Partitioning time series to improve process-based models with machine learning

Abstract

Ecosystems are involved in global biogeochemical cycles that regulate climate and provide essential services to human societies. Mechanistic models are required to describe ecosystem dynamics and anticipate their response to anthropogenic pressure, but their adoption has been limited in practice because of issues with parameter identification and because of model inaccuracies. While observations could be used to directly estimate parameters and improve models, model nonlinearities as well as shallow, incomplete and noisy datasets complicate this process. Here, we propose a machine learning (ML) framework relying on a mini-batch method combined with automatic differentiation and state-of-the-art optimizers. By splitting the data into mini-batches with a short time horizon, we show both analytically and numerically that the mini-batch method regularizes the learning problem. When combined with the proposed numerical implementation, the resulting ML framework can efficiently learn the parameter of complex dynamical models and is a workhorse for model selection. We evaluate the performance of the ML framework in recovering the dynamics of a simulated food-web. We show that it can efficiently learn from noisy, incomplete and independent time series, accurately estimating the model parameters and providing reliable short-term forecasts. We further show that the ML framework can provide statistical support for the true generating model among several candidates. In summary, the proposed ML framework can efficiently learn from data and elucidate mechanistic pathways to improve our understanding and predictions of ecosystem dynamics.

Processes analogous to ecological interactions and dispersal shape the dynamics of economic activities

“…To obtain the maximum likelihood of each model we employ the machine learning framework detailed in [10],…”

“…The likelihood of model M i is maximised by training M i against segments of data comprising only K < T (c) data points of the full time series, where the parameters and the initial conditions for each segment are estimated. The segmentation method ensures convergence towards the maximum likelihood estimate, provided that the choice of K is appropriate, given the data and the model investigated [10]. A large K might induce convergence towards a local minimum, while a low K might flatten the likelihood landscape, where all models would be assigned equal support.…”

“…We therefore use K = 20 throughout all the experiments detailed in the manuscript, and discard countries where data is available for less than K = 20 years. We employ the Julia package PiecewiseInference.jl [10] for the numerical implementation. We use the gradient descent optimiser ADAM [57] during the first 800 epochs to converge in the basin of attraction of the maximum likelihood estimate.…”

“…While biological analogies have resulted in useful insights into the plausible drivers of economic growth [1], most investigations of the proposed pathways have been qualitative. However, computational tools have recently made it possible to test biological hypotheses against data to gain a quantitative understanding of the ecological and evolutionary processes shaping the dynamics of ecological systems [9,10,11]. These tools could leverage the qualitative insights gained from biological analogies and provide a quantitative framework to investigate the forces shaping economic change.…”

“…We contrast M null with alternative dynamic community models coupling the dynamics between economic activities, including both negative and positive ecological interactions between the activities (M α − , M α + ), the spatial dispersal of the activities (M δ ), and their transformations into other economic activities (M µ ). We use the machine learning framework of [10] to estimate the maximum likelihood of each model for 96 countries. We use a model selection technique to evaluate the statistical support for each alternative model, based on a dataset of national exports from 1962 to 2020, taken as a proxy for the temporal development of the capital of economic activities.…”