Project Grant 2608264
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $139,995 on June 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop robust, scalable, and statistically principled methods for integrating and analyzing multimodal data with emphasis on uncertainty quantification. The research addresses the challenge of nonparametric estimation when multiple high-dimensional and heterogeneous data sources—such as...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $330,000 on January 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop randomized algorithms for operator learning in Sobolev spaces with application to parametric partial differential equations. The project addresses computational constraints in neural network-based operator learning by designing and analyzing randomized training algorithms...
- The National Science Foundation Division of Mathematical Sciences awarded $214,876 to the University of California, Los Angeles on October 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049). The project develops a rigorous theoretical foundation for multi-operator learning, establishing a mathematical framework to understand how neural networks can efficiently learn across collections of complex physical systems. The work addresses gaps between empirical advances in deep...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $271,080 on January 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop AI models that reason constructively about complex mathematical problems and advance formal proof systems. The collaborative research project, spanning January 1, 2026, through December 31, 2028, and performed in Los Angeles, California, aims to synergize artificial...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $120,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to advance structural properties of the universe of mathematics through research in forcing, large cardinals, and descriptive set theory. The recipient will investigate three specific subjects: the tree property of cardinal numbers and its connection to large cardinal axioms and...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $1.08 million on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop a human-centered, AI-assisted framework for interactive mathematical reasoning and discovery. The project, running through August 31, 2029, establishes effective human-AI collaboration paradigms that adapt to user expertise while preserving interpretability and...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $145,000 on August 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop rigorous mathematical theory predicting localization and delocalization transitions in complex disordered quantum systems. The research focuses on non-mean-field random matrices and addresses fundamental questions about when electrons, waves, and other excitations remain...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $1,263,600 on September 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to establish a Research Training Group in Statistics and Data Theory based in UCLA's Department of Statistics & Data Science. The award funds an integrated research and training ecosystem spanning high school through postdoctoral levels. Undergraduate students will participate in...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $120,000 on June 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop theory and methodology for statistical inference on spatiotemporal rates of change and gradients, with applications to boundary assessment that tracks significant changes in spatiotemporal response. The project develops methodology and software for quantifying and understanding...
- The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $200,000 on July 1, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to conduct mathematical research on interactions of Fourier restriction with fractal geometry and number theory. The investigator uses harmonic analysis tools to understand refined behavior of the Fourier transform under special geometric conditions relevant to applications including the...
The National Science Foundation Division of Mathematical Sciences awarded the University of California, Los Angeles $300,000 on August 15, 2026, under the Mathematical and Physical Sciences program (CFDA 47.049) to develop mathematical foundations and scalable algorithms for high-dimensional sampling and generative modeling. The project develops a unified mathematical and computational framework for sampling and generative modeling applicable to high-dimensional problems in scientific inference and artificial intelligence. Research focuses on three connected directions, including determining when numerical errors in low-dimensional marginals remain small as problem dimensionality increases. The work targets applications in astronomical observation interpretation, uncertainty quantification in scientific models, and turbulent-flow data generation. UCLA will release open-source software, integrate project findings into interdisciplinary courses with freely available educational materials, and provide research opportunities for students from precollege through graduate study. Performance occurs at UCLA's Los Angeles, California location through the Office of Research Administration, with an ultimate completion date of July 31, 2029. The project strengthens probabilistic computation to advance U.S. leadership in mathematics and artificial intelligence while broadening participation in mathematical and computational science.
Mod # | Description | ReasonForModification | Federal Obligation | Date |
|---|---|---|---|---|
| Not listed | $300.0k | 8/5/26 |