Learning to learn ecosystems from limited data -- a meta-learning approach

TL;DR

A meta-learning framework with time-delayed feedforward neural networks to predict the long-term behaviors of ecological systems as characterized by their attractors is developed and it is shown that the framework is capable of accurately reconstructing the "dynamical climate" of the ecological system with limited data.

Abstract

A fundamental challenge in developing data-driven approaches to ecological systems for tasks such as state estimation and prediction is the paucity of the observational or measurement data. For example, modern machine-learning techniques such as deep learning or reservoir computing typically require a large quantity of data. Leveraging synthetic data from paradigmatic nonlinear but non-ecological dynamical systems, we develop a meta-learning framework with time-delayed feedforward neural networks to predict the long-term behaviors of ecological systems as characterized by their attractors. We show that the framework is capable of accurately reconstructing the ``dynamical climate'' of the ecological system with limited data. Three benchmark population models in ecology, namely the Hastings-Powell model, a three-species food chain, and the Lotka-Volterra system, are used to demonstrate the performance of the meta-learning based prediction framework. In all cases, enhanced accuracy and robustness are achieved using five to seven times less training data as compared with the corresponding machine-learning method trained solely from the ecosystem data. A number of issues affecting the prediction performance are addressed.

Figures (13)

• Figure 1: Illustration of the proposed meta-learning framework for reconstructing ecosystems from limited data. (a) Adaptation phase, where the neural-network architecture is trained on various datasets from synthetic nonlinear chaotic systems so it learns the skill of learning and therefore can better learn the target ecosystem. (b) Illustration of the Reptile algorithm, a gradient-based meta-learning method - see text for details. (c) Deployment phase in which the trained meta-learning framework is applied to the target ecosystem, accomplishing the objective of predicting its long-term dynamics or attractor from limited time-series data. (d) An illustration of the comparison of the data requirements for achieving similar performance by our proposed meta-learning framework and standard machine-learning (vanilla model) in reconstructing the Hastings-Powell system.
• Figure 2: Main result: long-term ecosystem prediction by the meta-learning and vanilla frameworks. (a,b) Attractor reconstruction by the two frameworks. (c,d) Intercepted snippets of the three time series of the ground truth and prediction by the two frameworks. (e) DV versus the training length for the meta-learning and vanilla frameworks. (f) Stability indicator of prediction ($R_s({\rm DV}_c)$) versus the training length for the meta-learning and vanilla frameworks. The upper, middle, and lower panels in (e) and (f) are from the chaotic Hastings-Powell, food chain, and Lotka-Volterra systems, respectively. To reduce the statistical fluctuations, the DVs, their shaded variabilities and the $R_s({\rm DV}_c)$ values are calculated from an ensemble of 50 independently trained neural machines.
• Figure 3: Robustness of ecosystem forecasting against environmental noise. The top, middle, and bottom rows are attractor-prediction results for the chaotic Hastings-Powell, food chain, and Lotka-Volterra systems, respectively. The left and right columns are results from the meta-learning and vanilla frameworks, respectively. The same training lengths are used in all cases. The average prediction DV and the error bar are obtained from 50 independent training and testing runs. For meta-learning, the DVs remain small and approximately constant when the noise amplitude is below $10^{-2}$. Overall, the prediction results from meta-learning are more accurate and robust against noise than the vanilla framework.
• Figure 4: Selecting the synthetic chaotic systems for the adaptation phase of meta-learning. (a) Illustration of greedy algorithm. Stated with the three systems in the sampled systems pool, one or several systems is (are) selected which lead to the best improvement in performance. (b) Ensemble averaged DV (with 50 independent realizations) versus the number of sampled systems pool $n_s$. As $n_s$ increases, the average DV decreases rapidly but later increases again.
• Figure 5: Architecture of a time-delayed feedforward neural network. There are three main components: the input layer, a number of hidden layers, and the output layer, where $u(t), u(t-\tau), \cdots, u(t-m\tau)$ are the present and historical signal with $\tau$ being the time delay and $m$ being the embedding dimension. The output is $v(t)$.