arXiv subjects

Fred Daum

Publications and source records attributed to Fred Daum.

4 recordsLinked to original sources

arXiv2025

The Future of Artificial Intelligence and the Mathematical and Physical Sciences (AI+MPS)

This community paper developed out of the NSF Workshop on the Future of Artificial Intelligence (AI) and the Mathematical and Physics Sciences (MPS), which was held in March 2025 with the goal of understanding how the MPS domains (Astronomy, Chemistry, Materials Research, Mathematical Sciences, and Physics) can best capitalize on, and contribute to, the future of AI. We present here a summary and snapshot of the MPS community's perspective, as of Spring/Summer 2025, in a rapidly developing field. The link between AI and MPS is becoming increasingly inextricable; now is a crucial moment to strengthen the link between AI and Science by pursuing a strategy that proactively and thoughtfully leverages the potential of AI for scientific discovery and optimizes opportunities to impact the development of AI by applying concepts from fundamental science. To achieve this, we propose activities and strategic priorities that: (1) enable AI+MPS research in both directions; (2) build up an interdisciplinary community of AI+MPS researchers; and (3) foster education and workforce development in AI for MPS researchers and students. We conclude with a summary of suggested priorities for funding agencies, educational institutions, and individual researchers to help position the MPS community to be a leader in, and take full advantage of, the transformative potential of AI+MPS.

cs.AI↗

arXiv2021

Stability and Convergence of Stochastic Particle Flow Filters

In this paper, we examine dynamic properties of particle flows for a recently derived parameterized family of stochastic particle flow filters for nonlinear filtering and Bayesian inference. In particular, we establish that particles maintain desired posterior distribution without the Gaussian assumption on measurement likelihood. Adopting the concept of Lyapunov stability, we further show that particles stay close but do not converge to the maximum likelihood estimate of the posterior distribution. The results demonstrate that stability of particle flows is maintained for this family of stochastic particle flow filters.

eess.SP↗

arXiv2021

A New Parameterized Family of Stochastic Particle Flow Filters

In this paper, we are interested in obtaining answers to the following questions for particle flow filters: Can we provide a theoretical guarantee that particle flow filters give correct results such as unbiased estimates? Are particle flows stable and under what conditions? Can we have one particle flow filter, rather than multiple seemingly different ones? To answer these questions, we first derive a parameterized family of stochastic particle flow filters, in which particle flows are driven by a linear combination of prior knowledge and measurement likelihood information. We then show that several particle flows existing in the literature are special cases of this family. We prove that the particle flows are unbiased under the assumption of linear measurement and Gaussian distributions, and that estimates constructed from the stochastic flows are consistent. We further establish several finite time stability concepts for this new family of stochastic particle flows. The results reported in this paper represent a significant development toward establishing a theoretical foundation for particle flow filters.

eess.SP↗

arXiv2017

Stochastic Particle Flow for Nonlinear High-Dimensional Filtering Problems

A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to nonlinear filtering problems. They do so by defining a continuum of densities between the prior probability density and the posterior, i.e. the filtering density. Building on these methods' successes, we propose a novel filter. The new filter aims to address the shortcomings of sequential Monte Carlo methods when applied to important nonlinear high-dimensional filtering problems. The novel filter uses equally weighted samples, each of which is associated with a local solution of the Fokker-Planck equation. This hybrid of Monte Carlo and local parametric approximation gives rise to a global approximation of the filtering density of interest. We show that, when compared with state-of-the-art methods, the Gaussian-mixture implementation of the new filtering technique, which we call Stochastic Particle Flow, has utility in the context of benchmark nonlinear high-dimensional filtering problems. In addition, we extend the original particle flow filters for tackling multi-target multi-sensor tracking problems to enable a comparison with the new filter.

stat.ME↗