Data-driven mechanistic modeling for complex systems design

​My primary research goal is to connect the speed and automation of top-down data-driven model selection methods with the explanatory power of bottom-up mechanistic modeling. Mechanistic modeling provides a powerful framework for systems design and optimization, but relies on close integration of model development and experimental validation. Data science methods promise rapid, automated, descriptions and predictions for complex systems, generally without knowledge of underlying mechanism. By combining the two, I can more rapidly develop explanatory mechanistic models that can be used to optimize system performance and design engineering solutions.

Data driven methods for inferring nonlinear dynamics. 

Inferring the structure and dynamics of complex systems is critical to understanding and controlling their functionality.  With colleagues, I have developed a suite of tools for automated model generation and evaluation in complex systems, including those with rational functions in the dynamics and hybrid systems with multiple dynamic regimes. Many of these methods are based around Sparse Identification of Nonlinear Dynamics (SINDy) developed by Brunton, Proctor, and Kutz.

Data assimilation for hidden, sparse inference (DAHSI) is a model identification method combining a variational annealing method for parameter estimation with sparsity-promoting constraints. Variational annealing is a data assimilation method which works well for chaotic and oscillatory or spiking systems, such as neural models, when some of the state-variables are hidden or unmeasured.  We assume we have one hidden variable and demonstrate recovery of the Lorenz-63 system and Colpitts, as well as model-selection from real data from a Lorenz-like circuit system.
  •  H. Ribera, S. Shirman, A. V. Nguyen, N. M. Mangan. "Model selection of chaotic systems from data with hidden variables using sparse data assimiliation." Chaos 32, 063101 (2022). 
Implicit-SINDy is a data-driven method for inferring nonlinear dynamical systems which combines a compact feature library, implicit formulation to enable discovery of rational functions, and sparsity promoting non-convex optimization.  In contrast to other algorithms, the models constructed using implicit-SINDy are biologically and physically interpretable. These rapidly constructed models provide mechanistic understanding that could be leveraged for therapeutic gene modulation—to treat genetic diseases, metabolic engineering—to design novel biochemical pathways and products, and intervention in infectious disease network—such as outbreak detection and response.​​By coupling (explicit) SINDy with Akaike information criteria we can perform model selection from a comprehensive feature library, validate on out-of-sample data, and rank the set of down-selected models. This framework avoids a combinatoric or greedy search through model-space and provides statistical comparison between likely models in an automated fashion.  Many complex systems have multiple dynamic regimes where the equations or coefficients may vary in time. Sudden switching at internally or externally driven events can be difficult to detect, and existing model selection techniques are ill-suited to these types of systems. Hybrid-SINDy works by clustering data-points from geometrically similar coordinates in measurement space, and performing model selection and out-of-sample validation on clusters locally in this space. Through a frequency analysis of strongly supported models across all clusters we can identify switching points, distinct dynamical regimes, and the appropriate models within these regimes.

Development and Physical Constraints

We are working with Erik Andersen's group to undesrtand how C. elegans regulate their growth during development. We are interested in the complex mapping between environmental signals, genetic rules, and physical and chemical constraints on growth.  Physical constraints setting the stretchiness of the C. elegans cuticle may be responsible for cueing developmental decisions to move between laval stages. By sensing the material limits of cuticle stretch C. elegans may be able to measure their size and change their eating behavior or reallocate metabolic resources in preparation for the next developmental stage.
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Spatial organization in cells enhances throughput of biochemical pathways
Synthetic biology has the potential to revolutionize production of high value products like biofuels, alternatives to plastic, and pharmaceuticals.  In nature,  most species organize their biochemical reactions within the cell to reduce leakage of substrates out of the cell, minimize the effects of volatile or toxic intermediates, and avoiding unwanted competitive reactions.​ By mapping out which of these organizational strategies work best for a variety of chemical pathways, we can formulate design rules for bioengineering. Engineering photosynthetic organisms such as cyanobacteria, algea, and plants, would increase production of compounds and food from inorganic CO2 and sunlight. We are also interested in how spatial organization of a few metabolic reactions (2-3) can be used to direct flux within the entire metabolic network.
Systems-level modeling to optimize renewable energy systems
I am passionate about research which enhances alternative energy. My interest in biological metabolic networks was originally inspired by the potential to bioengineer living biofuel factories. I have also worked on design rules for solar cells and wind turbine arrays.
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