Leveraging plant physiological dynamics using physical reservoir computing – Scientific Reports

In this study, we demonstrate physical reservoir computing on 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. Second, we highlight current limitations and future improvements to plant PRC. Finally, we spotlight applications and the broader impact PRC with plants can have on the plant science community.

Literature reports that a significant negative correlation exists between leaf thickness and transpiration rate E³⁷, explaining why predicting the latter is the best performing task for both strawberry plants in Fig.3. Though studies on multiple species investigated the correlation between photosynthetic rate \(P_n\) and leaf thickness, none have reported significant results^37,38.

The unexpected drop of NMSE in the curve for the control experiment in Fig.4b is the result of the correlation between the light intensity \(I_\text PAR\) and air temperature \(T_\text air\). This correlation arises due to three effects. First, there is limited correlation between air temperature \(T_\text air\) and most thickness clips of the control experiment (except for \(x_3\)). Correlation values range from 0.0 to 0.64 with an average correlation of 0.31 ( 0.22). Though combined, a set of clips is still good at predicting the air temperature (see Figs.3, 4a) 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 10,000s for the control experiment. The mismatch between train and validation error is probably due to the model overfitting the data at a delay of 5000s. At an increased mismatch at a delay of 10,000s, the model might generalise better. Therefore, the test error is minimal. Correlation matrices are depicted in the supporting information. Third, there is also the natural correlation arising from using a realistic day-night pattern. The temperature is naturally higher during the day due to strong solar radiation and colder at night due to the lack thereof.

Plants show best performance for eco-physiological tasks. This is not unexpected since these tasks are intertwined with their physiology. Moreover, strong couplings exist between plant-processes such as stomatal conductivity, transpiration rate, photosynthesis and leaf thickness due to common driving elements (e.g. water potential and light availability)³⁵. The observation that domain-specific computers are better at solving problems within their domain has already been reported in literature. For instance, is has been shown that a soft silicone arm-based computer³⁹ and a vortex computer⁴⁰ can outperform conventional machine learning techniques.

For the benchmark tasks, it is essential to compare with other PRC substrates. However, comparing NMSE values from Fig.3 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^15,36. These substrates perform better on benchmark tasks. For instance, for the NARMA-10 task, photonic reservoirs have NMSE values of 0.035⁴¹ and for the Santa-Fe time-series prediction task, NMSE values of 0.06 are reported in literature for photonic reservoirs⁴². However, a plant is optimised for fitness, not as a medium for computing⁴³, resulting in low or fast degrading performance in Fig.4c, d. 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 that work with biological media exclusively focus on classification tasks^{21,44,45,46,47}, a problem distinct from regression. We opted to study regression tasks since these are more relevant from a plant eco-physiological point of view. Additionally, biological signals are also inherently noisy⁴⁸. This noise is difficult to filter given that the reservoir studied here has only up to eight state observations. Despite these limitations, this study is a pivotal first step towards reservoir computing with plants.

Often, the effect of the reservoir size is studied in literature^15,36, 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 Fig.4a. This illustrates that an increased number of observations and PRC 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 increases⁴⁹. 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 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 merely all plant processes are impacted by the plants water status^35,50.

The results presented in Figs.3 and 4 are promising. 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 biopotential⁵¹, sap flow⁵² or leaf length⁵⁰ might be better suited for than leaf thickness certain tasks.

We identify three main issues with PRC for plants: the effect of uncontrolled and uncharacterised inputs, non-stationarity of plants and 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 sound⁵³. None of these factors is easily controlled and/or kept constant. As a result, these additional input sources possibly distort the applied input signals⁵⁴. 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 developing⁵⁵ and over time, they violate the fading-memory requirement. This requirement is sometimes also called the echo-state property. By selecting leaf thickness, we avoided drastic short-term non-stationary variations in the plant, since leaf thickness in mature leaves saturated. Consequently, the echo-state property is approximately met for the duration of the experiment given that leaf thickness in this stage oscillates around this saturated value based on environmental conditions. However, on a larger timescale, the system remains non-stationary since leaves eventually die off. 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 learning⁵⁶. In this regard, physical reservoir computing with plants will never be identical to more classic reservoirs such as memristors. This research can form a starting point towards a further generalisation of physical reservoir computing to non-stationary systems. In literature, an extension of the information processing capacity from time invariant to time-variant systems was recently proposed⁵⁷. This masks an important first step towards a generalised computing framework for time-variant systems. Third, plants continuously sense environmental changes and act accordingly. Hence, they do not respond in discrete time. In this study, we did not investigate the implications this has on the reservoir performance and the observed dynamics.

After all, plants are complex integrated systems that contain 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 incidence⁹. 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^7,55. Consequently, a plant-based reservoir also operates at these timescales though not all of them are observable using leaf thickness sensors. Alternative sensor technologies can be applied to study other processes, though experimentally evaluating them is time consuming and slow. As such, one could rely on plant models with sufficient details such as functional structural plant models (FSPMs)⁵⁸ to investigate suitable reservoir-like plant processes and evaluate sensor technologies in silico. Employing advanced plant models can not only provide information on suitable processes at different organisational levels (and thus also sensing technologies), but also on the timescales⁵⁹ as which we can perform reservoir computing.

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.

Considering the plant as an information processing unit leads to a more holistic view of plant phenotyping, integrating the effect of plant responses over all environmental cues, thus stepping away from only considering specific aspects. While the work presented here is fundamental research on PRC with plants, applications in breeding and phenotyping can already be identified. For instance, in Fig.4b, we observed a slight dip around 200500s. As a result, there might be a lag between a change in light intensity and the resulting difference in leaf thickness⁶⁰. This dip may imply a time lag of 200500s 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 such relationships (i.e. reducing the time lag) 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^61,62. Reservoir computing can provide the means to characterise this mismatch. More generally, plant reservoir computing may help to identify plants that are able to respond more appropriately to environmental drivers, thereby extending the phenotyping capabilities for breeding. In a broader phenotyping context, PRC can provide a means to interpret plant responses. It allows for the interpretation of experiments in which many environmental factors fluctuate instead of varying only a few. This is a more realistic setting that can help us better understand how plants react and interact with their surroundings in ecological and agricultural settings¹¹. Yet, applications need not be limited to breeding and phenotyping. By means of PRC, plants can become active participants in the control loops of agricultural systems. This is in stark contrast to following a predefined trajectory or relying on (in)direct measurements or manual assessment to detect sub-optimal growing conditions. Consequently, stress experienced by plants can be rapidly discovered and actions for rectification of the stress cause can be taken earlier. PRC with plants can thus form an alternative to conventional machine learning approaches that are being introduced in agriculture. For such agricultural systems, extensive domain knowledge and datasets are typically needed to achieve good results⁶³. By investigating a more plant-centric method, we hope an alternative approach will arise that avoids such problems and is better able to bootstrap itself though global rewards for instance in the case of Hebbian learning⁵⁶.

To summarise, in this work, we presentedto the best of our knowledgethe first application of physical reservoir computing with plants, more specifically strawberry (Fragaria \(\times\) ananassa). We investigated several types of tasks, including environmental, eco-physiological and benchmark tasks. The results indicate that plants are not suited for general-purpose (digital) computation but are potentially highly interesting for plant-specific tasks and applications in phenotyping. Plants are best at solving eco-physiological and environmental tasks, more specifically transpiration rate E, photosynthesis rate \(P_n\) and light intensity \(I_\text PAR\).