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EXPLORE IDM’S CURRENT RESEARCH PUBLICATIONS

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Samuel H. Rudy, Steven L. Brunton, Joshua L. Proctor, and J. Nathan Kutz

SCIENCE ADVANCES

We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity-promoting techniques to select the nonlinear and partial derivative terms of the governing equations that most accurately represent the data, bypassing a combinatorially large search through all possible candidate models. The method balances model complexity and regression accuracy by selecting a parsimonious model via Pareto analysis. Time series measurements can be made in an Eulerian framework, where the sensors are fixed spatially, or in a Lagrangian framework, where the sensors move with the dynamics. The method is computationally efficient, robust, and demonstrated to work on a variety of canonical problems spanning a number of scientific domains including Navier-Stokes, the quantum harmonic oscillator, and the diffusion equation. Moreover, the method is capable of disambiguating between potentially nonunique dynamical terms by using multiple time series taken with different initial data. Thus, for a traveling wave, the method can distinguish between a linear wave equation and the Korteweg–de Vries equation, for instance. The method provides a promising new technique for discovering governing equations and physical laws in parameterized spatiotemporal systems, where first-principles derivations are intractable.

2017 AMERICAN CONTROL CONFERENCE (ACC)

Utilizing the concept of observability, in conjunction with tools from graph theory and optimization, this paper develops an algorithm for network synthesis with privacy guarantees. In particular, we propose an algorithm for the selection of optimal weights for the communication graph in order to maximize the privacy of nodes in the network, from a control theoretic perspective. In this direction, we propose an observability-based design of the communication topology that improves the privacy of the network in presence of an intruder. The resulting adaptive network responds to the intrusion by changing the topology of the network-in an online manner- in order to reduce the information exposed to the intruder.

INFECTIOUS DISEASE MODELING

The emergence of Zika and Ebola demonstrates the importance of understanding the role of sexual transmission in the spread of diseases with a primarily non-sexual transmission route. In this paper, we develop low-dimensional models for how an SIR disease will spread if it transmits through a sexual contact network and some other transmission mechanism, such as direct contact or vectors. We show that the models derived accurately predict the dynamics of simulations in the large population limit, and investigate ℛ0 and final size relations.

SIAM NEWS

Ordinary and partial differential equations are widely used throughout the engineering, physical, and biological sciences to describe the physical laws underlying a given system of interest. We implicitly assume that the governing equations are known and justified by first principles, such as conservation of mass or momentum and/or empirical observations. From the Schrödinger equation of quantum mechanics to Maxwell’s equations for electromagnetic propagation, knowledge of the governing laws has allowed transformative technology (e.g., smart phones, internet, lasers, and satellites) to impact society. In modern applications such as neuroscience, epidemiology, and climate science, the governing equations are only partially known and exhibit strongly nonlinear multiscale dynamics that are difficult to model. Scientific computing methods provide an enabling framework for characterizing such systems, and the SIAM community has historically made some of the most important contributions to simulation-based sciences, including extensive developments in finite-difference, finite-element, spectral, and reduced-order modeling methods.

PLOS

Using a computational model of the Caenorhabditis elegans connectome dynamics, we show that proprioceptive feedback is necessary for sustained dynamic responses to external input. This is consistent with the lack of biophysical evidence for a central pattern generator, and recent experimental evidence that proprioception drives locomotion. The low-dimensional functional response of the Caenorhabditis elegans network of neurons to proprioception-like feedback is optimized by input of specific spatial wavelengths which correspond to the spatial scale of real body shape dynamics. Furthermore, we find that the motor subcircuit of the network is responsible for regulating this response, in agreement with experimental expectations. To explore how the connectomic dynamics produces the observed two-mode, oscillatory limit cycle behavior from a static fixed point, we probe the fixed point’s low-dimensional structure using Dynamic Mode Decomposition. This reveals that the nonlinear network dynamics encode six clusters of dynamic modes, with timescales spanning three orders of magnitude. Two of these six dynamic mode clusters correspond to previously-discovered behavioral modes related to locomotion. These dynamic modes and their timescales are encoded by the network’s degree distribution and specific connectivity. This suggests that behavioral dynamics are partially encoded within the connectome itself, the connectivity of which facilitates proprioceptive control.

 

ARXIV.ORG

We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which typically limits the number candidate models considered due to the intractability of computing information criteria. Using a recently developed sparse identification of nonlinear dynamics algorithm, the sub-selection of candidate models near the Pareto frontier allows for a tractable computation of AIC (Akaike information criteria) or BIC(Bayes information criteria) scores for the remaining candidate models. The information criteria hierarchically ranks the most informative models, enabling the automatic and principled selection of the model with the strongest support in relation to the time series data. Specifically, we show that AIC scores place each candidate model in the strong support, weak support or no support category. The method correctly identifies several canonical dynamical systems, including an SEIR (susceptibleexposed-infectious-recovered) disease model and the Lorenz equations, giving the correct dynamical system as the only candidate model with strong support

Akullian, Adam PhD, Onyango, Mathews MPH, Klein, Daniel PhD, Odhiambo, Jacob MBChB, Bershteyn, Anna PhD

MEDICINE

Voluntary Medical Male Circumcision (VMMC) for human immunodeficiency virus (HIV) prevention has scaled up rapidly among young men in western Kenya since 2008. Whether the program has successfully reached uncircumcised men evenly across the region is largely unknown. Using data from two cluster randomized surveys from the 2008 and 2014 Kenyan Demographic Health Survey (KDHS), we mapped the continuous spatial distribution of circumcised men by age group across former Nyanza Province to identify geographic areas where local circumcision prevalence is lower than the overall, regional prevalence. The prevalence of self-reported circumcision among men 15 to 49 across six counties in former Nyanza Province increased from 45.6% (95% CI = 33.2–58.0%) in 2008 to 71.4% (95% CI = 67.4–75.0%) in 2014, with the greatest increase in men 15 to 24 years of age, from 40.4% (95% CI = 27.7–55.0%) in 2008 to 81.6% (95% CI = 77.2–85.0%) in 2014. Despite the dramatic scale-up of VMMC in western Kenya, circumcision coverage in parts of Kisumu, Siaya, and Homa Bay counties was lower than expected (P < 0.05), with up to 50% of men aged 15 to 24 still uncircumcised by 2014 in some areas. The VMMC program has proven successful in reaching a large population of uncircumcised men in western Kenya, but as of 2014, pockets of low circumcision coverage still existed. Closing regional gaps in VMMC prevalence to reach 80% coverage may require targeting specific areas where VMMC prevalence is lower than expected.

Akullian, Adam PhD, Onyango, Mathews MPH, Klein, Daniel PhD, Odhiambo, Jacob MBChB, Bershteyn, Anna PhD

MEDICINE

Voluntary Medical Male Circumcision (VMMC) for human immunodeficiency virus (HIV) prevention has scaled up rapidly among young men in western Kenya since 2008. Whether the program has successfully reached uncircumcised men evenly across the region is largely unknown. Using data from two cluster randomized surveys from the 2008 and 2014 Kenyan Demographic Health Survey (KDHS), we mapped the continuous spatial distribution of circumcised men by age group across former Nyanza Province to identify geographic areas where local circumcision prevalence is lower than the overall, regional prevalence. The prevalence of self-reported circumcision among men 15 to 49 across six counties in former Nyanza Province increased from 45.6% (95% CI = 33.2–58.0%) in 2008 to 71.4% (95% CI = 67.4–75.0%) in 2014, with the greatest increase in men 15 to 24 years of age, from 40.4% (95% CI = 27.7–55.0%) in 2008 to 81.6% (95% CI = 77.2–85.0%) in 2014. Despite the dramatic scale-up of VMMC in western Kenya, circumcision coverage in parts of Kisumu, Siaya, and Homa Bay counties was lower than expected (P < 0.05), with up to 50% of men aged 15 to 24 still uncircumcised by 2014 in some areas. The VMMC program has proven successful in reaching a large population of uncircumcised men in western Kenya, but as of 2014, pockets of low circumcision coverage still existed. Closing regional gaps in VMMC prevalence to reach 80% coverage may require targeting specific areas where VMMC prevalence is lower than expected.

PNAS

The renewed effort to eliminate malaria and permanently remove its tremendous burden highlights questions of what combination of tools would be sufficient in various settings and what new tools need to be developed. Gene drive mosquitoes constitute a promising set of tools, with multiple different possible approaches including population replacement with introduced genes limiting malaria transmission, driving-Y chromosomes to collapse a mosquito population, and gene drive disrupting a fertility gene and thereby achieving population suppression or collapse. Each of these approaches has had recent success and advances under laboratory conditions, raising the urgency for understanding how each could be deployed in the real world and the potential impacts of each. New analyses are needed as existing models of gene drive primarily focus on nonseasonal or nonspatial dynamics. We use a mechanistic, spatially explicit, stochastic, individual-based mathematical model to simulate each gene drive approach in a variety of sub-Saharan African settings. Each approach exhibits a broad region of gene construct parameter space with successful elimination of malaria transmission due to the targeted vector species. The introduction of realistic seasonality in vector population dynamics facilitates gene drive success compared with nonseasonal analyses. Spatial simulations illustrate constraints on release timing, frequency, and spatial density in the most challenging settings for construct success. Within its parameter space for success, each gene drive approach provides a tool for malaria elimination unlike anything presently available. Provided potential barriers to success are surmounted, each achieves high efficacy at reducing transmission potential and lower delivery requirements in logistically challenged settings.

IFAC-PAPERSONLINE

Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using regression methods, including sparse regression. Specifically, we generalize the sparse identification of nonlinear dynamics (SINDY) algorithm to include external inputs and feedback control. This method is demonstrated on examples including the Lotka-Volterra predator-prey model and the Lorenz system with forcing and control. We also connect the present algorithm with the dynamic mode decomposition (DMD) and Koopman operator theory to provide a broader context.