A perspective on bridging scales and design of models using low-dimensional manifolds and data-driven model inference
KAUST DepartmentBiological and Environmental Sciences and Engineering (BESE) Division
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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AbstractSystems in nature capable of collective behaviour are nonlinear, operating across several scales. Yet our ability to account for their collective dynamics differs in physics, chemistry and biology. Here, we briefly review the similarities and differences between mathematical modelling of adaptive living systems versus physico-chemical systems. We find that physics-based chemistry modelling and computational neuroscience have a shared interest in developing techniques for model reductions aiming at the identification of a reduced subsystem or slow manifold, capturing the effective dynamics. By contrast, as relations and kinetics between biological molecules are less characterized, current quantitative analysis under the umbrella of bioinformatics focuses on signal extraction, correlation, regression and machine-learning analysis. We argue that model reduction analysis and the ensuing identification of manifolds bridges physics and biology. Furthermore, modelling living systems presents deep challenges as how to reconcile rich molecular data with inherent modelling uncertainties (formalism, variables selection and model parameters). We anticipate a new generative data-driven modelling paradigm constrained by identified governing principles extracted from low-dimensional manifold analysis. The rise of a new generation of models will ultimately connect biology to quantitative mechanistic descriptions, thereby setting the stage for investigating the character of the model language and principles driving living systems.
CitationTegnér J, Zenil H, Kiani NA, Ball G, Gomez-Cabrero D (2016) A perspective on bridging scales and design of models using low-dimensional manifolds and data-driven model inference. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374: 20160144. Available: http://dx.doi.org/10.1098/rsta.2016.0144.
SponsorsThis work was supported by the following grants to J.T.: Hjärnfonden, ERC Consolidator, Torsten Söderberg Foundation, Stockholm County Council, Swedish Excellence Center for e-Science and Swedish Research Council (3R program MH and project grant NT). H.Z. was supported by Swedish Research Council (NT). N.K. was supported by a fellowship from VINNOVA. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
PublisherThe Royal Society
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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