The National Science Foundation (NSF) awarded a $175,000 project grant under the Mathematical and Physical Sciences (CFDA 47.049) program to Embry-Riddle Aeronautical University, Inc. The grant, effective August 1, 2024 through July 31, 2027, will support collaborative research to develop data-driven methods for realizing and predicting the behavior of state-space dynamical systems using low-complexity algorithms. The project aims to leverage advanced machine learning techniques to efficiently...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will provide $300,000 to the Trustees of Indiana University to conduct research on chaotic systems and topological Lyapunov exponents. The research aims to develop new methods for quantifying the sensitivity of chaotic systems, with a focus on the "butterfly effect" and how small changes in initial conditions can lead to dramatically different outcomes. The...
This National Science Foundation (NSF) Project Grant award under the Mathematical and Physical Sciences (CFDA 47.049) program seeks to advance the understanding of dynamical systems and the evolution from ordered to chaotic behavior. The $249,103 award to the Research Foundation of the City University of New York, effective July 1, 2024 through June 30, 2026, will support research aimed at developing new conceptual ideas, approaches, and theoretical frameworks to transcend the limitations of...
This $300,000 National Science Foundation (NSF) Engineering (CFDA 47.041) Project Grant award to President and Fellows of Harvard College aims to develop efficient and reliable control algorithms for stochastic nonlinear dynamical systems. The research will introduce a novel "Spectral Dynamic Embedding" approach to reformulate nonlinear system dynamics in a way that enables tractable optimization and rigorous analysis of optimal control policies. Potential applications include...
This $250,000 Project Grant award from the National Science Foundation (NSF) Engineering program (CFDA 47.041) aims to address challenges in stochastic nonlinear control and learning for dynamical systems through a novel "Spectral Dynamic Embedding" approach. Led by the Georgia Tech Research Corporation, the research intends to develop computationally efficient control algorithms suitable for applications in robotics, aerospace, manufacturing, and beyond. The key innovations involve...
This Project Grant award, with a total funding amount of $166,285, was provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program. The award supports the development of new mathematical approaches for analyzing complex bifurcations in high-dimensional dynamical systems. This work aims to enable quantitative and qualitative progress in the study of data-driven, detailed, and phenomenologically-reduced models with complex...
This $256,573 National Science Foundation Project Grant under the Mathematical and Physical Sciences program (CFDA 47.049) will support research exploring algebraic aspects of chaotic dynamical systems with hyperbolic behavior at Texas A&M University from July 2022 through June 2025. Specifically, the award will fund investigations into the connections between hyperbolic dynamical systems and group theory, automata theory, and other branches of algebra. The research aims to clarify whether...
The National Science Foundation Division of Mathematical Sciences awarded a $198,055 Project Grant to the Georgia Tech Research Corporation from September 1, 2023 through August 31, 2028 under the Mathematical and Physical Sciences federal grant program (CFDA 47.049). The award will support research investigating chaotic dynamics in dynamical systems with noise, and applying tools from smooth ergodic theory and probability theory to rigorously analyze chaotic behavior in practical systems....
This $299,990 project grant from the National Science Foundation (NSF) Division of Chemical, Bioengineering, Environmental, and Transport Systems will support research at Virginia Polytechnic Institute & State University under the NSF Engineering program (CFDA 47.041) to improve understanding of chaotic fluid convection dynamics. The three-year award beginning April 1, 2022 will use dynamical systems theory and large-scale computing to study fluid dynamics in a shallow heated layer and...
This Project Grant award, provided by the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049), will fund fundamental research on mathematical models that describe complex interactions, growth, and motion in random, irregular environments. The $200,000 award, effective from July 1, 2025 to June 30, 2027, aims to discover general mathematical laws governing such stochastic systems, which have applications in diverse areas like traffic flow, communication...
This Project Grant award of $200,000 from the National Science Foundation's (NSF) Engineering program (CFDA 47.041) supports research at Embry-Riddle Aeronautical University that aims to establish new methods for analyzing and designing highly chaotic engineering systems. The project investigates how expanding the dimensionality of problem spaces and incorporating topological modeling techniques from knot theory can enhance the analysis, visualization, and design of complex chaotic systems. The research also explores how knot theory-informed reinforcement learning with human-in-the-loop interactions can improve design quality, guidance, and decision-making. This work seeks to offer a new approach for understanding chaos that integrates visual, mathematical, and symbolic reasoning, while also engaging broader audiences through immersive learning tools and curriculum development. The award period runs from June 1, 2025 to May 31, 2027.