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Imagine an oracle that correctly predicts the outcome of every particle physics experiment, the products of every chemical reaction, or the function of every protein. Such an oracle would revolutionize science and technology as we know them. However, as scientists, we would not be satisfied with the oracle itself. We want more. We want to comprehend how the oracle conceived these predictions. This feat, denoted as scientific understanding, has frequently been recognized as the essential aim of science. Now, the ever-growing power of computers and artificial intelligence poses one ultimate question: How can advanced artificial systems contribute to scientific understanding or achieve it autonomously? We are convinced that this is not a mere technical question but lies at the core of science. Therefore, here we set out to answer where we are and where we can go from here. We first seek advice from the philosophy of science to understand scientific understanding. Then we review the current state of the art, both from literature and by collecting dozens of anecdotes from scientists about how they acquired new conceptual understanding with the help of computers. Those combined insights help us to define three dimensions of android-assisted scientific understanding: The android as a I) computational microscope, II) resource of inspiration and the ultimate, not yet existent III) agent of understanding. For each dimension, we explain new avenues to push beyond the status quo and unleash the full power of artificial intelligence's contribution to the central aim of science. We hope our perspective inspires and focuses research towards androids that get new scientific understanding and ultimately bring us closer to true artificial scientists., Comment: 13 pages, 3 figures, comments welcome!

Optimization strategies driven by machine learning, such as Bayesian optimization, are being explored across experimental sciences as an efficient alternative to traditional design of experiment. When combined with automated laboratory hardware and high-performance computing, these strategies enable next-generation platforms for autonomous experimentation. However, the practical application of these approaches is hampered by a lack of flexible software and algorithms tailored to the unique requirements of chemical research. One such aspect is the pervasive presence of constraints in the experimental conditions when optimizing chemical processes or protocols, and in the chemical space that is accessible when designing functional molecules or materials. Although many of these constraints are known a priori, they can be interdependent, non-linear, and result in non-compact optimization domains. In this work, we extend our experiment planning algorithms Phoenics and Gryffin such that they can handle arbitrary known constraints via an intuitive and flexible interface. We benchmark these extended algorithms on continuous and discrete test functions with a diverse set of constraints, demonstrating their flexibility and robustness. In addition, we illustrate their practical utility in two simulated chemical research scenarios: the optimization of the synthesis of o-xylenyl Buckminsterfullerene adducts under constrained flow conditions, and the design of redox active molecules for flow batteries under synthetic accessibility constraints. The tools developed constitute a simple, yet versatile strategy to enable model-based optimization with known experimental constraints, contributing to its applicability as a core component of autonomous platforms for scientific discovery., Comment: 15 pages, 5 figures (SI with 13 pages, 8 figures)

Numerous challenges in science and engineering can be framed as optimization tasks, including the maximization of reaction yields, the optimization of molecular and materials properties, and the fine-tuning of automated hardware protocols. Design of experiment and optimization algorithms are often adopted to solve these tasks efficiently. Increasingly, these experiment planning strategies are coupled with automated hardware to enable autonomous experimental platforms. The vast majority of the strategies used, however, do not consider robustness against the variability of experiment and process conditions. In fact, it is generally assumed that these parameters are exact and reproducible. Yet some experiments may have considerable noise associated with some of their conditions, and process parameters optimized under precise control may be applied in the future under variable operating conditions. In either scenario, the optimal solutions found might not be robust against input variability, affecting the reproducibility of results and returning suboptimal performance in practice. Here, we introduce Golem, an algorithm that is agnostic to the choice of experiment planning strategy and that enables robust experiment and process optimization. Golem identifies optimal solutions that are robust to input uncertainty, thus ensuring the reproducible performance of optimized experimental protocols and processes. It can be used to analyze the robustness of past experiments, or to guide experiment planning algorithms toward robust solutions on the fly. We assess the performance and domain of applicability of Golem through extensive benchmark studies and demonstrate its practical relevance by optimizing an analytical chemistry protocol under the presence of significant noise in its experimental conditions., Comment: 37 pages, 25 figures; additional experiments, expanded discussions and references

Bayesian optimization has emerged as a powerful strategy to accelerate scientific discovery by means of autonomous experimentation. However, expensive measurements are required to accurately estimate materials properties, and can quickly become a hindrance to exhaustive materials discovery campaigns. Here, we introduce Gemini: a data-driven model capable of using inexpensive measurements as proxies for expensive measurements by correcting systematic biases between property evaluation methods. We recommend using Gemini for regression tasks with sparse data and in an autonomous workflow setting where its predictions of expensive to evaluate objectives can be used to construct a more informative acquisition function, thus reducing the number of expensive evaluations an optimizer needs to achieve desired target values. In a regression setting, we showcase the ability of our method to make accurate predictions of DFT calculated bandgaps of hybrid organic-inorganic perovskite materials. We further demonstrate the benefits that Gemini provides to autonomous workflows by augmenting the Bayesian optimizer Phoenics to yeild a scalable optimization framework leveraging multiple sources of measurement. Finally, we simulate an autonomous materials discovery platform for optimizing the activity of electrocatalysts for the oxygen evolution reaction. Realizing autonomous workflows with Gemini, we show that the number of measurements of a composition space comprising expensive and rare metals needed to achieve a target overpotential is significantly reduced when measurements from a proxy composition system with less expensive metals are available., Comment: 12 pages, 5 figures, 2 tables

Research challenges encountered across science, engineering, and economics can frequently be formulated as optimization tasks. In chemistry and materials science, recent growth in laboratory digitization and automation has sparked interest in optimization-guided autonomous discovery and closed-loop experimentation. Experiment planning strategies based on off-the-shelf optimization algorithms can be employed in fully autonomous research platforms to achieve desired experimentation goals with the minimum number of trials. However, the experiment planning strategy that is most suitable to a scientific discovery task is a priori unknown while rigorous comparisons of different strategies are highly time and resource demanding. As optimization algorithms are typically benchmarked on low-dimensional synthetic functions, it is unclear how their performance would translate to noisy, higher-dimensional experimental tasks encountered in chemistry and materials science. We introduce Olympus, a software package that provides a consistent and easy-to-use framework for benchmarking optimization algorithms against realistic experiments emulated via probabilistic deep-learning models. Olympus includes a collection of experimentally derived benchmark sets from chemistry and materials science and a suite of experiment planning strategies that can be easily accessed via a user-friendly python interface. Furthermore, Olympus facilitates the integration, testing, and sharing of custom algorithms and user-defined datasets. In brief, Olympus mitigates the barriers associated with benchmarking optimization algorithms on realistic experimental scenarios, promoting data sharing and the creation of a standard framework for evaluating the performance of experiment planning strategies, Comment: 15 pages, 4 figures, 4 tables (with SI: 22 pages, 11 figures, 15 tables). Changes: minor fixes to text and references. Two paragraphs added in Sec. III

Designing functional molecules and advanced materials requires complex design choices: tuning continuous process parameters such as temperatures or flow rates, while simultaneously selecting catalysts or solvents. To date, the development of data-driven experiment planning strategies for autonomous experimentation has largely focused on continuous process parameters despite the urge to devise efficient strategies for the selection of categorical variables. Here, we introduce Gryffin, a general purpose optimization framework for the autonomous selection of categorical variables driven by expert knowledge. Gryffin augments Bayesian optimization based on kernel density estimation with smooth approximations to categorical distributions. Leveraging domain knowledge in the form of physicochemical descriptors, Gryffin can significantly accelerate the search for promising molecules and materials. Gryffin can further highlight relevant correlations between the provided descriptors to inspire physical insights and foster scientific intuition. In addition to comprehensive benchmarks, we demonstrate the capabilities and performance of Gryffin on three examples in materials science and chemistry: (i) the discovery of non-fullerene acceptors for organic solar cells, (ii) the design of hybrid organic-inorganic perovskites for light harvesting, and (iii) the identification of ligands and process parameters for Suzuki-Miyaura reactions. Our results suggest that Gryffin, in its simplest form, is competitive with state-of-the-art categorical optimization algorithms. However, when leveraging domain knowledge provided via descriptors, Gryffin outperforms other approaches while simultaneously refining this domain knowledge to promote scientific understanding., Comment: 19 pages, 6 figures (SI: 16 pages, 14 figures). Expanded background, discussion, minor fixes and changes

Superconducting circuits have emerged as a promising platform to build quantum processors. The challenge of designing a circuit is to compromise between realizing a set of performance metrics and reducing circuit complexity and noise sensitivity. At the same time, one needs to explore a large design space, and computational approaches often yield long simulation times. Here we automate the circuit design task using SCILLA, a software for automated discovery of superconducting circuits. SCILLA performs a parallelized, closed-loop optimization to design circuit diagrams that match pre-defined properties such as spectral features and noise sensitivities. We employ it to discover 4-local couplers for superconducting flux qubits and identify a circuit that outperforms an existing proposal with similar circuit structure in terms of coupling strength and noise resilience for experimentally accessible parameters. This work demonstrates how automated discovery can facilitate the design of complex circuit architectures for quantum information processing., Comment: 23 pages, 7 figures; shortened Sec. II Methodology; clarified Fig. 2; minor clarifying edits and typo corrections

Fast and inexpensive characterization of materials properties is a key element to discover novel functional materials. In this work, we suggest an approach employing three classes of Bayesian machine learning (ML) models to correlate electronic absorption spectra of nanoaggregates with the strength of intermolecular electronic couplings in organic conducting and semiconducting materials. As a specific model system, we consider PEDOT:PSS, a cornerstone material for organic electronic applications, and so analyze the couplings between charged dimers of closely packed PEDOT oligomers that are at the heart of the material's unrivaled conductivity. We demonstrate that ML algorithms can identify correlations between the coupling strengths and the electronic absorption spectra. We also show that ML models can be trained to be transferable across a broad range of spectral resolutions, and that the electronic couplings can be predicted from the simulated spectra with an 88 % accuracy when ML models are used as classifiers. Although the ML models employed in this study were trained on data generated by a multi-scale computational workflow, they were able to leverage leverage experimental data.

Fundamental advances to increase the efficiency as well as stability of organic photovoltaics (OPVs) are achieved by designing ternary blends which represents a clear trend towards multi-component active layer blends. We report the development of high-throughput and autonomous experimentation methods for the effective optimization of multi-component polymer blends for OPVs. A method for automated film formation enabling the fabrication of up to 6048 films per day is introduced. Equipping this automated experimentation platform with a Bayesian optimization, a self-driving laboratory is constructed that autonomously evaluates measurements to design and execute the next experiments. To demonstrate the potential of these methods, a four-dimensional parameter space of quaternary OPV blends is mapped and optimized for photo-stability. While with conventional approaches roughly 100 mg of material would be necessary, the robot based platform can screen 2,000 combinations with less than 10 mg and machine learning enabled autonomous experimentation identifies the stable compositions with less than 1 mg.

Discovering and optimizing commercially viable materials for clean energy applications typically takes over a decade. Self-driving laboratories that iteratively design, execute, and learn from material science experiments in a fully autonomous loop present an opportunity to accelerate this research. We report here a modular robotic platform driven by a model-based optimization algorithm capable of autonomously optimizing the optical and electronic properties of thin-film materials by modifying the film composition and processing conditions. We demonstrate this platform by using it to maximize the hole mobility of organic hole transport materials commonly used in perovskite solar cells and consumer electronics. This demonstration highlights the possibilities of using autonomous laboratories to discover organic and inorganic materials relevant to materials sciences and clean energy technologies., Comment: 43 pages, 9 figures

The discovery of novel materials and functional molecules can help to solve some of society's most urgent challenges, ranging from efficient energy harvesting and storage to uncovering novel pharmaceutical drug candidates. Traditionally matter engineering -- generally denoted as inverse design -- was based massively on human intuition and high-throughput virtual screening. The last few years have seen the emergence of significant interest in computer-inspired designs based on evolutionary or deep learning methods. The major challenge here is that the standard strings molecular representation SMILES shows substantial weaknesses in that task because large fractions of strings do not correspond to valid molecules. Here, we solve this problem at a fundamental level and introduce SELFIES (SELF-referencIng Embedded Strings), a string-based representation of molecules which is 100\% robust. Every SELFIES string corresponds to a valid molecule, and SELFIES can represent every molecule. SELFIES can be directly applied in arbitrary machine learning models without the adaptation of the models; each of the generated molecule candidates is valid. In our experiments, the model's internal memory stores two orders of magnitude more diverse molecules than a similar test with SMILES. Furthermore, as all molecules are valid, it allows for explanation and interpretation of the internal working of the generative models., Comment: 6+3 pages, 6+1 figures

In this work we introduce PHOENICS, a probabilistic global optimization algorithm combining ideas from Bayesian optimization with concepts from Bayesian kernel density estimation. We propose an inexpensive acquisition function balancing the explorative and exploitative behavior of the algorithm. This acquisition function enables intuitive sampling strategies for an efficient parallel search of global minima. The performance of PHOENICS is assessed via an exhaustive benchmark study on a set of 15 discrete, quasi-discrete and continuous multidimensional functions. Unlike optimization methods based on Gaussian processes (GP) and random forests (RF), we show that PHOENICS is less sensitive to the nature of the co-domain, and outperforms GP and RF optimizations. We illustrate the performance of PHOENICS on the Oregonator, a difficult case-study describing a complex chemical reaction network. We demonstrate that only PHOENICS was able to reproduce qualitatively and quantitatively the target dynamic behavior of this nonlinear reaction dynamics. We recommend PHOENICS for rapid optimization of scalar, possibly non-convex, black-box unknown objective functions.

Understanding the relationship between the structure of light-harvesting systems and their excitation energy transfer properties is of fundamental importance in many applications including the development of next generation photovoltaics. Natural light harvesting in photosynthesis shows remarkable excitation energy transfer properties, which suggests that pigment-protein complexes could serve as blueprints for the design of nature inspired devices. Mechanistic insights into energy transport dynamics can be gained by leveraging numerically involved propagation schemes such as the hierarchical equations of motion (HEOM). Solving these equations, however, is computationally costly due to the adverse scaling with the number of pigments. Therefore virtual high-throughput screening, which has become a powerful tool in material discovery, is less readily applicable for the search of novel excitonic devices. We propose the use of artificial neural networks to bypass the computational limitations of established techniques for exploring the structure-dynamics relation in excitonic systems. Once trained, our neural networks reduce computational costs by several orders of magnitudes. Our predicted transfer times and transfer efficiencies exhibit similar or even higher accuracies than frequently used approximate methods such as secular Redfield theory

We present a study on the evolution of the Fenna-Matthews-Olson bacterial photosynthetic pigment-protein complex. This protein complex functions as an antenna. It transports absorbed photons - excitons - to a reaction center where photosynthetic reactions initiate. The efficiency of exciton transport is therefore fundamental for the photosynthetic bacterium's survival. We have reconstructed an ancestor of the complex to establish whether coherence in the exciton transport was selected for or optimized over time. We have also investigated on the role of optimizing free energy variation upon folding in evolution. We studied whether mutations which connect the ancestor to current day species were stabilizing or destabilizing from a thermodynamic view point. From this study, we established that most of these mutations were thermodynamically neutral. Furthermore, we did not see a large change in exciton transport efficiency or coherence and thus our results predict that exciton coherence was not specifically selected for.

Obtaining the exciton dynamics of large photosynthetic complexes by using mixed quantum mechanics/molecular mechanics (QM/MM) is computationally demanding. We propose a machine learning technique, multi-layer perceptrons, as a tool to reduce the time required to compute excited state energies. With this approach we predict time-dependent density functional theory (TDDFT) excited state energies of bacteriochlorophylls in the Fenna-Matthews-Olson (FMO) complex. Additionally we compute spectral densities and exciton populations from the predictions. Different methods to determine multi-layer perceptron training sets are introduced, leading to several initial data selections. In addition, we compute spectral densities and exciton populations. Once multi-layer perceptrons are trained, predicting excited state energies was found to be significantly faster than the corresponding QM/MM calculations. We showed that multi-layer perceptrons can successfully reproduce the energies of QM/MM calculations to a high degree of accuracy with prediction errors contained within 0.01 eV (0.5%). Spectral densities and exciton dynamics are also in agreement with the TDDFT results. The acceleration and accurate prediction of dynamics strongly encourage the combination of machine learning techniques with ab-initio methods.