With ARES, we successfully built and demonstrated an autonomous research system capable of learning to grow CNTs by developing an AI planner and linking it to an automated growth reactor with in situ characterisation used as feedback control to iteratively define, conduct and analyse experiments. ARES continuously improved its ability to target growth rates over a series of hundreds of experiments. Each robotically controlled experiment consisted of synthesising CNTs by a chemical vapour deposition (CVD) process where the ARES AI planner supplied the growth conditions—temperature, pressure, and partial pressures of ethylene, hydrogen and water vapour.

A unique feature of ARES is the use of a laser to individually heat small (10 μm) pillars of silicon pre-seeded with catalyst15,31–34 for the CVD reaction (see experimental details and Supplementary Figure S1 for a schematic diagram of the instrumentation). We chose cobalt as the growth catalyst (2 nm film on a 10 nm thick alumina support), which was deposited uniformly onto the micro-pillars. Each pillar was thermally isolated on a wafer of thousands of pillars, making it in effect an independent micro-reactor. This enabled hundreds of experiments to be conducted in series by moving from one pillar to the next, with the ability to change all the experimental input conditions (i.e., temperature, pressure and gas composition). In addition, because of our unique configuration, ARES conducted its series of experiments without the need to exchange substrates from the growth chamber, thus enabling such high experimental throughput with minimal human intervention. Recently we demonstrated rapid automated experimentation with rates of up to 100 experiments per day (compared to 1 per day for conventional methods) for a series of 534 experiments in multi-dimensional parameter space.15

The ARES heating laser also served as the excitation source for Raman spectroscopy, enabling in situ acquisition of spectra during CNT growth. The characteristic Raman peak from CNTs, called the G band, corresponds to tangential vibrations of the carbon atoms, and its intensity is representative of the yield.31 ARES uses the increase in intensity of the G band with time during each experiment to determine the CNT growth rate, ν exp (taken as the maximum experimentally observed growth rate, see Supplementary Figure S2). The experimental growth rate was used as the signal for the ARES feedback loop.

Our overall objective for ARES was to autonomously learn to control the growth rate of CNTs using AI and closed-loop feedback over many experimental iterations. And so, building on our previous work, we implemented an AI planner that proposed new experimental growth conditions based on an analysis of a database of prior experiments, iteratively improving its ability to predict growth rates. The AI experimental planner was comprised of a random forest model35 with growth conditions exercised through a genetic algorithm.36 This combination was chosen for its ability to capture nonlinear relationships between input and output variables within disjoint design spaces,37 which we deemed appropriate for the complexity of nanotube growth. It is currently implemented in a customised version of the Lockheed Martin Nanotechnology Material Data Mining, Modeling & Management (NMD-M3) software tool.38 Before the first autonomous experiments, an initial set of 84 experiments was conducted to provide a database of prior knowledge needed for the random forest planner to build its first model. These experiments were designed to span the growth parameter input space in a grid style and were executed in automated mode, i.e., with pre-planned conditions supplied by the user but executed without user intervention.

Once the initial database was established, ARES performed a series of more than 600 experiments in autonomous mode, where the AI planner generated input conditions for each experiment. For each experimental iteration the AI planner received an objective growth rate from the user. It then analysed the database of prior experiments and generated new experimental growth conditions expected to achieve a predicted growth rate, ν pred , that targeted the user-supplied objective growth rate. Because the database incompletely spans the experimental parameter space, the predicted growth rate can differ from the objective, a known effect arising from domain applicability.39 After each experiment the database of prior experimental results was updated with the resultant experimental growth rate, and the planner refined its model representation to reflect the latest information. Over the course of the experimental campaign the user periodically modified the objective growth rate to cause ARES to probe a broader span of the experimental parameter space, which increased its domain coverage. To test for convergence between the predicted and experimentally achieved growth rates, series of experiments were grouped into tasks of 29–94 experiments. The objective growth rate was held constant for later tasks, but varied within some earlier tasks (see Supplementary Table S1).

The results of the convergence test are shown in Figure 1a, which compares the experimental growth rates to the growth rates predicted by ARES. Note that as ARES gained more experience, i.e., as the cumulative number of experiments increased, the spread between experimental and predicted growth rates became smaller, thus demonstrating experimental convergence. We quantified convergence by normalising the difference between experimentally obtained and predicted growth rates: Δ = ν exp − ν pred ν pred in Figure 1b. The mean values of Δ, μ Δ and their s.d.s., σ Δ , for each task enabled a statistical treatment of the data to analyse the trend towards convergence. As ARES learned to target growth rates, the mean difference from the prediction trended towards zero, implying that it successfully predicted the experimental growth rate. Moreover, the s.d. reduced to approximately 30%. To understand the context of these s.d. values, we conducted a series of experiments using the same input conditions, and analysed the statistical spread in the experimental growth rate. We found that the intrinsic variability in the system, which we termed the noise floor, over 20–30 experiments ranged from 20 to 30%, which is similar to the value found by Oliver et al. for their automated CNT growth furnace.14 By the end of the experimental campaign the variability in the experimental values matched the noise floor. Thus we conclude that ARES was able to target growth rates to the degree of variability intrinsic to our system. Hereafter we use ‘on-target’ to refer to experiments whose growth rates matched the predicted growth rates within the variability of the system.

Figure 1 Demonstration of ARES learning to target CNT growth rates. (a) Experimental and predicted growth rates. (b) Mean (μ Δ )and s.d. (σ Δ ) of the normalised difference between experimental and predicted growth rates. Initially the experimental rates were scattered far from the predicted (i.e., large σ Δ and μ Δ deviating from zero). As ARES learned over hundreds of experimental iterations the experimental rates converged (shaded area) to the predicted ones. This resulted in μ Δ trending towards zero, and σ Δ trending towards 30%, the noise floor of the system. Full size image

Having achieved experimental convergence we endeavoured to analyse the results with ex situ characterisation and data mining. We extracted a subset of experiments that achieved the targeted growth rate. Scanning electron microscopy imaging after growth confirmed that experimental growth rates measured in situ were commensurate with CNT yield. Figure 2 shows the results of growth experiments that achieved on-target rates of 500, 3,000 and 16,000 s−1, and demonstrates that the density of CNTs in the scanning electron microscope images is proportional to the experimentally observed growth rates.

Figure 2 SEM images demonstrating correlation between growth rate and yield of CNTs. On-target experiments with growth rates near the predicted ones of (a) 500, (b) 3,000 and (c) 16,000 (s−1). The time over which the nanotubes grew was approximately the same. The amount of nanotubes in the images increased in proportion to the growth rate. Scale bars: 500 nm. Full size image

We then analysed the progression of experimental conditions selected by ARES that led to growth rate convergence. In each iteration, the initial sampling of growth conditions from the genetic algorithm was inherently stochastic, yielding a ranked list of suggested experiments where predictions closest to the objective were prioritised. In order to avoid proposing the same experiment repeatedly, suggestions from using the genetic algorithm were further filtered based on proximity to existing data (assessed by Euclidian distance), to prioritise selection of ‘different’ experiments. In an early task, when models were trained from a limited and sparse data-set, this strategy led to emphasis on a broad range of parameter choices (Figures 3a and b) and resulted in few experiments matching the predictions: Only 8% were on-target. In a later task (Figures 3c and d) models were trained from a three times larger data-set. The resulting improvement in models’ fidelity led to better match between predictions and experiments (68% of on-target experiments) and a narrow range of experimental parameters selected by the filtering algorithm. The narrow ranges of parameter choices in Task 10 are significant, representing convergence on a set of growth conditions that can be used as a growth recipe.

Figure 3 Variability in the experimental parameter space with learning. Experimental conditions chosen by ARES in Task 3, before convergence (a, b), and in Task 10, after convergence (c, d), are compared over four experimental parameters (temperature, water concentration, and H 2 and C 2 H 4 partial pressures). Red dots represent successful, on-target experiments. (a, b) Before convergence ARES sampled a wide range of growth conditions, and only 8% of experiments were on-target. (c, d) After convergence ARES sampled a narrow range of growth conditions, with 68% on-target experiments, demonstrating its ability to autonomously optimise multiple experimental parameters. Full size image

We then analysed the entire database of experiments for insights into growth kinetics. The average water/ethylene ratio in Task 10 is 1.6×10−3 (Supplementary Figure S3a), which is comparable to the 1×10−3 reported to maximise CNT yield and growth rate by Futaba et al.40,41 We also found that the rate dependence on the temperature (Supplementary Figure S3b) corresponds to the well-established Puretzky model42 with activation energy E a =1.1±0.3 eV, which is within the 0.6–1.5 eV range reported in the literature and is interpreted as the activation energy of the precursor decomposition reaction on the catalyst surface.42–44

The data mining results highlight ARES’ ability to search across a complex, multi-dimensional parameter space. All of these growth parameters are known to significantly affect CNT growth, and typically require extensive experimentation and serial optimisation by conventional methods.40,41 The ability of the ARES planner to optimise multiple experimental parameters simultaneously and converge on the predictions highlights its efficacy in solving complex materials research problems that challenge human researchers using conventional, non-autonomous research processes.