Systems and methods for use in Bayesian optimisation

Abstract

Fig 1 Performing a Bayesian Optimisation, BO, process 300 to determine input parameter values to a system, from a parameter space of possible input parameter values, that optimise an output of the sys

Description

Field Aspects herein relate to computer implemented methods for performing a Bayesian Optimisation process for determining a plurality of input parameter values to a system, from a parameter space of possible input parameter values, that optimise an output of the system. Background Optimisation algorithms such as Bayesian Optimisation are used in many technical disciplines to determine optimal parameters values or optimal combinations of parameter values in a technical system. In chemical engineering, for example, optimisation may be used to design efficient chemical reactors or to determine the optimal conditions at which such reactors might be used. In an example scenario, inflow rate of reagents and the temperature of a reactor may be optimised to produce a maximal amount of yield or product from the reactor. Furthermore, the shape and configuration of the reactor (e.g. the reactor geometry) may also be optimised to further improve the product yield. As another example, in a reactor where Nitrogen and Carbon is fed to yeast cells, Bayesian Optimisation can be used to find the combination of parameter values (e.g. Nitrogen, Carbon, vitamins, trace minerals, and / or Temperature) that maximises the cell yield after a given time period (e.g. 72 hours). A tutorial on Bayesian Optimisation can be found in the paper by Peter Frazier (2018) entitled: “A Tutorial on Bayesian Optimization"', arXiv 1807.02811. The algorithm works iteratively, in that for any given problem, an initial combination of parameters is selected (which may be a “best guess”) and an experiment using the initial parameters is performed (either via simulation or via real-world experimentation). A new set of parameter values for experimentation are then selected by applying an acquisition function on a regression model (e.g. most commonly a Gaussian process regression), that (i.e. the acquisition function) is defined to determine the next point in the parameter space that should be sampled (or queried) for most efficient convergence to an optimum. Bayesian Optimisation can be expensive computationally (if the experiments are run via simulation), in terms of monetary value (if the experiments are run in real laboratories) and / or in terms of time. Thus, there is interest in incorporating cheaper-to-query approximations into Bayesian Optimisation processes where possible. In Multi-Fidelity Bayesian Optimisation (MFBO), experiments, or simulations can be run with more than one fidelity (e.g. at more than one accuracy level). For example, simulations may be run at different resolutions (e.g. at different fidelities). Alternatively, real-life experimental data may be obtained in facilities with different known levels of accuracy. Experiments or simulations at the different fidelity levels may be associated with different “costs”, be that monetary costs associated with running the experiments, or computational resource costs associated with running computer simulations. In MFBO, the Bayesian Optimisation takes these factors into consideration and in each iteration, not only outputs the next set of parameter values that should be sampled, but also outputs the fidelity level at which the respective experiment or simulation should be performed. In such scenarios, the fidelity is optimised by taking an overall cost-level for the entire optimisation process into account, along with the costs associated with running a simulation or real-world (e.g. lab) experiment at each fidelity level. In such optimisation processes, the MFBO process tends to select the low-fidelity experiment at the beginning of the process and the higher fidelity process towards the end of the optimisation process. As an example of MFBO, consider a scenario in which there are two experimental set-ups that can be used in each iteration, Reactor 1 and Reactor 2. Experiments can be performed in both, but R1 is expensive and accurate (e.g. high fidelity), while R2 is cheap and approximate (e.g. low fidelity). With MFBO, both experimental setups, R1 and R2 can be “pooled”, to find the optimum parameter values faster and at lower cost than using either R1 or R2 for all experiments. This can be used in many applications, one example being cell yield optimisation. This is achieved by querying Gaussian process models of each R1 and R2 after each experiment, to determine the level of Information Gain that can be expected from running an experiment with each model, weighted by their cost. At some points it is determined to be more informative to run a cheap, but only approximate R2 experiment a few times, before running a high-fidelity expensive R1 experiment. In general, it is observed that MFBO tends to query the cheap low-fidelity R2 in the beginning of an optimisation experimental campaign and relies more on the high-fidelity R1 at later stages. The paper by Mikkola et al. (2023) entitled "Multi-Fidelity Bayesian Optimisation with Unreliable Information Sources” describes another MFBO process that is modified to account for a scenario where one of the fidelity experiments is fundamentally unreliable or “uninformative”, e.g. due to bias or similar. This is known as robust-MFBO, or r-MFBO. Figure 1 in this paper contains a graph showing how the MFBO setup (the pink line in Figure 1 of the paper) outperforms the single-fidelity approach (SFBO, e.g. such as the classic Bayesian Optimisation described in the Frazier 2018 reference above), at least in the beginning of the optimisation process. The graph shows that r-MFBO can handle the case where the low-fidelity auxiliary R2 is not actually informative (which would happen in scenarios where e.g. a bias constant is introduced that can distort (often quite dramatically) the experimental result, making it less representative / accurate). r-MFBO assumes the classic MFBO algorithm, and introduces two conditions to the optimisation loop which, if true, result in selection of the low fidelity experimental set up: Condition 1: checks if the variation around the high-fidelity is significantly low, according to a user chosen parameter c1. Condition 2: checks if the low-fidelity is informative “enough” according to a user chosen parameter c2. When both conditions are true, the low-fidelity experiment is queried. The model is then updated with the newly acquired data-points, and the next iteration of the optimisation is then performed. This leads to more robust performance in the uninformative low-fidelity case. Generally, rMFBO helps alleviate the performance loss due to misleading information of a low / auxiliary fidelity that was assumed to be reliable. Usually, the unreliability of a low-fidelity is not immediately obvious to the user due to e.g. human failure (data entry mistakes) or sensor degradation, this method can help to compensate for such unreliability. Summary of Invention As described in the Background section, there are various types of Bayesian Optimisation processes, from the traditional SFBO which queries or samples data from a single experimental set-up, to MFBO where experimental setups with different fidelities are sampled and the costs associated with sampling each different fidelity type taken into consideration. r-MFBO is a further advancement to these optimisation processes, that produces more rapid convergence than MFBO in multi-fidelity scenarios where there is low informational gain through one of the fidelities. MFBO and r-MFBO only apply however where all the experimental set-ups (or simulations) can be freely queried according to the needs of the r-MFBO process, for specific costs. However, this isn’t always the case. For example, experimental setups (e.g. reactors, laboratories, and the like) can be decommissioned or upgraded. In such scenarios, there may be historical data applicable to a particular optimisation problem taken at one fidelity using a reactor, R3, that is no longer freely and individually available for new experiments, while R1 and R2 may still be available for querying in subsequent new experiments / iterations of the optimisation. It is an objective of embodiments herein to provide robust optimisation processes in such circumstances. According to a first aspect herein there is a computer implemented method for performing a Bayesian Optimisation, BO, process for determining a plurality of input parameter values to a system, from a parameter space of possible input parameter values, that optimise an output of the system. The BO process has access to a first experimental set-up that is queryable as part of the BO process, and a first set of historical data obtained from queries of a second experimental set-up. The second experimental set-up is not queryable as part of the BO process. The method comprises: i) determining a first point in the parameter space to query by maximising an acquisition function of the BO process that takes a first dataset comprising data obtained from previous queries of the first experimental set up into account; ii) determining a second point in the parameter space to query by maximising the acquisition function, taking both the first dataset and the first set of historical data obtained from the queries of the second experimental set-up into account; iii) selecting one of the first point and the second point according to one or more criteria related to a level of relevance predicted to be obtained by querying the first experimental set-up using the first point compared to the second point; and iv) initiating a query of the first experimental set up with input parameter values corresponding to the selected point. In this way, the BO process herein can take historical data into account, in a similar manner to transfer learning, even if the historical data set was obtained on an experimental set up that is no longer queryable and / or had a different set up conditions or other fixed constraints. Each query is improved compared to if the historical data weren’t taken into account and thus, the process herein converges faster, resulting in an improved outcome, in less time and based on fewer resources. In some embodiments, if in step iii) the second point in the parameter space is selected, in step iv) the first experimental set up is queried with input parameter values corresponding to the second point. In other words, the first experimental set up is queried. In some embodiments, the method further comprises: v) obtaining a result from the query in step vi); and updating the first dataset with the result of the query. In some embodiments, the BO process further has access to a second set of historical data obtained from one or more other experimental set-ups that are not queryable as part of the BO process. In such embodiments, in step ii), the step of maximising the second acquisition function further takes the second set of historical data into account. In some embodiments, the BO process further has access to a third experimental set-up that is queryable as part of the BO process. In such embodiments, in step ii), the step of maximising the acquisition function further takes data obtained from previous queries of the third experimental set up into account. In some embodiments, the method of any one of the preceding claims wherein the first experimental set-up is of higher fidelity than the second experimental set up. In some embodiments, steps i), ii), iii) and iv) are repeated to perform a sequence of queries on the first experimental set up, each query having input parameter values corresponding to a respective selected point. In some embodiments, the method further comprises taking parameter values corresponding to the best output across the iterations as the optimised parameter values output by the BO process. In some embodiments, the method further comprises sending an instruction to operate the system using the optimised parameter values output by the BO process. In this way, a fully automated laboratory can be facilitated. In some embodiments, the first experimental set up and / or the second experimental set up are real-world approximations of the system. In some embodiments, the first experimental set up and / or the second experimental set up are computer implemented simulations of the system. In some embodiments, the system is a biological, chemical or physical system. In some embodiments, the system comprises a reaction chamber; the input parameters relate to one or more variables that affect a yield of a reaction performed in the reaction chamber: and the output is the yield of the reaction when the reaction is performed in the reaction chamber. The reaction can be a biological or chemical reaction. In some embodiments, the reaction chamber is a yeast cell reactor; the input parameters comprise concentrations or types of nutrients and / or one or more incubation conditions in the chamber; and the output is yield of ethanol produced by the reaction. According to a second aspect, there is an apparatus for performing a Bayesian Optimisation, BO, process for determining a plurality of input parameter values to a system, from a parameter space of possible input parameter values, that optimise an output of the system. The BO process has access to a first experimental set-up that is queryable as part of the BO process, and a first set of historical data obtained from queries of a second experimental set-up, wherein the second experimental set-up is not queryable as part of the BO process. The apparatus comprises: a memory comprising instruction data representing a set of instructions; and a processor configured to communicate with the memory and to execute the set of instructions. The set of instructions, when executed by the processor, cause the processor to: i) determine a first point in the parameter space to query by maximising an acquisition function of the BO process that takes a first dataset comprising data obtained from previous queries of the first experimental set up into account; ii) determine a second point in the parameter space to query by maximising the acquisition function, taking both the first dataset and the first set of historical data obtained from the queries of the second experimental set-up into account; iii) select one of the first point and the second point according to one or more criteria related to a level of relevance predicted to be obtained by querying the first experimental setup using the first point compared to the second point; and iv) initiate a query of the first experimental set up with input parameter values corresponding to the selected point. In some embodiments, the processor is further caused to perform the method of the first aspect. In some embodiments, the apparatus further comprises the first experimental set up and in step iv, the processor is caused to send an instruction to the first experimental set up; and in response to the instruction, the first experimental set up is caused to perform an experiment with input parameter values corresponding to the selected point; and send results of the experiment to the processor upon completion. In a third aspect there is a computer program comprising instructions which, when executed by a computer cause the computer to perform the method of the first aspect. In a fourth aspect there is a computer readable storage medium comprising instructions which when executed by a computer cause the computer to carry out the method of the first aspect. Brief Description of the Drawings The invention will now be described with respect to the drawings in which: Fig. 1a illustrates a system according to an embodiment herein; Fig. 1b illustrates an example system according to some embodiments herein; Fig. 2 illustrates a computer node according to embodiments herein; Fig. 3 illustrates a method according to embodiments herein; Fig. 4 illustrates a system according to some embodiments herein; Fig. 5a shows a first set of experimental results; and Fig. 5b shows a second set of experimental results. Description The disclosure herein relates to a new Bayesian Optimisation (BO) process. The BO processes herein can generally be used to determine an optimal combination of input parameter values to a system that optimise an output of the system. The skilled person will be familiar with BO processes which generally involve iteratively sampling or querying different points in a parameter space of possible input parameter values, and learning from the results of previous queries in order select subsequent points in the parameter space to query, to eventually determine the optimal parameter value combinations. It will be appreciated that the words “optimal” or “optimised” as used herein may refer to combinations of parameter values that are close to optimal, within a threshold error value of optimal, the “best” parameters found within a certain time period, or for a certain cost expenditure, or any other measure of the “best parameters” found during the process. Bayesian Optimisation is generally well-suited to black-box problems where the process has access to input and output data, but without detailed knowledge of how the outputs are obtained from the inputs. In such scenarios, the input x is transformed to the output Y via a black-box function f : X^Y and the optimisation is performed via experiments through systematic exploration and exploitation processes. An example system 100 is illustrated in Fig. 1a. The systems herein can be any real-world system or process suitable for optimisation using Bayesian Optimisation. As an example, the system may be any biological, chemical or physical system. Various examples are given in Appendix I below. As an example, the system may be a reaction in a reaction chamber. In such embodiments, the input parameters to the BO process correspond to the (real-life) variables that affect the yield of a reaction performed in the reaction chamber. The output is the yield of the reaction when the reaction is performed in the reaction chamber. It will be appreciated that a reaction, as used herein, may refer to any type of chemical or biological (e.g. bio-chemical) reaction. Examples include, but are not limited to, a biological reaction in which yeast cells are used to produce synthetic fuels, and chemical reactions in which the chemical yield of the chemical reaction is optimised (e.g. chemical reaction yield maximisation). In these examples, the reaction chamber is the vessel in which the reaction is performed. In examples where the reaction is a chemical reaction, the input parameters may include, but are not limited to one or more reagents and / or one or more reaction conditions. For example, the input parameters may relate to the choice of solvents, ligands, bases and / or any other inputs to the reaction. Other example inputs may include but are not limited to, the reaction conditions, e.g. the Temperature, light levels, pressure levels (e.g. height above sea level) or any other variable or parameter value that can be changed that might have an effect on the output. For example, chemists are interested in optimising methanol synthesis, as described in the article: “Optimization of methanol yield and carbon dioxide utilization in methanol synthesis process" by Rui Kong and Yu Lin: Vol. 2 (2024): 3rd International Conference on Advances in Materials, Machinery, Electrical Engineering (AMMEE 2024). This system is illustrated in Fig 1b. Here, temperature and reactor 104 geometry are input parameters whose values need to be optimised over to maximise methanol synthesis. Many other input parameters can be added to the optimisation problem that could help increase yield even further. In examples where the system is a biological reaction, the input parameters may include but are not limited to: one or more nutrients (e.g. vitamins and / or trace minerals) and or one or more incubation conditions (e.g. temperature, light pressure, etc). In cell biology, yield optimisation, is a common goal, too. Yeast, animal or human cells are grown in laboratory settings which can be optimised in regards to temperature, reactor conditions among others. For example, in the paper by Cosenza et al. (2023) entitled: “Multi-objective Bayesian algorithm automatically discovers low-cost high-growth serum-free media for cellular agriculture application”, cell yield is maximised using Bayesian Optimisation on the input parameters of Nitrogen, Carbon, Vitamins and Trace materials. Yield is measured via growth of lipids in weight or the optical density of the cells. The optimal combination of input parameter values leads to the maximum yield. In terms of transfer learning BO, historical records of similar cell yield experiments can help accelerate the discovery of these optimal conditions. As noted in the background section, in an example reactor where Nitrogen and Carbon is fed to yeast cells, Bayesian Optimisation can be used to find the combination of parameter values (e.g. Nitrogen, Carbon, vitamins, trace minerals, and / or temperature) that maximises the cell yield after a given time period (e.g. 72 hours). Although many examples herein relate to chemical and / or biological reactions, it will be appreciated that the processes described herein can be applied to a wide range of other types of optimisation problems, and are not limited to Chemical and / or Biological reactions. For example, the BO processes herein can be used in physical systems. For example, in design problems, to optimise the design (e.g. shape, volume, number or position of inflows / outflows from the reaction chamber) of a reaction chamber in order to maximise the fluid flow through the chamber (or to maximise yield from the chamber). In other examples, the BO process herein could be used in vehicle design (ground-based or aerial vehicles such as cars, vans, lorries, trains, planes) in order to determine optimal design shapes that minimise drag or turbulence when the vehicle is in motion. Embodiments herein are at least partly computer implemented and as such can be performed by one or more computer nodes. Figure 2 shows a node (e.g. a computing node) that may form part of some embodiments herein. A node 200 may generally be configured (e.g. operative) to perform any of the methods and functions described herein, such as the method 300 described below. The node 200 comprises a processor 202, a memory 204 and set of instructions 206. The memory holds instruction data (e.g. such as compiled code) representing set of instructions 206. The processor may be configured to communicate with the memory and to execute the set of instructions. The set of instructions, when executed by the processor, may cause the processor to perform any of the methods herein, such as the method 300 described below. Processor (e.g. processing circuitry or logic) 202 may be any type of processor, such as, for example, a central processing unit (CPU), a Graphics Processing Unit (GPU), a Neural Processing Unit (NPU), or any other type of processing unit. Processor 202 may comprise one or more sub-processors, processing units, multi-core processors or modules that are configured to work together in a distributed manner to control the node in the manner described herein. The node 200 may comprise a memory 204. In some embodiments, the memory 204 of the node 200 can be configured to store program code or instructions that can be executed by the processor 202 of the node 200 to perform the functionality described herein. The memory 204 of the node 200, may be configured to store any data or information referred to herein, such as, for example, requests, resources, information, data, signals, or similar that are described herein. The processor 202 of the node 200 may be configured to control the memory 204 of the node 200 to store such information. In some embodiments, the node 200 may be a virtual node, e.g. such as a virtual machine or any other containerised computer node. In such embodiments, the processor 202 and the memory 204 may be portions of larger processing and memory resources respectively. It will be appreciated that a computing node 200 may comprise other components to those illustrated in Fig 2. For example, node 200 may comprise a power supply (e.g. mains or battery power supply). The node 200 may further comprise a wireless transmitter and / or wireless receiver to communicate wirelessly with other computing nodes. In some embodiments, the node 200 may have a wired connection with which to communicate with other computing nodes. Such wireless and / or wired connections may be used, for example to send instructions to one or more experimental set ups in order to instruct said experimental setups to perform an experiment or query according to embodiments herein. Equally, such wired or wireless connections may be used to receive results from the one or more experimental set ups, as part of the BO process. In some embodiments, the node 200 may further comprise a user input device such as a mouse, keyboard, or touch pad, for receiving input user data. In some embodiments, the node 200 may further comprise a display for displaying any of the data described herein, such as for example, any of the outputs (or intermediate data products) of any of the methods described herein. In some embodiments, as illustrated in Figure 4, the node 200 may form part of a larger system, such as an automated or semi-automated laboratory. In such embodiments, the node 200 may (as noted above) send instructions to an experimental set up 400 (e.g. equipment) associated with the automated or semiautomated laboratory, to cause the equipment to perform experiments (e.g. with input parameter values as determined using the methods and processes described herein). The node 200 may further send and / or receive data from a database 402. Such a database may store information such as the results of historical queries as described herein. Turning now to Fig. 3, there is a method 300 for performing a BO process for determining a plurality of input parameter values to a system, from a parameter space of possible input parameter values, that optimise an output of the system. The method 300 can be performed by one or more computer nodes 200, as described above. In embodiments herein, the optimisation problem may be to determine the combination of input parameter values that produce the “best” output. As noted above, the optimal or best output, maybe the best output found during the experiments performed as part of the BO process. Best or optimal does not necessarily refer to what is objectively the ’’best possible” output on all scenarios. Furthermore, the “best” may refer to the combination of input parameters that maximise the output yield. In other examples, the best may refer to the combination of input parameters that minimise an error term, or difference in particular values, depending on how the efficacy of the reaction is measured. In embodiments of the method 300, the BO process has access to a first experimental set-up that is queryable as part of the BO process, and a first set of historical data obtained from queries of a second experimental set-up. The second experimental set-up is not queryable as part of the BO process. In brief, the method 300 comprises the following steps. In a first step 302, the method 300 comprises i) determining a first point in the parameter space to query by maximising a acquisition function of the BO process that takes a first dataset comprising data obtained from previous queries of the first experimental set up into account. In a second step 304, the method 300 comprises ii) determining a second point in the parameter space to query by maximising the acquisition function taking both the first dataset and the first set of historical data obtained from the queries of the second experimental set-up into account. In a third step 306 the method 300 comprises iii) selecting one of the first point and the second point according to one or more criteria related to a level of relevance information gain predicted to be obtained by querying the first experimental set-up using the first point compared to the second point. In a fourth step 308 the method 300 comprises iv) initiating a query of the first experimental set up with input parameter values corresponding to the selected point. In more detail, an experimental set up, as used herein can refer to a computer simulation of the system, or any other model of the system. In other embodiments, an experimental set up can be a real-world instance (e.g. mock-up, test rig, or other approximation) of the system. The first experimental set up is freely and individually queryable. As such, the method 300 may involve formulating and / or sending an instruction to the first experimental set up to cause the first experimental set up to perform a query (e.g. perform an experiment) with input parameter values that have been determined as part of the BO process. The second experimental set up is not queryable as part of the BO process. The second experimental set up may have, for example, been dismantled, discarded, upgraded, or is otherwise unavailable for querying. As another example, there may be ownership issues that prevent the second experimental se up from being queried. The historical data set contains the results of previous queries that were run on the second experimental set up. These may have been reported or obtained e.g. via an academic paper, or any other type of database. As such, in some embodiments herein, only the first experimental set up can be queried. Each “query” corresponds to an experiment or simulation run on the first experimental set up. The query effectively samples a point in the multi-dimensional parameter space of possible input parameter value combinations to the system, and the result of the query is a measure of the output of the system when input parameter values corresponding to the queried point in the parameter space are input to the system. The methods herein can generally be used to learn (or incorporate learnings) from historical data taken under slightly different conditions to the present system or experimental set up of interest. As such, the queryable first experimental set up may be an experimental set up of interest (e.g. that is intended for subsequent use) and the historical data from the second experimental set up may be historical data obtained on a similar, but non-identical system. Some example scenarios are outlined in the first row of Appendix I. For example, a BO process may be performed for a 2 litre reaction chamber (representing the first experimental set up), and there may be historical data available that was taken in a 1 litre reaction chamber. The BO process herein allows useful learnings to be obtained from the earlier data, despite the fact that it has a slightly different set up conditions. In another example, experiments may be made using similar (but nonidentical) cell-biologies. E.g. historical data may be available for a related strain of cell to what is currently being used in the first experimental set up. In another example, the historical data may have been taken at a different site, e.g. with different ambient conditions, or at different heights above sea level. In another example the input materials to a chemical reaction may have changed. Even a change of supplier can result in subtle, but non-negligible effects on a chemical reaction. The examples above illustrate how the BO process described herein is akin to a transfer learning scenario. In some embodiments, the first and second experimental set-ups can have different fidelities. For example, computer simulations can be run at different resolutions, and real-world experiments (test-rigs, test set-ups and the like) can have different levels of accuracy and / or bias. As an example, the first experimental set up may be higher fidelity than the second experimental set up. This could be the case, for example, if the first experimental set up supersedes the second experimental set up (e.g. if the second experimental set up is old, retired, or otherwise biased). In some embodiments, where the first experimental set up is a computer implemented simulation, a continuum of resolutions of simulation may be possible, e.g. it may be possible to specify a different fidelity for each query. Generally, therefore, embodiments herein relate to scenarios in which the BO process has access to two types of data: a first dataset comprising data obtained using the first experimental set up that can be freely queried. The first dataset can be added to with the results of further queries each time a query or experiment is run on the first experimental set up. The second type of data available to the BO process is historical data obtained from queries that were performed on a second experimental set up that is no longer queryable as part of the BO process (and may have a different fidelity and / or different conditions as described above). Embodiments herein represent a modification to existing BO processes and provide a mechanism for determining the level of information that can be gained from the historical data, and, whether, in each iteration of the BO process, it would be better, e.g. more informative (or relevant) to select the next point to query based on just the first dataset (the results of queries or experiments performed on the first experimental set up) or, all of the available data, including the historical data that was obtained using the second experimental set up. It will be appreciated that the methods herein can be extended to third and subsequent experimental set ups. For example, there may be a third experimental set up that is queryable as part of the BO process. In such embodiments, only the first and third experimental set-ups are queryable. As such, as part of the BO process, in each iteration, the process may determine which of the experimental setups that are freely queryable (e.g. which of the first experimental set up and the third experimental set up) should be queried, and with which input parameter values. It will be further appreciated, that there may be a second set of historical data obtained from one or more other experimental setups that are not queryable by the BO process. There may thus be historical datasets from different sources available to the BO process. There may generally be various steps preceding steps i-iv of the method 300. For example, preceding the method 300 there may be one or more initialisation steps. For example, the BO processes herein may be initialised by receiving user input that sets various parameters that are to be used in the BO process. Example initialisation parameters that may be set in an initialisation step include, but are not limited to: a budget, cost of the first experimental set up (and / or costs associated with any other experimental set ups that are queryable, where applicable), fidelities of the first and / or second experimental set ups, an acquisition function (alpha), hyperparameters c1 and c2, and / or a relevance measure(s). These possible inputs to the BO process are described below. Budget: A budget may be set for the BO process. Generally, the budget sets one or more criteria or thresholds that define when the BO process should be ended, e.g. when no further iterations (e.g. queries) should be performed. As an example, there may be costs, such as monetary or computational costs associated with performing queries, and in some embodiments, the budget sets a cumulative ‘cost’ that should not be exceeded over the course of performing the BO process. In other examples, the budget may be a time budget, setting out a maximum time period over which the iterations can be run for. In other examples, if the budget is infinite (e.g. very low monetary or computational costs per iteration, or if there are no time constraints), a convergence criteria may be defined. E.g. the budget may indicate that the BO process should be terminated when the results converge within a particular threshold (a convergence threshold may be referred to as “lambda”). It will be appreciated that these are merely examples, and that other types of budgets may equally be set for a BO process. Costs of the (queryable) experimental set ups: cost values associated with performing an experiment on each queryable experimental set up (e.g. the first experimental set up and / or any subsequent queryable experimental set ups, if applicable) may be provided as input to the BO process. As noted above, cost may be measured e.g. in terms of a monetary, computational cost, time cost, or any other cost measure. Fidelities of the experimental set ups: In some embodiments, the fidelities of the first and / or second experimental set ups may be provided as input to the BO process. In some embodiments described below, where there is more than one queryable experimental set up, the fidelities, or relative fidelities of each queryable set up may be provided as input to the BO process. Acquisition Function (alpha): BO processes maximise an acquisition function with respect to a probabilistic model (which can, for example be a Gaussian Process) of the system of interest. The skilled person will be familiar with acquisition functions, probabilistic models and how these are set up. Various acquisition functions that can be used for the purposes herein are described in the paper by Mikkola et al. (2003) cited above. Hyperparameter values: as will be described in more detail below, in BO processes herein, a first ‘candidate’ point in the parameter space and a second ‘candidate’ point in the parameter space are selected in each iteration of the BO process, taking different portions of the available results data into consideration. Whether the first or second point is then selected for querying, is determined according to one or more (configurable) criteria. The one or more criteria may be user specified. In some embodiments, hyperparameters (e.g. thresholds, limits or the like) may be provided as input to the BO process for use in the criteria. Relevance Measure A mathematical function, user chosen, that calculates the ‘relevance’ of the low-fidelity or historical data. As will be familiar to the skilled person, a BO process generally aims, for a given black-box function to identify input parameters to the black-box function that result in an optimised output (optimised may refer to a maximum, minimum, or some other specified output, depending on the particular problem) of the black-box function, while simultaneously minimising incurred costs associated with searching and querying the input parameter space. Once the BO process is initialised, the steps of the method 300 are then performed in an iterative manner, sampling the parameter space to determine the point in the parameter space (e.g. the combination of input parameter values) that maximise the output of the system. In the first iteration of the BO process, there may be no previous experimental data taken with the first experimental set up. As such, in the first iteration, an initial point in the parameter space may be selected to start the BO process off. The initial point may be selected in different ways. In some examples, the initial point may be selected by maximising the acquisition function based on the first set of historical data obtained from the queries of the second experimental set-up. (This would correspond to performing steps ii) and iv) of the method 300, e.g. predicting the next point to query based on just the historical data from the second experimental set up, because the first dataset is empty at this point). This is merely an example however, and in other examples, the first query may be based on an arbitrary (“best guess”) point in the parameter space, either a random number from a random number generator, or an expert’s guess; a query based on the best output reported in the historical data obtained using the second experimental data; a query based on findings reported in an academic paper, or any other initial query. Once any initialisation steps are performed, the method 300 proceeds according to the steps outlined above. In step 302, the method 300 comprises i) determining a first point in the parameter space to query by maximising the acquisition function (that may e.g. have been received as input in an initiation step as described above), of the BO process. The acquisition function is maximised taking the data obtained from any previous queries of the first experimental set up into account. In this step, the BO process effectively determines the next point in the parameter space to query based on only the data obtained from the queryable experimental set up. In examples where this data is higher fidelity, this may mean selecting the point based on the higher fidelity data only. The skilled person will be familiar with maximising an acquisition function. In step 304, the same process is repeated and a second point in the parameter space is determined, however in step 304, the acquisition function is maximised taking both the first dataset and the first set of historical data obtained from the queries of the second experimental set-up into account. In step 304, the costs of the first and second experimental set ups may be disregarded (or set equal to one another), since they are all the same cost (the historical data is just a simple database query). As such, in steps 302 and 304 two points are selected for possible querying, one based just on the data from the first (freely queryable) experimental set up and one based on both the data from the first (freely queryable) experimental set up and the historical dataset from queries performed on the second (no longer queryable) experimental set up. The first and second points may be considered “candidate points”. One of the first point and the second point is then selected in step 306 as the next point to query. The point to be queried is selected using one or more criteria related to a level of relevance that the results of each query are predicted to have. Relevance in this sense might refer to informational relevance, informational gain, or any other measure of the relevance or quality of the output. The concept of information gain in the context of BO processes will be familiar to the skilled person, and again is described in the paper by Mikkola et al. (2003) cited above. As an example, in step 306, the criteria may be based on one or more user chosen criteria. In some examples, two thresholds may be defined, “c1” and “c2”. As an example, c1 may relate to a variance of the results obtained using the first experimental set up. “Variance” in this sense is the variation, e.g. how much the signal changes. Higher variance can sometimes can be interpreted as less reliable. Technically, this condition ensures that similar performance is achieved as SFBO, when the auxiliary is irrelevant, so the more variance it has the less ‘relevant’ it is, as a heuristic. c2 may relate to the information gain the historical data set. The selection of one of the first and second points may be made according to a relationship such as: “if the variance of the first data set is less than c1 and the information gain expected from the historical data set is more than c2, then use the first point, ELSE select the second point”. The choice of values of the hyperparameters cl and c2 is application specific, and informed best by simulation studies. In general, regardless of the choice of values for these two hyperparameters (c1 and c2), experiments performed by the applicant suggest that the BO process herein (e.g. the method 300 outperforms the known Transfer-Learning BO (TLBO) processes. It will be appreciated that this is merely an example however and that other criteria (or even a single criterion) may be appropriate in some circumstances. In step 308, whichever point in the parameter space is chosen, is then queried using the first experimental set up. For example, if the second point is selected, then the parameter values corresponding to the second point are used as input to the first experimental set up as a query for the first experimental set up. Put another way, irrespective of whether the first or second point is chosen, the first experimental set up is queried with the parameter values of the selected point. Step 308 may comprise sending an instruction (e.g. sending a first message) to the first experimental set up to cause the first experimental set up to perform the query. Following the query, the method 300 may further comprise receiving the results of the query performed in step iv. For example, the method may comprise receiving a second message from the first experimental set up, the second message indicating the results of the query. In a subsequent step, vi, the method 300 may then comprise updating the first data set with the results of the new query. In other words, the new point is added to the first data set containing the results of queries obtained using the first data set. Performing steps 302-308 results in an improved selection of the next point in the parameter space to query, enabling historical data to be taken into account, as well as data from a queryable experimental set up. This reduces the number of iterations in the BO process needed to determine the optimal input parameters in the parameter space, and speeds up convergence when compared to taking the data from the queryable experimental set up alone. Each iteration results in the selection of input parameter values that will lead to the optimal or “best” points faster. The full process (e.g. over a plurality of iterations) is faster (e.g. a faster optimisation), since each individual iteration is faster. Faster optimisation leads to less resource usage / cost of optimisation. The method may then be repeated, in an iterative manner whereby steps i)-iv) are repeated to perform a sequence of queries on the first experimental set up, each query having input parameter values corresponding to a respective selected point. In this way, the parameter space is explored to determine a set of input parameter values that maximise the output of the system. As noted above, the steps i)-iv) may be iterated over until one or more stop criteria is reached. As an example, if a budget was set as one of the input parameters, then steps i)-iv) may be iterated over until a cumulative cost associated with performing the sequence of queries reaches a cost budget. As noted above, the cost budget may be set in terms of any cost or resource measurement, e.g. cost, computing resources, time etc. The output of the BO process is the set of parameters values corresponding to the best or most desired output of the system. These parameter values correspond to the optimised parameter values. It will be appreciated that the “best” values may often be the highest output values of the system (e.g. such as in the chemical and / or biological reaction examples). However, in other scenarios, the best output may be when the output is minimised (e.g. a BO process may be performed to minimise wind turbulence in a jet engine, for example). Once the process is concluded and the optimal parameters have been determined, the method 300 may further comprise instructing (or sending and instruction to) the first experimental set up (or another experimental set up) to instruct the first experimental set up to run with the optimised input parameter values. Thus, the method 300 can be used to determine optimal input parameter values for a system and cause the system to run with said optimal input parameter values in an automated manner. This is relevant, for example, to automated laboratory processes, where the system may be a chemical or biological reaction chamber in the laboratory. An embodiment of the BO process described above is represented in pseudocode as illustrated below. Referring back to the background section of the application, the rMFBO process (described in Mikkola et al. (2023)) tackles a failure mode of the earlier MFBO process wherein if the auxiliary / low-fidelity reactor R2 is not actually informative, then the MFBO will be worse, compared to using rMBFO. The embodiment of the pseudocode below applies rMFBO to the related, but distinct, “Transfer Learning” BO setting (TLBO). In this setting, as described above, it is not possible to query any other fidelity apart from the current high-fidelity R1. In TLBO, we ‘transfer’ data from the auxiliary R2 fidelity, where we might have a database of 100 experiments from the R2 setup that has since been destroyed. In this pseudocode example, the first experimental set up is referred to as the TARGET and the second experimental set up is referred to as the SOURCE. As such, in examples herein, the TARGET is queryable, whereas the SOURCE is not queryable. Variable definitions: c1: user chosen parameter: see condition 1 c2: user chosen parameter: see condition 2 budget: how much money, or other resource can be spent, alternatively if budget is ‘infinite’ some will use convergence criteria defined below as lambda acquisition function: the mathematical criteria we use to decide which experiment to run next relevance measure s: a mathematical function, user chosen, that calculates the ‘relevance’ of the low-fidelity Pseudocode: • INPUT: budget, costs of fidelities, acquisition function alpha, hyperparameters c1 and c2, relevance measure s • Initialise dataset the source and target fidelity datasets • Perform Bayesian updates on the means and variances for both SOURCE, TARGET • Until budget is spent, do: • —I x_target = choose next point based on TARGET data only* • —I x_source = choose next point based on TARGET data AND SOURCE data** • —| IF [CONDITION 1: variance of TARGET <c1 ] AND [CONDITION 2: information gain in SOURCE >c2]*“: • —|—| run TARGET experiment with chosen SOURCE experiment point (x_source) • —|—| Perform Bayesian updates on the SOURCE means and variances • —|—| calculate pseudo-observation with chosen TARGET experiment point (x_target) • — |—| update source dataset with pseudo-observation from experiment • —|—| run TARGET experiment with chosen source experiment point (x_target)““ • —|—| update TARGET dataset with result from TARGET experiment • —| END IF • —|Perform Bayesian updates on the means and variances for both SOURCE, TARGET • Return final recommendation (e.g. maximum yield) from space satisfying condition 1 Notes: * This step corresponds to step 302 of the method 300 as described above ** This step corresponds to step 304 of the method 300 as described above ***This step corresponds to step 306 of the method 300 as described above ****These steps correspond to step 308 of the method 300 as described above Compared to previously described BO processes, such as that described in Mikkola et al. (2023), it is always the TARGET (e.g. first experimental data set up) that is queried, irrespective of whether the point to be queried is determined based on just the data from the first experimental set up, or both the data from the first experimental set up and the historical data set up. This provides a framework for taking historical data into account from experimental set ups that can no longer be queried, by, in each iteration of the BO processing, assessing whether the addition of the historical data will increase the relevance of the result of a point selected, or whether more information would be gained by disregarding the historical information and just using the data from the queryable experimental set up (e.g. the first dataset). It will be appreciated that generally, the process described above might be extended in various ways. As an example, there may be more than one historical data source (e.g. multiple sources). For example, there may be a second set of historical data comprising results from one or more other experimental set-ups that are not queryable as part of the BO process. E.g. other experimental set ups that have been retired, upgraded, or are inaccessible for some other reason. In such examples, the method 300 may be modified to take the additional information into account by, in step 304, above, selecting the second point in the parameter space by maximising the acquisition function, taking the first dataset, the first set of historical data and the second set of historical data into account. With respect to the pseudo code described above, the SOURCE of the data is usually indicated by a discrete or continuous index in an additional column of data (usually one of them is 0 and the other is 1) and can be extended to any number of sources or targets. These embodiments provide the opportunity to learn from more than one source of historical data, even if the experimental set up that it is derived from is no longer queryable itself. In another embodiment, there may be more than one queryable experimental set up (e.g. multiple targets). For example, there may be a first experimental set up that is queryable, a second experimental set up that is not queryable (and where only historical data is available from historic queries on this experimental set up), and a third experimental set up that is also queryable. The first and third experimental set ups may have different fidelities and / or different costs associated with performing queries on them. In such scenarios, the BO process may determine which combination of data to base the selection of the next point in the parameter space on e.g. just the first dataset, the first data set and the first historical data set, just a third dataset comprising results from the third experimental set up, or a permutation thereof. If there are multiple targets but nothing differentiates them, they may as well be just merged into one target. In classical MFBO for instance the targets are different because of their cost. In other examples, the targets may be differentiated by fidelity. In this scenario, the pseudocode example described above might be modified as follows:: • —| x_target = choose next point based on desired TARGET data only • —I x_source = choose next point based on desired TARGET AND other TARGET data AND ALL SOURCE data . —| IF [CONDITION 1: variance of TARGET <c1 ] AND [CONDITION 2: information gain in SOURCE >c2]: This is merely one example, however, and there may be other possibilities depending on the reasons why there are multiple targets. The pseudo code above provides the opportunity to combine historical data from redundant experimental set ups with the results of two or more experimental set ups that are queryable (e.g. potentially with different fidelities and costs). Experimental Data In statistical research, algorithms are compared via synthetic benchmarks (so called ‘analytic test functions’, i.e. closed-form mathematical formulas that closely represent solution spaces one would find in physics or chemistry) that allow complete control over the problem space. For Bayesian Optimisation, a commonly used test function is the Hartmann function, as described here: https: / / www.sfu.ca / ~ssurjano / hart6.html The Hartmann test function was used to evaluate the BO process described herein (i.e. the method 300). The benchmark scenarios used the following: • Test function • Baseline method against which the new method is compared, e.g. In this case, TLBO was used as a baseline. The TLBO process is described in the paper: ‘'Transfer Learning for Bayesian Optimizations Survey” by Bai et al. (2023) (arXiv:2302.05927). • Proposed method to evaluate, e.g. the method 300 described herein. • “Oracle” to showcase best possible performance. • Number of iterations per trial, ie how many times the BO loop is run (here: 10) • Number of trials, ie how many times we restart a trial, so we can average results and calculate confidence intervals (here: 10) For our evaluation of the method 300, we create two scenarios: A. Reliable SOURCE data the results of which are shown in Fig. 5a. Line 502 corresponds to the previous TLBO process (the dash-dot lines show the error on the points 502); 504 corresponds to the method 300 described herein (dashed lines represent the error associated with the points 504) and 506 corresponds to the Oracle described below (the dotted lines indicate the error associated with the Oracle). The x-axis of Fig. 5a shows the number of iterations of the respective processes and the y-axis indicates the best cumulative output. B. Unreliable SOURCE data the results of which are shown in Fig. 5b. Line 508 corresponds to the previous TLBO process (the dash-dot lines show the error on the points 508); 510 corresponds to the method 300 described herein (dashed lines represent the error associated with the points 510) and 512 corresponds to the Oracle described below (the dotted lines indicate the error associated with the Oracle). The x-axis of Fig. 5b shows the number of iterations of the respective processes and the y-axis indicates the best cumulative output. The “oracle” is described here: (https: / / datascience.stackexchange.com / questions / 24631 / what-is-oracle-in-statistics) The oracle transfers from the target itself to show the best possible performance (506 and 512 in Figs 5a and 5b respectively). In this empirical example, it can be seen that the method 300 described herein recovers about 85% of the optimisation performance compared to the earlier TLBO algorithm, as it converges on average close to the global optimum of “-3” after 10 iterations. Experiments such as these demonstrate that the processes herein works and delivers improvements over previous processes. Similar experiments have been performed to compare the method 300 against other BO processes, with similar results. Turning now to other embodiments, it will be appreciated that the method 300 may be embodied in a computer program. For example, a computer program product may comprise a computer readable medium, the computer readable medium having computer readable code embodied thereon. The computer readable code can be configured such that, on execution by a suitable computer or processor, the computer or processor is caused to perform the method or methods described herein (such as the method 300). A computer program may take different forms, for example, source code, compiled code, executable code, or any other type of code. It will be appreciated that the source code of computer programs may be written in a wide variety of different programming languages, and may take different architectural designs. For example, the functionality described herein may be split across various different sub-routines. Furthermore, the skilled person will appreciate that many different ways of splitting the functionality between the different sub-routines will be possible. The sub-routines may be stored together in one executable file to form a self-contained program. Furthermore, computer programs may call external and / or standard libraries of computer code for performing certain sub-tasks associated with the functionality described herein. In another embodiment, there is a computer program product comprising non-transitory computer readable media, having stored thereon a computer program as described above. Examples of computer readable media include, but are not limited to: ROM, such as a CD ROM, a semi-conductor ROM or a magnetic recording medium such as a hard disk. In another embodiment, there is a carrier containing a computer program. Examples of carriers include but are not limited to an electronic signal, optical signal, radio signal, computer storage medium, or similar. The carrier of a computer program may be any entity or device (e.g. hardware) capable of carrying the program. As an example, a carrier may be a computer readable media as described above. In other examples a carrier may be a transmissible carrier such as an electronic or optical signal, which may be conveyed via electrical or optical cable or by radio or other means. Variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure and the appended claims. In the claims, the word “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these claims cannot be used to advantage. Any reference signs in the claims should not be construed as limiting the scope. Appendix I —Example Scenario Reactor T ransfer (e.g. different sizes, from 1 litre to 2 litres) Similar Cell Biology (e.g. cell-line optimisation) Site Transfer (e.g. Japan -> UK, 200m sea level -> 400m sea level) Input Materials Change System Any chemical, biological or physical system. Any chemical, biological or physical system. Any chemical, biological or physical system. Any chemical, biological or physical system. INPUT Parameters One or more reagents: e g. solvents, ligands, bases, and / or one or more reaction conditions: e.g. concentrations One or more nutrients e.g. vitamins and trace materials And / or one or more incubation conditions e.g. temperature, One or more reagents: e.g. solvents, ligands, bases, and / or one or more reaction conditions: e.g. concentrations One or more reagents: e.g. solvents, ligands, bases, and / or one or more reaction conditions: e.g. concentrations OUTPUTS Output measure to be minimised or maximised, e.g. yield, optimal concentration of reagents and reaction conditions Output measure to be minimised or maximised, e.g. yield, optimal concentration of reagents and reaction conditions Output measure to be minimised or maximised, e.g. yield, optimal concentration of reagents and reaction conditions Output measure to be minimised or maximised, e.g. yield, optimal concentration of reagents and reaction conditions Example SOURCE DATA (e.g. historical data) Experiment at 90 degrees Celsius Animal cell experiment Reactor in Japan, 200m sea level reactor Chemical supplier A for experiment Example TARGET DATA (e.g. queryable experimental set up) experiment at 120 degrees Celsius human cell experiment Reactor in the UK 400m sea level reactor chemical supplier B for same experiment, slightly different purity of raw input

Claims

1. A computer implemented method (300) for performing a Bayesian Optimisation, BO, process for determining a plurality of input parameter values to a system, from a parameter space of possible input parameter values, that optimise an output of the system;the method being characterised in the BO process having access to a first experimental set-up that is queryable as part of the BO process, and a first set of historical data obtained from queries of a second experimental setup, wherein the second experimental set-up is not queryable as part of the BO process, the method comprising:i) determining (302) a first point in the parameter space to query by maximising an acquisition function of the BO process that takes a first dataset comprising data obtained from previous queries of the first experimental set up into account;ii) determining (304) a second point in the parameter space to query by maximising the acquisition function, taking both the first dataset and the first set of historical data obtained from the queries of the second experimental set-up into account;iii) selecting (306) one of the first point and the second point according to one or more criteria related to a level of relevance predicted to be obtained by querying the first experimental setup using the first point compared to the second point; andiv) initiating (308) a query of the first experimental set up with input parameter values corresponding to the selected point.

2. The method of claim 1 wherein, if in step iii) the second point in the parameter space is selected, in step iv) the first experimental set up is queried with input parameter values corresponding to the second point.

3. The method of claims 1 or 2 wherein the method further comprises:v) obtaining a result from the query in step iv); andvi) updating the first dataset with the result of the query.

4. The method of any one of the preceding claims wherein the BO process further has access to a second set of historical data obtained from one or more other experimental set-ups that are not queryable as part of the BO process; andwherein in step ii), the step of maximising the second acquisition function further takes the second set of historical data into account.

5. The method of any one of the preceding claims wherein the BO process further has access to a third experimental set-up that is queryable as part of the BO process; andwherein, in step ii), the step of maximising the acquisition function further takes data obtained from previous queries of the third experimental set up into account.

6. The method of any one of the preceding claims wherein the first experimental set-up is of higher fidelity than the second experimental set up.

7. The method of any one of the preceding claims further comprising repeating steps i), ii), iii) and iv) to perform a sequence of queries on the first experimental set up, each query having input parameter values corresponding to a respective selected point.

8. The method of claim 7 further comprising:taking parameter values corresponding to the best output across the iterations as the optimised parameter values output by the BO process.

9. The method of claim 8 further comprising:sending an instruction to operate the system using the optimised parameter values output by the BO process.

10. The method of any one of the preceding claims wherein:- the first experimental set up and / or the second experimental set up are real-world approximations of the system; or- the first experimental set up and / or the second experimental set up are computer implemented simulations of the system.

11. The method of any one of the preceding claims wherein the system is a biological, chemical or physical system.

12. The method of claim 11 wherein the system comprises a reaction chamber;the input parameters relate to one or more variables that affect a yield of a reaction performed in the reaction chamber: andthe output is the yield of the reaction when the reaction is performed in the reaction chamber.

13. The method of claim 12 wherein the reaction is a biological or chemical reaction.

14. The method of claim 13 wherein:the reaction chamber is a yeast cell reactor;the input parameters comprise concentrations or types of nutrients and / or one or more incubation conditions in the chamber; andthe output is yield of ethanol produced by the reaction.

15. An apparatus for performing a Bayesian Optimisation, BO, process for determining a plurality of input parameter values to a system, from a parameter space of possible input parameter values, that optimise an output of the system;the apparatus being characterised in the BO process having access to a first experimental set-up that is queryable as part of the BO process, and a first set of historical data obtained from queries of a second experimental setup, wherein the second experimental set-up is not queryable as part of the BO process, the apparatus comprising:a memory comprising instruction data representing a set of instructions; anda processor configured to communicate with the memory and to execute the set of instructions, wherein the set of instructions, when executed by the processor, cause the processor to:i) determine a first point in the parameter space to query by maximising an acquisition function of the BO process that takes a first dataset comprising data obtained from previous queries of the first experimental set up into account;ii) determine a second point in the parameter space to query by maximising the acquisition function, taking both the first dataset and the first set of historical data obtained from the queries of the second experimental set-up into account;iii) select one of the first point and the second point according to one or more criteria related to a level of relevance predicted to be obtained by querying the first experimental set-up using the first point compared to the second point; andiv) initiate a query of the first experimental set up with input parameter values corresponding to the selected point.

16. The apparatus of claim 15 wherein the processor is further caused to perform the method of any of claims 2 to 14.

17. The apparatus of claim 15 or 16 further comprising the first experimental set up;wherein, in step iv, the processor is caused to send an instruction to the first experimental set up; andin response to the instruction, the first experimental set up is caused to perform an experiment with input parameter values corresponding to the selected point; andsend results of the experiment to the processor upon completion.

18. A computer program comprising instructions which, when executed by a computer cause the computer to perform the method of any of claims 1 to 14.

19. A computer readable storage medium comprising instructions which when executed by a computer cause the computer to carry out the method of any one of claims 1 to 14.

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