Experimental Demonstration of a Plant as Computing Resource for Physical Reservoir Computing #

Plants are complex organisms subject to a wide variety of environmental factors, which in turn influence a plant’s physiology and phenotype. We propose to interpret this complex input-driven system as a reservoir in physical reservoir computing (PRC), a computing paradigm originating from computer science that employs a physical substrate as a computing element. In this chapter, we present the first application of PRC to plants using Fragaria × ananassa (strawberry). We show that plants outperform a control experiment in environmental and ecophysiological tasks using only eight leaf thickness sensors. We also investigate benchmark tasks such as the nonlinear auto-regressive moving average (NARMA) task and a delay line. Results indicate that plants are not suitable for general-purpose computation but are well-suited for ecophysiological tasks. This first demonstration of PRC with plants is an important milestone towards a more holistic view of phenotyping and a better understanding of information processing by plants.

Introduction #

We already discussed in Reservoir Computing with Plants how we can map the PRC framework to plants. This mapping is inspired by existing implementations such as a soft silicone arm and tensegrity robot (Figure 4.1). Here, we review the most important aspects.

Plants are high-dimensional nonlinear dynamical systems. Despite the absence of a brain-like organ and their inability to move, plants are capable of reacting effectively to their dynamic environment, just like animals and humans (Citation: Loon, 2016) Loon, L. (2016). The Intelligent Behavior of Plants. Trends in Plant Science, 21(4). 286–294. https://doi.org/10.1016/j.tplants.2015.11.009 . Plants continuously sense their environment and optimise their physiological responses accordingly (Citation: Taiz & Zeiger, 2010 Taiz, L. & Zeiger, E. (2010). Plant Physiology, Fifth Edition (Fifth edition). Sinauer Associates, Inc.. ; Citation: Arsova, Foster& al., 2020) Arsova, B., Foster, K., Shelden, M., Bramley, H. & Watt, M. (2020). Dynamics in plant roots and shoots minimize stress, save energy and maintain water and nutrient uptake. New Phytologist, 225(3). 1111–1119. https://doi.org/10.1111/nph.15955 . Moreover, they exhibit the ability to learn and have the ability to use past events for future planning (memory) integrated store/recall systems of memory (Citation: Thellier & Lüttge, 2013) Thellier, M. & Lüttge, U. (2013). Plant memory: a tentative model. Plant Biology (Stuttgart, Germany), 15(1). 1–12. https://doi.org/10.1111/j.1438-8677.2012.00674.x (see also Mapping the Physical Reservoir Framework to Plants).

We can consider the plant as a computing unit, able to process multiple signals to provide an integrated response that maximises fitness to the prevailing environmental conditions, as discussed by Citation: Scheres & Putten (2017) Scheres, B. & Putten, W. (2017). The plant perceptron connects environment to development. Nature, 543(7645). 337–345. https://doi.org/10.1038/nature22010 . In plant reservoir computing, figure 4.1d, the environmental cues are the input of the (plant) reservoir. Plant sensors are used to characterise the plant’s state. These state observations are combined to solve tasks such as prediction of ecophysiological parameters or detection of drought stress.

In this chapter, we demonstrate plant reservoir computing. While former studies have theorised on computing with plants (Citation: Adamatzky, Harding& al., 2018 Adamatzky, A., Harding, S., Erokhin, V., Mayne, R., Gizzie, N., Baluška, F., Mancuso, S. & Sirakoulis, G. (2018). Computers from Plants We Never Made: Speculations. InStepney, S. & Adamatzky, A. (Eds.), Inspired by Nature: Essays Presented to Julian F. Miller on the Occasion of his 60th Birthday. (pp. 357–387). Springer International Publishing. https://doi.org/10.1007/978-3-319-67997-6_17 ; Citation: Adamatzky, 2019) Adamatzky, A. (2019). Plant leaf computing. Biosystems, 182. 59–64. https://doi.org/10.1016/j.biosystems.2019.02.004 , to the best of our knowledge, this is the first experimental evidence of PRC with plants. We show that by observing the plant’s dynamical state with contact-based sensors, we can map temporal input patterns from leaf thickness sensors with a simple linear readout function to estimate (i) the environmental conditions, (ii) ecophysiological tasks, and (iii) computational benchmark tasks.

Materials and Methods #

To evaluate the computing properties of plants, we set up a series of experiments on Fragaria × ananassa (strawberry) where we monitor key environmental variables and gas exchange activity of the plants. While plants violate the fading memory property over their entire lifetime, we only consider a short period of their mature growing stage when performing the experiments. Each experiment lasts for eight days in a growth chamber. Inside the growth chamber, light intensity, air temperature and relative humidity are modulated, and the plant’s responses are captured using eight randomly placed leaf-thickness sensors. All three modulations follow a typical day-night pattern, based on actual weather data where additional randomness was inserted into the light intensity and direction by alternating which set of lamps was turned on without overly affecting the total light intensity. Although these are three main abiotic drivers that influence a plant’s ecophysiology (Citation: Jones, 2013) Jones, H. (2013). Plants and Microclimate: A Quantitative Approach to Environmental Plant Physiology (3). Cambridge University Press. https://doi.org/10.1017/CBO9780511845727 , we consider the light intensity as the main input. The other two abiotic drivers mainly serve to preserve a realistic day-night pattern where plants experience higher temperatures and lower humidity during the day and the inverse at night.

Plants continuously sense their environment and optimise their physiological responses accordingly (Citation: Taiz & Zeiger, 2010 Taiz, L. & Zeiger, E. (2010). Plant Physiology, Fifth Edition (Fifth edition). Sinauer Associates, Inc.. ; Citation: Arsova, Foster& al., 2020) Arsova, B., Foster, K., Shelden, M., Bramley, H. & Watt, M. (2020). Dynamics in plant roots and shoots minimize stress, save energy and maintain water and nutrient uptake. New Phytologist, 225(3). 1111–1119. https://doi.org/10.1111/nph.15955 . Consequently, these are excellent factors that serve as input to the plant reservoir. Leaf thickness is an interesting trait to monitor since it can vary rapidly and is also influenced by the modulated environmental drivers (Citation: Afzal, Duiker& al., 2017 Afzal, A., Duiker, S. & Watson, J. (2017). Leaf thickness to predict plant water status. Biosystems Engineering, 156. 148–156. https://doi.org/10.1016/j.biosystemseng.2017.01.011 ; Citation: De Swaef, Vermeulen& al., 2015) De Swaef, T., Vermeulen, K., Vergote, N., Van Lommel, J., Van Labeke, M., Bleyaert, P. & Steppe, K. (2015). Plant sensors help to understand tipburn in lettuce. International Society for Horticultural Science (ISHS). https://doi.org/http://dx.doi.org/10.17660/ActaHortic.2015.1099.3 . However, these clips are also sensitive to temperature fluctuations. Therefore, to validate that the plant is the main source of computation, we also set up a control experiment where the thickness clips are not mounted on a plant. Yet, a plant is placed into the growth chamber to capture real gas exchange data. This negative control is necessary because there might be a complex interaction of the environment and the sensor system that can also have properties resembling a reservoir.

In total, three experiments were conducted in the growth chamber. Each experiment used the same input modulation traces (light intensity, air temperature and air humidity), but the observed traces might differ slightly due to random changes and settling behaviour of the growth chamber. Moreover, three different plants were used to collect physiological data. As a result, the target signals for each of the tasks considered are experiment-specific, although some are very similar.

Experimental Setup #

The general experimental design follows Experimental Design and the experiments were conducted in the same growth chamber as in Reservoir Computing with a Snapshot Hyperspectral Camera and Development of a Sensor-Platform for Measuring Dynamic Plant Properties. The light configuration differs between the experiments, though. No halogen lights were used to limit heating inside the growth chamber due to the lights. The arrangement is also different. Lamps were mounted on the top and three sides of the frame for illumination. We used 57 light emitting diode (LED) lamps (PARATHOM DIM PAR16 50 36D OSRAM GmbH, Munich, Germany). The LED lights were arranged in groups that could be individually turned on and off. A detailed overview of the grid is depicted in figure 7.1, while the entire setup is depicted in figure 7.2. This is very similar to figure 5.3.

The modulation of the environmental conditions (light intensity, temperature and relative humidity) was performed using the Gloxinia sensor platform (see Development of a Sensor-Platform for Measuring Dynamic Plant Properties). This platform also performed sensor readout. Each experiment featured a digital light sensor (APDS9306, Broadcom Inc., San Jose, California, USA), relative humidity and temperature sensor (SHT35, Sensirion AG, Switzerland) and leaf thickness clips (AH-303, AgriHouse, Berthoud, CO, USA). Furthermore, a single mature leaf was inserted into a transparent leaf chamber of the LI-6400XT photosynthesis system (LI-COR, Lincoln, NE, USA) to acquire gas exchange measurements (transpiration and photosynthesis). The Gloxinia system also controlled the sampling time steps of the LI-6400XT, using a custom circuit that was connected to the manual sample button on the infrared gas analyser (IRGA). Each leaf thickness sensor was sampled every second, while the gas exchange measurement had a sample period of 3s. Faster sampling was not possible due to the limitations of the device.

To ensure that the conditions in the leaf chamber were as similar as possible to those of the rest of the plant, we used an external temperature probe (Vaisala 50Y, Vaisala, Helsinki, Finland) to recreate the temperature outside the leaf chamber. This also prevented the chamber from heating up due to the incoming radiation. Moreover, the gas inlet was also positioned close to the plant for maximum consistency. Figure 7.2 depicts the setup for a strawberry experiment. An image of each experimental setup is provided for each experiment in the dataset. Individual sensor locations are also indicated by a digit in figure 7.13, figure 7.14 and figure 7.15.

To simulate a variable light environment, we varied the light pattern semi-randomly. It was assumed that each group of lights contributes equally to the PAR. Based on the maximally observed PAR in the measurement trace, a certain set of lights is turned on.

Data Preprocessing #

The data was first manually inspected and cleaned to ensure no transient behaviour was included in the analysis. Sometimes the data logging also had to restart due to an error condition occurring because of interference of the high-power and low-power circuits. A restart event resulted in data loss for approximately one minute. Data within this time interval was reconstructed using linear interpolation. The first three hours and last hour of data were also discarded to remove transient effects due to the start or end of the experiment. Data was reconstructed to simplify the computation of several benchmark tasks.

Linear interpolation was also used to match the sampling rate of the gas exchange system, leaf thickness and environmental measurements. Unless specified otherwise, data was not processed and/or filtered further.

Train, Validation and Test Data Split and Model Training #

The time-series data generated in the three experiments here are highly correlated. To reduce this correlation, we used a data split into train and test data with interleaving (figure 7.3). Each day was assigned to either the train or test data. Eight hours were discarded between days. This ensures that night-time conditions are not overly represented in the dataset and that there is a decreased correlation between both the train and test datasets. However, because a day-night environmental pattern was followed in the growth chamber, the decreased correlation is limited in time. The correlation for all leaf thickness clips of strawberry 1 is presented in figure 7.4. Indeed, we first see a decreasing correlation until five to seven hours in the experiment, when the correlation increases again. This is due to the day-night pattern of the input variables.

In accordance with the general ideas of PRC discussed in Physical Reservoir Computing, a simple learning rule was selected. We used linear regression with Tikhonov or L2-regularisation (Citation: Tikhonov, 1963) Tikhonov, A. (1963). On the solution of ill-posed problems and the method of regularization. Doklady Akademii Nauk SSSR, 151. 501–504. Retrieved from http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=dan&paperid=28329&option_lang=eng . This is a simple model that converges rapidly. The Scikit-learn framework was used to train the system (Citation: Pedregosa, Varoquaux& al., 2011) Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., Dubourg, V., Vanderplas, J., Passos, A., Cournapeau, D., Brucher, M., Perrot, M. & Duchesnay, É. (2011). Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research, 12. 2825−2830. Retrieved from http://jmlr.csail.mit.edu/papers/v12/pedregosa11a.html . The main equation and loss criterion were already discussed in Generalisation, Bias and Variance.

We sweeped the hyperparameter \lambda from 1e-10 to 1e10 using logarithmic spacing. For each hyperparameter value, the model was optimised, and the best model was selected using a leave-one-out strategy: we used the data of a single day for validation and all the other days for training. This assignment was also permuted such that all days are used for validation. The final choice for \lambda was again optimised using all the training data. The final performance was computed on the test data.

Regression Tasks #

We consider regression problems solely in this chapter since all the ecophysiological measurements performed are continuous variables. Three types of regression prediction targets are considered: (i) environmental targets, which also form the input of the reservoir; (ii) photosynthetic rate P_n and transpiration rate E as ecophysiological tasks based on the gas exchange data; and (iii) computational benchmarks. All tasks are listed in table 7.1.

Reconstructing the environmental input of the reservoir is an interesting task to evaluate how the information at the input is retained by the reservoir. Estimating gas exchange activity ( P_n and E ) from leaf thickness is an interesting biologically relevant task that demonstrates practical applications of PRC with plants.

We selected photosynthetic rate P_n , and transpiration rate E as ecophysiological parameters since these gas exchange measurements are not directly measurable using leaf thickness sensors. The gas exchange sensor device does measure other parameters such as stomatal conductance and leaf temperature, but these are not included since they are highly dependent on temperature, and so are the (leaf) thickness clips.

Computational benchmarks are computed to evaluate the nonlinear and memory properties of plants on a more theoretical basis. This is done using two tasks: NARMA and a delay line. The NARMA task is a benchmark task often used to evaluate PRC media (Citation: Nakajima, Hauser& al., 2015 Nakajima, K., Hauser, H., Li, T. & Pfeifer, R. (2015). Information processing via physical soft body. Scientific Reports, 5. 10487. https://doi.org/10.1038/srep10487 ; Citation: Atiya & Parlos, 2000) Atiya, A. & Parlos, A. (2000). New results on recurrent network training: unifying the algorithms and accelerating convergence. IEEE Transactions on Neural Networks, 11(3). 697–709. https://doi.org/10.1109/72.846741 . This task has a parameter n that influences the amount of nonlinearity and memory, higher values of n result in more difficult tasks. We use a slightly modified version such that the memory dependencies operate at the minute scale. Consequently, we increased the memory dependency of the task. This was done because otherwise the time-dependencies were too extensive, resulting in too much smoothing and even stability issues for large values of n:

The parameters \alpha, \beta, \gamma and \delta are chosen as 0.3, 0.05, 1.5 and 0.1 respectively (Citation: Nakajima, Hauser& al., 2015) Nakajima, K., Hauser, H., Li, T. & Pfeifer, R. (2015). Information processing via physical soft body. Scientific Reports, 5. 10487. https://doi.org/10.1038/srep10487 . We do not consider general-purpose tasks such as MNIST digit recognition or a 2-bit XOR task, as is demonstrated in other PRC research (Citation: Vandoorne, Mechet& al., 2014 Vandoorne, K., Mechet, P., Vaerenbergh, T., Fiers, M., Morthier, G., Verstraeten, D., Schrauwen, B., Dambre, J. & Bienstman, P. (2014). Experimental demonstration of reservoir computing on a silicon photonics chip. Nature Communications, 5. 3541. https://doi.org/10.1038/ncomms4541 ; Citation: Du, Cai& al., 2017) Du, C., Cai, F., Zidan, M., Ma, W., Lee, S. & Lu, W. (2017). Reservoir computing using dynamic memristors for temporal information processing. Nature Communications, 8(1). 2204. https://doi.org/10.1038/s41467-017-02337-y . In the context of reservoir computing with plants, we do not consider these tasks as relevant since plants are unlikely to outperform conventional computing devices for such tasks. Instead, we focus on plant-specific tasks that are more relevant with respect to future applications in plant ecophysiology and phenotyping.

Since models are not transferable between experiments, we estimate the variability due to sensor placement by selecting seven out of eight sensors. Since individual plants might also have considerably different dynamics, we repeated the experiments for two strawberry plants.

All regression tasks from table 7.1 use the measurement data as the target value for \hat{y}, including the benchmark tasks. Though, the NARMA tasks use a modified version of the light intensity signal I_{\text{PAR}} . I_{\text{PAR}} is re-scaled to have a zero mean and amplitude of 0.2. This is done to match the input signal used in other research (Citation: Nakajima, Hauser& al., 2015) Nakajima, K., Hauser, H., Li, T. & Pfeifer, R. (2015). Information processing via physical soft body. Scientific Reports, 5. 10487. https://doi.org/10.1038/srep10487 and ensure that the output does not diverge since the general form of NARMA is not stable for arbitrary input.

Overall, the dataflow is as depicted in figure 4.4 and very similar to that of figure 5.6. The input of the PRC system are the environmental factors, while the input of the linear machine learning pipeline are the reservoir observations: leaf thickness data. This data is fit to the three targets types: environmental, ecophysiological and benchmark targets, listed in table 7.1.

Leaf Thickness Sensor Calibration #

The leaf thickness sensors used here are sensitive to temperature fluctuations, though they are not equipped with a temperature sensor. In Development of a Sensor-Platform for Measuring Dynamic Plant Properties, clips were calibrated using the air temperature value, but here each clip was retrofitted with a thermistor (NXFT15WF104FA2B100, Murata Manufacturing Co., Ltd., Kioto, Japan) that was used for calibration. A linear calibration was performed based on a calibration experiment. During this experiment, the temperature was increased from 10°C to 30°C. While it is not necessary for PRC to calibrate the leaf thickness sensors to absolute thickness values, we performed a calibration to obtain fully calibrated sensor values. The clips were calibrated using the calibration card from AgriHouse (AH-300C).

Plant Material #

Plants used in Reservoir Computing with a Snapshot Hyperspectral Camera and this chapter were grown in the same location. All three experiments used a Fragaria × ananassa (strawberry) plant. The plants were grown in close proximity in a greenhouse at ILVO (Caritasstraat 39, 9090 Melle, Belgium), thus ensuring that they experienced a very similar growing history. The plants received regular watering to avoid soil water deficit, based on their needs and were grown inside the greenhouse for over one year. All plants are cuttings from the same base plant and were kept free from pests and diseases.

Results #

Evaluation of the Reservoir Performance for Biologically Relevant Tasks #

Initially, we focus on the biologically relevant tasks. These are the tasks from categories (i) environmental and (ii) ecophysiological (table 7.1). Figure 7.5 visualises the performance using boxplots. Plants outperform the control experiment for I_{\text{PAR}} , P_n and E , while the control is better at computing T_\text{air} and h . This result is not unexpected since thickness clips are sensitive to temperature fluctuations due to heating of the analogue electronics and expansion of the plastic used in the clips. A calibration was performed, but due to nonlinear effects, the model is still able to reconstruct T_\text{air} and h better in the control experiment.

We also observe that sometimes there can be considerable variation between plants: for instance, strawberry 2 is slightly better at estimating P_n than strawberry 1, while the inverse is true for E , yet performance for I_{\text{PAR}} is similar. These differences are probably due to the measurement technique applied for capturing P_n and E , which are monitored for one specific leaf. Consequently, there can be a considerable difference between the selected leaf and other leaves, while I_{\text{PAR}} is an integrated measurement, performed on the same location in both experiments and independent of the plant.

The absolute value of the Pearson correlation coefficients between environmental, ecophysiological and leaf thickness measurements are depicted in figure 7.6. The correlation matrix shows that most leaf thickness values x_i of the control experiment are much less correlated to the environmental conditions than the first strawberry experiment, except for x_7. We also observe that there is considerable correlation between the environmental factors too, especially between T_\text{air} and h for both experiments (0.84 and 0.83). While this is undesirable, this is the result of applying a realistic day-night pattern. Indeed, during the day, light intensity and temperature slowly increase in the morning and decrease as nightfall approaches, while the inverse typically happens for relative humidity.

To provide more insight into the normalised mean squared error (NMSE) scores depicted in figure 7.5, we also visualise time-series of the most interesting tasks in figure 7.7. All readouts are used to generate the plots, so no variability data is available. Figure 7.8 zooms in on the grey shaded region of figure 7.7. This region was not used for training. In the control experiment, the strawberry plant used to obtain the gas exchange data were less active than the other strawberry plants. NMSE values of the test data are also depicted in the upper left corner of each subfigure. From figure 7.7, we observe that the strawberry reservoirs are more effective (i.e., lower NMSE values), resolving the highs and lows better. In figure 7.8 we observe that strawberry-based reservoirs are better at capturing the dynamic behaviour of each specific ecophysiological task. For example, in the case of I_{\text{PAR}} , we see that detailed variation is not captured by the control experiment but is captured by the strawberry experiments. Similar observations can be made for P_n and E . We point out that NMSE also has its limitations; some of the scores for strawberry 2 are close to the baseline of 1.0, similar to the control experiment. Yet, we see that the variation in the target signal is better captured by the plant.

The narrow peaks observed for E in figure 7.8 are an artefact of the measurement device due to slight variations between the measurement channel and reference channel as a result of variable relative humidity. More details are provided in Materials and Methods.

Evaluation of the Reservoir Properties #

It is vital to study the characteristics of the reservoir to stimulate the development of better plant-based reservoirs and to improve data extraction efficiency. To this end, we evaluate the performance on three benchmark tasks: a delay line, polynomial fit and the NARMA task. Moreover, the reservoir size is also a key parameter to investigate.

The effect of the number of readouts of the reservoir (i.e.\ the number of thickness clips) on the environmental and ecophysiological tasks is depicted in figure 7.9. As expected, performance increases if we increase the number of observations. Furthermore, the variability decreases because a larger set of sensors is able to capture the dynamics present in the reservoir. However, the performance gain due to increasing readout size also decreases as it increases. This is expected since the larger readout size provides a fuller representation of the reservoir dynamics.

We investigate nonlinear and memory performance separately in figure 7.10 figure 7.11. As the delay increases on the I_{\text{PAR}} signal in figure 7.10, we initially observe that the NMSE value remains constant for all three experiments. This is due to the high correlation in leaf thickness among nearby time points. We also note that performance is slightly improved at delays of 500s and 200s for strawberry 1 and 2, respectively. As the delay on I_{\text{PAR}} increases further, performance decreases. Plants perform better than the control, but there is also variation between plants. Peculiar is a drop of the control to 0.4 at 10000. This is an artefact and the result of the temperature dependence of the clips.

The performance for nonlinear transformations of I_{\text{PAR}} is depicted in [figure 7.11](https://phd.olivierpieters.be/chapter/pprc/#nl-figure. The performance quickly degrades as the amount of nonlinearity increases. Strawberry 2 is slightly less performant than strawberry 1. Both reach the baseline for a polynomial degree of 6, when results are similar to those from the control experiment.

NARMA is a complex nonlinear task that can have long-lasting dependencies on the past. As a result, it is an excellently combined task to evaluate the reservoirs. NARMA tasks with n=2 to n=50 are depicted in figure 7.12. The NARMA task is based on the light intensity I_{\text{PAR}} . Plants are better at solving this task than the control experiment. However, both are not very performant on the task, since NMSE values are always near or above 0.5. This is also not surprising since plants are not well suited for general-purpose computation. Yet, it is interesting that small values of n perform similarly, which is due to the relatively slow variation of leaf thickness (see also figure 7.10).

Discussion #

In this chapter, we demonstrate PRC with strawberry plants. We show experimentally that plants outperform a control setup for non-trivial tasks such as light intensity I_{\text{PAR}} , transpiration rate E and photosynthesis rate P_n . Moreover, we also investigate performance on common benchmark tasks such as NARMA-10 and a delay line. In this discussion, we first match our results with literature and Reservoir Computing with a Snapshot Hyperspectral Camera. We also highlight current limitations and future improvements to plant PRC.

Performance Comparison with Literature #

Literature reports that a significant negative correlation exists between leaf thickness and transpiration rate E (Citation: Giuliani, Koteyeva& al., 2013) Giuliani, R., Koteyeva, N., Voznesenskaya, E., Evans, M., Cousins, A. & Edwards, G. (2013). Coordination of Leaf Photosynthesis, Transpiration, and Structural Traits in Rice and Wild Relatives ( (Genus Oryza). Plant Physiology, 162(3). 1632–1651. https://doi.org/10.1104/pp.113.217497 , explaining why predicting the latter is the best performing task for both strawberry plants. Though studies on multiple species investigated the correlation between photosynthetic rate P_n and leaf thickness, none have reported significant results (Citation: Giuliani, Koteyeva& al., 2013 Giuliani, R., Koteyeva, N., Voznesenskaya, E., Evans, M., Cousins, A. & Edwards, G. (2013). Coordination of Leaf Photosynthesis, Transpiration, and Structural Traits in Rice and Wild Relatives ( (Genus Oryza). Plant Physiology, 162(3). 1632–1651. https://doi.org/10.1104/pp.113.217497 ; Citation: Nikolopoulos, Liakopoulos& al., 2002) Nikolopoulos, D., Liakopoulos, G., Drossopoulos, I. & Karabourniotis, G. (2002). The Relationship between Anatomy and Photosynthetic Performance of Heterobaric Leaves. Plant Physiology, 129(1). 235–243. https://doi.org/10.1104/pp.010943 .

We only performed environmental and ecophysiological experiments in Reservoir Computing with a Snapshot Hyperspectral Camera, so we limit our comparison to those. Moreover, the number of ecophysiological parameters studied in this chapter is also more limited since we wanted to exclude parameters that were overly dependent on temperature. We compare the overall results from figure 7.5 to figure 5.8. The advantage of using subsampling, as demonstrated in figure 5.7 is small and does not gain more insight into the results. When comparing the leaf thickness results to Reservoir Computing with a Snapshot Hyperspectral Camera, we observe that NMSE values for I_{\text{PAR}} are better in the case of the hyperspectral camera than the leaf clips. However, this is no surprise since a camera directly observes light. Moreover, the overall results are better in case of the thickness clips since for in the hyperspectral experiment NMSE values ranged between 0.02 to 0.04 for plants and 0.02 to 0.03 for background materials. The thickness clips experiments has NMSE values of 0.25 and 0.28 for plants and 0.75 for the control experiment. While these values are a lot higher than for the hyperspectral data, they are significantly better than the control experiment, which is not the case in the hyperspectral experiments. P_n NMSE values from the leaf thickness experiment are similar to those from the hyperspectral experiment: 0.27 to 0.31 compared to 0.21 to 0.30 for plant1 in the leaf thickness and hyperspectral experiments respectively. Yet, plant2 has significantly worse performance with an NMSE of 0.56. Moreover, background materials have similar performance for P_n with values ranging between 0.34 to 0.62. This is not the case in figure 7.5. Both plants have similar performance, and the control is very close to the baseline prediction (0.93). For E , performance in figure 7.5) is clearly better than in figure 5.8. This is not surprising since leaf thickness has been shown to be a good proxy for water status in the plant (Citation: Meidner, 1990) Meidner, H. (1990). The Absorption Lag, Epidermal Turgor and Stomata. Journal of Experimental Botany, 41(9). 1115–1118. https://doi.org/10.1093/jxb/41.9.1115 . Again, we observe that the difference between plants and background materials in figure 5.8 is low: 0.41 to 0.60, and 0.31 to 0.66 for plants and background materials respectively. Yet, for the leaf thickness experiment, plant scores are 0.12 and 0.26, while the control score is much higher at 0.84. In summary, leaf thickness is a much more interesting plant trait to observe than reflectance variation using a hyperspectral camera for PRC.

For the benchmark tasks, it is essential to compare with other PRC substrates. However, comparing NMSE values from figure 7.5 with other substrates is not straightforward. On the one hand, there are many substrates specifically designed for reservoir computing, such as silicon photonics and memristor chips. These substrates perform better on benchmark tasks. For instance, for the NARMA-10 task, photonic reservoirs have NMSE values of 0.035 (Citation: Appeltant, Soriano& al., 2011) Appeltant, L., Soriano, M., Van der Sande, G., Danckaert, J., Massar, S., Dambre, J., Schrauwen, B., Mirasso, C. & Fischer, I. (2011). Information processing using a single dynamical node as complex system. Nature Communications, 2. 468. https://doi.org/10.1038/ncomms1476 and for the Santa-Fe time-series prediction task, NMSE values of 0.06 are reported in literature for photonic reservoirs (Citation: Nakajima, Tanaka& al., 2021) Nakajima, M., Tanaka, K. & Hashimoto, T. (2021). Scalable reservoir computing on coherent linear photonic processor. Communications Physics, 4(1). 1–12. https://doi.org/10.1038/s42005-021-00519-1 . However, a plant is optimised for fitness, not as a medium for computing (Citation: Anderson, 2016 Anderson, J. (2016). Plant fitness in a rapidly changing world. New Phytologist, 210(1). 81–87. https://doi.org/10.1111/nph.13693 ; Citation: Prakash, Stephens& al., 2020) Prakash, C., Stephens, K., Hoffman, D., Singh, M. & Fields, C. (2020). Fitness Beats Truth in the Evolution of Perception. Acta Biotheoretica. https://doi.org/10.1007/s10441-020-09400-0 . Moreover, many studies mainly focus on simulations since creating a physical reservoir is often time-consuming and expensive, especially if integrated circuits need to be designed. On the other hand, other studies work with biological media, but they exclusively focus on classification tasks (Citation: Dockendorf, Park& al., 2009 Dockendorf, K., Park, I., He, P., Príncipe, J. & DeMarse, T. (2009). Liquid state machines and cultured cortical networks: The separation property. Biosystems, 95(2). 90–97. https://doi.org/10.1016/j.biosystems.2008.08.001 ; Citation: Ju, Dranias& al., 2015 Ju, H., Dranias, M., Banumurthy, G. & VanDongen, A. (2015). Spatiotemporal Memory Is an Intrinsic Property of Networks of Dissociated Cortical Neurons. Journal of Neuroscience, 35(9). 4040–4051. https://doi.org/10.1523/JNEUROSCI.3793-14.2015 ; Citation: Jones, Stekel& al., 2007 Jones, B., Stekel, D., Rowe, J. & Fernando, C. (2007). Is there a Liquid State Machine in the Bacterium Escherichia Coli?. https://doi.org/10.1109/ALIFE.2007.367795 ; Citation: Dranias, Ju& al., 2013) Dranias, M., Ju, H., Rajaram, E. & VanDongen, A. (2013). Short-Term Memory in Networks of Dissociated Cortical Neurons. Journal of Neuroscience, 33(5). 1940–1953. https://doi.org/10.1523/JNEUROSCI.2718-12.2013 , a problem distinct from regression. We opted to study regression tasks since these are more relevant from a plant ecophysiological point of view. Additionally, biological signals are also inherently noisy (Citation: Bezrukov & Vodyanoy, 1995) Bezrukov, S. & Vodyanoy, I. (1995). Noise-induced enhancement of signal transduction across voltage-dependent ion channels. Nature, 378(6555). 362–364. https://doi.org/10.1038/378362a0 . This noise is difficult to filter given that the reservoir studied here has only up to eight state observations. Despite these limitations, these results are a pivotal first step towards reservoir computing with plants.

Often, the effect of the reservoir size is studied in literature (Citation: Vandoorne, Mechet& al., 2014 Vandoorne, K., Mechet, P., Vaerenbergh, T., Fiers, M., Morthier, G., Verstraeten, D., Schrauwen, B., Dambre, J. & Bienstman, P. (2014). Experimental demonstration of reservoir computing on a silicon photonics chip. Nature Communications, 5. 3541. https://doi.org/10.1038/ncomms4541 ; Citation: Du, Cai& al., 2017) Du, C., Cai, F., Zidan, M., Ma, W., Lee, S. & Lu, W. (2017). Reservoir computing using dynamic memristors for temporal information processing. Nature Communications, 8(1). 2204. https://doi.org/10.1038/s41467-017-02337-y , but this is more difficult for plants. Isolating a part of a plant and maintaining its growth as though it was still part of a larger entity is not possible. An integrated perspective is thus necessary. As a result, we study the number of observation points (or readouts) of the reservoir. The number of readouts also greatly affects performance (i.e. lower NMSE values for larger numbers of observations), as indicated in figure 7.9. This illustrates that an increased number of observations can improve the prediction accuracy of transpiration rate E and photosynthetic rate P_n beyond what is possible using a single sensor. In literature, this effect has also been reported, as well as the saturation effect for as the number of readouts increases (Citation: Pinna, Bourianoff& al., 2020 Pinna, D., Bourianoff, G. & Everschor-Sitte, K. (2020). Reservoir Computing with Random Skyrmion Textures. Physical Review Applied, 14(5). 054020. https://doi.org/10.1103/PhysRevApplied.14.054020 ; Citation: Vlachas, Pathak& al., 2020) Vlachas, P., Pathak, J., Hunt, B., Sapsis, T., Girvan, M., Ott, E. & Koumoutsakos, P. (2020). Backpropagation algorithms and Reservoir Computing in Recurrent Neural Networks for the forecasting of complex spatiotemporal dynamics. Neural Networks, 126. 191–217. https://doi.org/10.1016/j.neunet.2020.02.016 . Increasing the number of readouts has an effect on the fraction of observed dynamics. Full observability is not possible for plant-based reservoirs, even if the leaf thickness variation of each leaf is characterised. While short-term leaf thickness variations are a good proxy for plant water status dynamics, there are many more unknown factors such as hormones, metabolism, nutrient take-up and carbon dynamics. These are also part of the reservoir but not directly quantifiable using leaf thickness measurements, although correlations will exist with leaf thickness because nearly all plant processes are impacted by the plant’s water status (Citation: Barillot, De Swaef& al., 2020 Barillot, R., De Swaef, T., Combes, D., Durand, J., Escobar-Gutiérrez, A., Martre, P., Perrot, C., Roy, E. & Frak, E. (2020). Leaf elongation response to blue light is mediated by stomatal-induced variations in plant transpiration in Festuca arundinacea. Journal of Experimental Botany(eraa585). https://doi.org/10.1093/jxb/eraa585 ; Citation: McBurney, 1992) McBurney, T. (1992). The Relationship Between Leaf Thickness and Plant Water Potential. Journal of Experimental Botany, 43(3). 327–335. https://doi.org/10.1093/jxb/43.3.327 .

The unexpected drop of NMSE in the curve for the control experiment in figure 7.10 is the result of the correlation between the light intensity I_{\text{PAR}} and air temperature T_\text{air} . This correlation arises due to two effects. First, as depicted in figure 7.6, there is a limited correlation between air temperature T_\text{air} and most thickness clips of the control experiment (except for x_3). Though combined, a set of clips is still good at predicting the air temperature (see figure 7.9) for the control experiment. Second, the correlation between air temperature T_\text{air} and light intensity I_{\text{PAR}} is maximal at a delay of 4600s. Consequently, the train error is lowest for a delay of 5000s and the test error is lowest for 10000s for the control experiment. The mismatch between train and validation error is probably due to the model overfitting on the data at a delay of 5000s. At an increased mismatch at a delay of 10000s, the model might generalise better. Therefore, the test error is minimal. Naturally, this also occurs for the plant observation, yet we do not observe this effect because these observations have many more influencing factors due to being mounted on a plant.

While PRC with plants is far from being ready for use in the field, we can observe some of the potential already in these results. In figure 7.10, we observed a slight dip around 200 to 500s. There might be a lag between a change in light intensity and the resulting difference in leaf thickness (Citation: Meidner, 1990) Meidner, H. (1990). The Absorption Lag, Epidermal Turgor and Stomata. Journal of Experimental Botany, 41(9). 1115–1118. https://doi.org/10.1093/jxb/41.9.1115 . This dip may imply a time lag of 200 to 500s between acclimation of the leaf thickness and the changing light intensity. This lag can signify a suboptimal response of the leaf to the fast-changing light intensity. Quantifying, studying and improving this relationship is especially relevant for plants in the field since they are subject to fast-changing light intensities. Though optimising this dynamic behaviour of plants is often ignored and could even be more important than static performance (Citation: Kaiser, Morales& al., 2018 Kaiser, E., Morales, A. & Harbinson, J. (2018). Fluctuating Light Takes Crop Photosynthesis on a Rollercoaster Ride. Plant Physiology, 176(2). 977–989. https://doi.org/10.1104/pp.17.01250 ; Citation: Kromdijk, Głowacka& al., 2016) Kromdijk, J., Głowacka, K., Leonelli, L., Gabilly, S., Iwai, M., Niyogi, K. & Long, S. (2016). Improving photosynthesis and crop productivity by accelerating recovery from photoprotection. Science, 354(6314). 857–861. https://doi.org/10.1126/science.aai8878 . PRC can provide the means to characterise this mismatch.

Limitations and Future Improvements #

The results presented in figure 7.5 [figure 7.9](https://phd.olivierpieters.be/chapter/pprc/#reservoir-size, figure 7.10, [figure 7.11](https://phd.olivierpieters.be/chapter/pprc/#nl-figure and figure 7.12 are encouraging. Better sensor technology and calibration can likely reduce unwanted effects due to the sensor-environment interaction and improve signal extraction. Alternative sensor systems such as biopotential (Citation: Escalante-Pérez, Krol& al., 2011) Escalante-Pérez, M., Krol, E., Stange, A., Geiger, D., Al-Rasheid, K., Hause, B., Neher, E. & Hedrich, R. (2011). A special pair of phytohormones controls excitability, slow closure, and external stomach formation in the Venus flytrap. Proceedings of the National Academy of Sciences, 108(37). 15492–15497. https://doi.org/10.1073/pnas.1112535108 , sap flow (Citation: Vandegehuchte & Steppe, 2012) Vandegehuchte, M. & Steppe, K. (2012). Sapflow+: a four-needle heat-pulse sap flow sensor enabling nonempirical sap flux density and water content measurements. New Phytologist, 196(1). 306–317. https://doi.org/10.1111/j.1469-8137.2012.04237.x or leaf length (Citation: Barillot, De Swaef& al., 2020) Barillot, R., De Swaef, T., Combes, D., Durand, J., Escobar-Gutiérrez, A., Martre, P., Perrot, C., Roy, E. & Frak, E. (2020). Leaf elongation response to blue light is mediated by stomatal-induced variations in plant transpiration in Festuca arundinacea. Journal of Experimental Botany(eraa585). https://doi.org/10.1093/jxb/eraa585 might be better suited for certain tasks than leaf thickness.

While the experiments presented here are mainly theoretical, they may result in practical applications in future work. Treating a plant as a computing entity can help to generalise plant behaviour and provide essential context to physiological studies. Each trait exhibited by a plant can be viewed as the result of the complex interaction between environmental queues and plant behaviour. Essentially, a plant can be viewed as a computational unit that analyses the incoming environmental signals and optimises its physiology accordingly.

We identify three main issues with PRC for plants: (i) the effect of uncontrolled and uncharacterised inputs, (ii) non-stationarity of plants and (iii) plants do not experience their environment in discrete time. First, plants are sensitive to many signals, including the three environmental variables modulated here, but also chemicals (both airborne and in the soil), mechanical stimulation, electricity, and sound (Citation: Karban, 2015) Karban, R. (2015). Plant Sensing and Communication. University of Chicago Press. Retrieved from https://www.degruyter.com/document/doi/10.7208/9780226264844/html . None of these factors is easily controlled and/or kept constant. As a result, these additional input sources possibly distort the applied input signals (Citation: Soriano, Ortín& al., 2013) Soriano, M., Ortín, S., Brunner, D., Larger, L., Mirasso, C., Fischer, I. & Pesquera, L. (2013). Optoelectronic reservoir computing: tackling noise-induced performance degradation. Optics Express, 21(1). 12–20. https://doi.org/10.1364/OE.21.000012 . One could argue that the reservoir should be able to cope with these additional variations, but there are also limits to the observable processes using thickness clips. Second, plants are non-stationary entities. They keep on developing (Citation: Hilty, Muller& al., 2021) Hilty, J., Muller, B., Pantin, F. & Leuzinger, S. (2021). Plant growth: the What, the How, and the Why. New Phytologist, 232(1). 25–41. https://doi.org/10.1111/nph.17610 and over time, they violate the fading-memory requirement. As a result, online unsupervised learning algorithms are required to create a readout mechanism that is able to cope with changes in the reservoir. One way this can be tackled is using reward-modulated Hebbian learning (Citation: Gerstner & Kistler, 2002 Gerstner, W. & Kistler, W. (2002). Mathematical formulations of Hebbian learning. Biological Cybernetics, 87(5). 404–415. https://doi.org/10.1007/s00422-002-0353-y ; Citation: Burms, Caluwaerts& al., 2015) Burms, J., Caluwaerts, K. & Dambre, J. (2015). Reward-Modulated Hebbian Plasticity as Leverage for Partially Embodied Control in Compliant Robotics. Frontiers in Neurorobotics, 9. https://doi.org/10.3389/fnbot.2015.00009 . Third, plants continuously sense environmental changes and act accordingly. Hence, they do not respond in discrete time. In this chapter we did not investigate the implications this has on the reservoir performance and the observed dynamics.

After all, plants are complex integrated systems containing many coupled processes that occur at different timescales. For instance, photons are absorbed by chlorophyll molecules within 1fs, whereas chlorophyll fluorescence is emitted in 1ns after photon incidence (Citation: Taiz & Zeiger, 2010) Taiz, L. & Zeiger, E. (2010). Plant Physiology, Fifth Edition (Fifth edition). Sinauer Associates, Inc.. . More integrated processes such as stomatal opening and closure respond in the order of 20s after a change in illuminance. Hydraulic functioning (e.g., water transport) changes in the range of seconds to minutes, whereas organ growth rates vary in the order of minutes to hours (Citation: Jones, 2013 Jones, H. (2013). Plants and Microclimate: A Quantitative Approach to Environmental Plant Physiology (3). Cambridge University Press. https://doi.org/10.1017/CBO9780511845727 ; Citation: Hilty, Muller& al., 2021) Hilty, J., Muller, B., Pantin, F. & Leuzinger, S. (2021). Plant growth: the What, the How, and the Why. New Phytologist, 232(1). 25–41. https://doi.org/10.1111/nph.17610 . Consequently, a plant-based reservoir also operates at these timescales though not all of them are observable using leaf thickness sensors.

Our experiments are a first step towards plant-based PRC. Additional experiments and analysis are needed to reassure that the plant can indeed be used for PRC. While a plant is a highly nonlinear dynamic system (see also Mapping the Physical Reservoir Framework to Plants), we did not perform an analysis of the timescales at which the sensors observe the plant-reservoir. Moreover, the environmental and ecophysiological tasks do not evaluate the memory capacity. A more detailed analysis that builds, for instance, on figure 7.10 could help to better understand the (fading) memory properties of plants. Moreover, the underlying plant processes should also be investigated to explore the origins of the plant computing properties. This body of work highlights the next steps necessary for plant-based PRC.

Conclusion #

In this work, we presented – to the best of our knowledge – the first application of PRC-inspired computing with plants, more specifically strawberry (Fragaria × ananassa). We investigated several types of tasks, including environmental, ecophysiological and benchmark tasks. The results indicate that plants are not well suited for general-purpose computation but are potentially highly interesting for plant-specific tasks and applications in phenotyping. Plants are best at solving ecophysiological and environmental tasks, more specifically transpiration rate E , photosynthesis rate P_n and light intensity I_{\text{PAR}} .

Supplementary Figures #