five data points! 

Pd catalysts can exist in either in a dimer or monomer form depending on the ligands and there are no heuristic rules for predicting what form will be favoured by a particular ligand. Even DFT-computed dimerization energies fail to give inconsistent predictions.

The authors started with a database of 348 ligands each characterised with 28 different descriptors, which were dived into eight groups by k-mean clustering of the descriptors. The four ligands known to favour dimer formation where found in two clusters, with a combined size of 89 ligands. The prediction is thus that these 89 ligands are more likely to favour dimer formation, compared to the other 256. 

The authors decided to focus on the 66 ligands in the 89 subset that contain P-C bonds and computed 42 new DFT-computed descriptors that explicitly address dimer formation, such as the dimerization energy. Based these and the old descriptors the authors grouped the 66 ligands into six clusters, where two of the clusters, with a combined size of 25, contained the four known dimer-ligands. The prediction is this that the other 21 ligands also should form dimers.

It's a little unclear, but from I can tell the authors then experimentally tested nine of the 21 ligands, of which seven formed dimers. That's a very good hit rate starting from five data points!

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Real-World Molecular Out-Of-Distribution: Specification and Investigation

Prudencio Tossou, Cas Wognum, Michael Craig, Hadrien Mary, Emmanuel Noutahi (2023)
Highlighted by Jan Jensen

Part of Figure 1 from this report

Why do ML models perform much worse different test sets? There can be many reasons for such a shift in performance, but the main culprit is often a covariate shift meaning that the training and test set are quite different. This study seeks to quantify this effect for different molecular representations, ML algorithms, and datasets (both regression and classification).

The authors find that the difference between the test and train error (from a random split) is mostly governed by the representation (as opposed the the ML algorithm). Furthermore, representations that results in shorter distances between molecules (specifically 5-NN distances) on average are the ones that give a smaller difference in error between training and test set.  However, those representations do not necessarily result in lower test set errors. 

So you while you can't use representation distances to pick the representation you can use them to pick the best splitting method for obtaining your training set. The best test set it the one that with the shortest overall representation distance to the deployment set (i.e. the set you want to use your ML model on). The authors find that the best splitting method depends on the representation but is often scaffold splitting. 

Thanks to Cas Wogum for a very helpful discussion.

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Evolutionary Multiobjective Optimization of Multiligand Metal Complexes in Diverse and Vast Chemical Spaces

Hannes Kneiding, Ainara Nova, David Balcells (2023)
Highlighted by Jan Jensen

Figure 5 from the paper. (c) 2023 the authors. Reproduced under the CC BY ND license

The authors show that an NBO analysis can be used to identify the charges (as well as their coordination mode) of individual ligands in TM-complexes. This is a key property needed to properly characterise the ligands and, thus, the complex as a whole. They have manually checked the approach for 500 compounds and finds that it gives reasonable results in 95% of the cases. That number drops to 92% if coordination mode is also considered. They provide these, and many other, properties of 30K ligands extracted from the CSD.

The NBO analysis is based on PBE/TZV//PBE/DZV calculations, which are a bit costly, but it will be interesting to see whether lower theories (e.g. DZV//xTB) give similar results.

Based on this knowledge the authors build a data set of 1.37B square-planar Pd compounds and compute their polarizability and HOMO-LUMO gap. They then search this space for molecules with both large polarizabilities and HOMO-LUMO gaps using a genetical algorithm that optimises the Pareto front, and show that optimum solutions can be found by considering only 1% if the entire space. The GA code is not available yet, but should be released soon.

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Seeing is Believing: Brain-Inspired Modular Training for Mechanistic Interpretability

Ziming Liu, Eric Gan, Max Tegmark (2023)

Highlighted by Jan Jensen

Adapted from Figures 1 and 3 in the paper. (c) 2023 the authors 

While this fascinating paper is not about chemistry it could easily be applied to chemical problems without further modifications (except for graph convolution), so I feel justified in highlighting it here.

The paper introduces brain-inspired modular training (BIMT) which leads to relatively simple NNs that are easier to interpret. "Brain-inspired" comes from the fact that the brain is not fully connected like most NNs, since it is a 3D entity with physical connections (axons) and longer axons mean slower communication between neurons. The idea is to enforce this modularity during trainings by assigning positions to individual nodes and introducing a length-dependent penalty in the loss function (in addition to conventional L1 regularisation). This is combined with a swap operation that can swap neurons to decrease the loss.

The result is much simpler networks that, at least for relatively simple objectives, are intuitive and easier to interpret as you can see from the figure above. 

The code is available here (Google Colab version) It would be very interesting to apply this to chemical problems!

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Virtual Ligand Strategy in Transition Metal Catalysis Toward Highly Efficient Elucidation of Reaction Mechanisms and Computational Catalyst Design

Wataru Matsuoka, Yu Harabuchi, and Satoshi Maeda (2023)
Highlighted by Jan Jensen

This perspective shows how an old computational tool can be adapted to serve a new purpose. When I started in compchem changing, say, a few F atoms to and H atoms in a molecule often made the difference between waiting a few days and a few weeks for the calculations to finish. People therefore developed pseudo H atoms that could mimic the electronic effect of larger atoms or even entire functional groups. Some of these methods were later adapted to serve as boundary atoms in QM/MM calculations and now they have found a new use in screening for ligands in organometallic catalysts.

The use of pseudoatoms to model such ligands not only speeds up the individual calculations but also maps the chemical space on to just two dimensions, electronic and steric, that allows the space to be searched more efficiently. Once the desired combination of electronics and sterics is found corresponding real ligands are found by another, much faster, screen if commercially available or synthetically accessible ligands.

The authors use this approach to identify two phosphine ligands for a chemoselective Suzuki–Miyaura cross-coupling catalyst, complete with experimental verification.

The downside is that the parameterisation of these "virtual ligands" are a bit involved and very ligand-dependent. But an interesting approach non-the-less.

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eChem: A Notebook Exploration of Quantum Chemistry

Thomas Fransson, Mickael G. Delcey, Iulia Emilia Brumboiu, Manuel Hodecker, Xin Li, Zilvinas Rinkevicius, Andreas Dreuw, Young Min Rhee, and Patrick Norman (2023)
Highlighted by Jan Jensen

eChem is an e-book that mixes text and code to teach quantum chemistry. The code is based on VeloxChem, which is a Python-based open source quantum chemistry software package. 

While you can use VeloxChem to perform standard quantum chemical calculations, the really cool thing is that it gives you easy access to the basis set, integrals and orbitals, DFT grids and functionals, etc. This in turn allows you to write your own SCF or Kohn-Sham-SCF procedure. It's sorta like Szabo and Ostlund updated and taken to the next level. 

If you truly want to understand quantum chemistry this is the way to go! One of the co-authors, Xin Li, very kindly got it working on Google Colab, so it is very easy to start playing around with it yourself. 

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