This Project Grant from the National Science Foundation's Mathematical and Physical Sciences program totaling $449,995 supported research at the University of Texas at Austin from July 15, 2022 to June 30, 2025. The research aims to develop machine learning and parallel-in-time algorithms to efficiently simulate multiscale dynamical systems, reducing overall computation time for applications in physical science and engineering. Specifically, the researchers will construct effective solution...
This $350,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences Program (CFDA 47.049) supports research by the University of Texas at Austin to develop accurate mathematical models and computer simulations of complex non-equilibrium systems with memory effects. The research aims to advance understanding of diverse physical phenomena, such as biosystems, plasma evolution, and solid-state nanostructures, that impact fields ranging from molecular...
This Project Grant award from the National Science Foundation's Mathematical and Physical Sciences (CFDA 47.049) program provides $140,889 to Texas A&M University to conduct research connecting machine learning and numerical methods for partial differential equations. The key objectives are to leverage deep learning techniques to improve numerical methods for PDEs, and apply the theoretical understanding of finite element methods to better comprehend the success of deep neural networks....
The National Science Foundation Division of Mathematical Sciences awarded a $150,000 Project Grant to The University Corporation to support the development of fast methods for solving the Boltzmann equation through reduced order models, machine learning, and optimal transport from September 1, 2021 to August 31, 2024. This award supports research under the Mathematical and Physical Sciences program (CFDA 47.049), which aims to promote progress in the mathematical and physical sciences and...
This Project Grant award from the National Science Foundation's Division of Mathematical Sciences (CFDA 47.049 - Mathematical and Physical Sciences) provides $172,450 to Texas Tech University System to develop innovative time integration methods for simulating complex multiphysics systems with stiff and highly oscillatory behavior. The project aims to derive novel mixed exponential integrators, preconditioned rational exponential integrators, stiffly-accurate embedded multirate exponential...
This $300,000 Project Grant from the National Science Foundation's Division of Mathematical Sciences, under the Mathematical and Physical Sciences program (CFDA 47.049), will support the development of next-generation mathematical and algorithmic tools to address two key issues in applying machine learning to statistical modeling of time-evolving complex systems: a shortage of informative training data and the high computational costs of high-dimensional problems. Specifically, the...
This National Science Foundation Project Grant of $229,021 awarded on August 1, 2022 will support research at the University of Texas at Austin to develop mathematical frameworks in optimal transport applications to probability, machine learning, and kinetic theory through July 31, 2025. Under the Mathematical and Physical Sciences program (CFDA 47.049), the investigator will advance understanding of stochastic modeling, artificial intelligence algorithms, and kinetic theory by exploiting...
This Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program provides $150,922 to Lehigh University to conduct research on asymptotic problems in kinetic theory. The project focuses on developing novel mathematical tools to characterize the multi-scale behaviors of particle systems in applications such as medical imaging, gas dynamics, and nuclear fusion. Key objectives include rigorous analysis to connect microscopic, mesoscopic,...
This $296,555 Project Grant from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) will support the development of reduced basis enhancements for neural networks and their application to quantum materials simulation. Specifically, the University of Massachusetts Dartmouth will combine traditional reduced basis methods with deep learning techniques to build an analysis-driven computational emulator for parameterized partial differential equations....
This $125,000 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences (CFDA 47.049) program will enable the Florida Institute of Technology Inc. (Florida TECH) to utilize advanced machine learning algorithms to efficiently analyze and predict information within high-dimensional data matrices and tensor computations related to state-space dynamical systems. The key objectives are to: (I) utilize machine learning to predict future states of dynamical...