Phenomenological Modelling

Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa

Detecting causal interactions among climatic, environmental, and human forces in complex biophysical systems is essential for understanding how these systems function and how public policies can be devised that protect the flow of essential services to biological diversity, agriculture, and other core economic activities. Convergent Cross Mapping (CCM) detects causal networks in real-world systems diagnosed with deterministic, low-dimension, and nonlinear dynamics. If CCM detects correspondence between phase spaces reconstructed from observed time series variables, then the variables are determined to causally interact in the same dynamic system. CCM can give false positives by misconstruing synchronized variables as causally interactive. Extended (delayed) CCM screens for false positives among synchronized variables.

2020 ◽  
Author(s):  
Ray Huffaker ◽  
Eric S. McLamore

Abstract This protocol sets out a broadly-applicable framework for empirically reconstructing the dynamics of biosystems from observational data, modeling reconstructed dynamics phenomenologically with systems of ordinary differential equations extracted from the data, and detecting and quantifying causal interactions among system components. The protocol draws from well-established procedures in Nonlinear Time Series Analysis (NLTS) that can be run with existing R packages. The protocol was applied in McLamore et al. (2020)1 to develop a phenomenological digital proxy of a bioreactor (DIYBOT) from real-time sensor data. DIYBOT was used to investigate whether bioreactor dynamics self-corrected in response to contamination spikes of increasing degrees; and consequently, the extent to which corrective human-in-the-loop management might be required.


Author(s):  
Neal Wagner ◽  
Zbigniew Michalewicz ◽  
Sven Schellenberg ◽  
Constantin Chiriac ◽  
Arvind Mohais

2020 ◽  
Author(s):  
Nikolay Strigul ◽  
Adam Erickson

<div> <div> <div> <p>Management controls the spatial configuration of a number of landscapes globally, from forests to rangelands. The majority of landcover change and all land-use change is the result of human decision-making. As human populations and global temperatures continue to increase, an engineering approach is needed to ensure the persistence of biological diversity and natural capital critical to human well-being. Such an approach may be based on manipulating ecosystems to achieve desired future states, informed by the latest simulation models. Models of the land surface are now being used to inform policy in the form of planning and management practices. This often involves the application of models that include spatial dynamics and operate at a landscape scale. The strong correspondence between the resolution and extent of modeling and management activities at this scale, and ability to efficiently simulate the decadal-to-centennial time-scales of interest, provide managers with a credible scientific tool for anticipating future land states under different scenarios. The importance of such tools to managers has grown dramatically with the challenges posed by anthropogenic climate change. As ecosystem simulation models continually improve in precision, accuracy, and robustness, we posit that models may be mathematically optimized as a basis for optimizing the management of real-world systems. Since current ecosystem simulation models are coarse approximations of highly complex and dynamic real-world systems, such optimizations should ideally account for uncertainty and physical or biochemical constraints, thereby improving the tractability of the optimization problem. In this work, we demonstrate the emulation and optimization of a forest biogeochemistry model from the SORTIE-PPA family of models. In doing so, we provide the first demonstration of the concept of biosphere optimization (Erickson 2015), which may one day be extended to include computational genetic manipulation experiments. To perform this work, we utilize the open-source Earth-systems Research and Development Environment (ERDE) library, which contains built-in functions for performing these and other analyses with land models, with a particular focus on forests.</p> </div> </div> </div>


1998 ◽  
Vol 2 ◽  
pp. 141-148
Author(s):  
J. Ulbikas ◽  
A. Čenys ◽  
D. Žemaitytė ◽  
G. Varoneckas

Variety of methods of nonlinear dynamics have been used for possibility of an analysis of time series in experimental physiology. Dynamical nature of experimental data was checked using specific methods. Statistical properties of the heart rate have been investigated. Correlation between of cardiovascular function and statistical properties of both, heart rate and stroke volume, have been analyzed. Possibility to use a data from correlations in heart rate for monitoring of cardiovascular function was discussed.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Qing Yao ◽  
Bingsheng Chen ◽  
Tim S. Evans ◽  
Kim Christensen

AbstractWe study the evolution of networks through ‘triplets’—three-node graphlets. We develop a method to compute a transition matrix to describe the evolution of triplets in temporal networks. To identify the importance of higher-order interactions in the evolution of networks, we compare both artificial and real-world data to a model based on pairwise interactions only. The significant differences between the computed matrix and the calculated matrix from the fitted parameters demonstrate that non-pairwise interactions exist for various real-world systems in space and time, such as our data sets. Furthermore, this also reveals that different patterns of higher-order interaction are involved in different real-world situations. To test our approach, we then use these transition matrices as the basis of a link prediction algorithm. We investigate our algorithm’s performance on four temporal networks, comparing our approach against ten other link prediction methods. Our results show that higher-order interactions in both space and time play a crucial role in the evolution of networks as we find our method, along with two other methods based on non-local interactions, give the best overall performance. The results also confirm the concept that the higher-order interaction patterns, i.e., triplet dynamics, can help us understand and predict the evolution of different real-world systems.


2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ferenc Molnar ◽  
Takashi Nishikawa ◽  
Adilson E. Motter

AbstractBehavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized—and thus homogeneous—across the network, previous work suggests that the stability of synchronous states can be improved by making the generators homogeneous. Here, we show that a substantial additional improvement is possible by instead making the generators suitably heterogeneous. We develop a general method for attributing this counterintuitive effect to converse symmetry breaking, a recently established phenomenon in which the system must be asymmetric to maintain a stable symmetric state. These findings constitute the first demonstration of converse symmetry breaking in real-world systems, and our method promises to enable identification of this phenomenon in other networks whose functions rely on behavioral homogeneity.


Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 969
Author(s):  
Miguel C. Soriano ◽  
Luciano Zunino

Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon.


1995 ◽  
Vol 06 (04) ◽  
pp. 373-399 ◽  
Author(s):  
ANDREAS S. WEIGEND ◽  
MORGAN MANGEAS ◽  
ASHOK N. SRIVASTAVA

In the analysis and prediction of real-world systems, two of the key problems are nonstationarity (often in the form of switching between regimes), and overfitting (particularly serious for noisy processes). This article addresses these problems using gated experts, consisting of a (nonlinear) gating network, and several (also nonlinear) competing experts. Each expert learns to predict the conditional mean, and each expert adapts its width to match the noise level in its regime. The gating network learns to predict the probability of each expert, given the input. This article focuses on the case where the gating network bases its decision on information from the inputs. This can be contrasted to hidden Markov models where the decision is based on the previous state(s) (i.e. on the output of the gating network at the previous time step), as well as to averaging over several predictors. In contrast, gated experts soft-partition the input space, only learning to model their region. This article discusses the underlying statistical assumptions, derives the weight update rules, and compares the performance of gated experts to standard methods on three time series: (1) a computer-generated series, obtained by randomly switching between two nonlinear processes; (2) a time series from the Santa Fe Time Series Competition (the light intensity of a laser in chaotic state); and (3) the daily electricity demand of France, a real-world multivariate problem with structure on several time scales. The main results are: (1) the gating network correctly discovers the different regimes of the process; (2) the widths associated with each expert are important for the segmentation task (and they can be used to characterize the sub-processes); and (3) there is less overfitting compared to single networks (homogeneous multilayer perceptrons), since the experts learn to match their variances to the (local) noise levels. This can be viewed as matching the local complexity of the model to the local complexity of the data.


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