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 theories of optimal mass transportation and gradient flows. For stochastic models including weakly interacting diffusions, the project aims to derive a variational structure capturing phase transitions. In artificial intelligence, the work will obtain mean-field limits of parameter training and characterize successful algorithms like Wasserstein GANs and AlphaGo Zero. For kinetic theory, newly developed gradient flow formulations will provide insight into the Landau and Boltzmann equations. Research training for graduate students is also supported.
Mod # | Description | Reason For Modification | Federal Obligation (Click to sort descending) | Date (Click to sort ascending) |
|---|---|---|---|---|
| Not listed | $229.0k | 7/25/22 |