- Applied Mathematics
- Research in my group currently focuses on inference, prediction, and control of sparsely observed complex systems. We are motivated by the need to make decisions in the natural sciences where mitigating pest outbreaks, predicting harmful algal blooms and disease spread, determining environmental regulations (e.g. set limits to pollution, etc) and setting harvest limits affect the health and livelihoods of millions of people. Ecosystems are comprised of hundreds to thousands of species but we often have data for a small fraction of them. Unlike in the physical sciences, there are no well-vetted models of how ecosystems work that can be leveraged to make predictions. So there’s clearly a need for mathematical methods that allow us to make inferences in these large, sparsely observed networks, to make predictions about future system states, and to guide management. To do so, we make use of a wide range of mathematical tools – primarily nonlinear dynamics and chaos, function approximation and machine learning, and optimal control theory.
- Mathematical methods for inference, prediction, and control of sparsely observed complex systems
- Use of mathematical tools such as primarily nonlinear dynamics and chaos, function approximation and machine learning, and optimal control theory
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