# Applied Mathematics Group

### Applied mathematics lies at the intersection of science and technology, mathematical methods, and scientific computing.

We develop and apply the mathematics necessary to model and solve real-world problems. Our team consists of mathematicians, statisticians, engineers, and physicists who work together and with domain scientists at Brookhaven and elsewhere on large-scale, interdisciplinary challenges. Our mission research areas include climate change, materials science, accelerator science, biomedicine, plant pathology, energy systems, and quantum computing. Our mathematical research involves modeling and simulation, uncertainty quantification, reduced order modeling, scientific machine learning, optimization, optimal experimental design, decision science, large-scale integrated computational/experimental workflows, and scalable algorithms for implementing these methods on high-performance computing platforms.

We welcome researchers of different disciplinary/technical backgrounds who are motivated to solve important STEM challenges in the national interest by developing and applying new mathematical and computational methods.

### Group Projects

Brookhavenâ€™s research, as part of the larger multi-institution Framework for Antarctic System Science in E3SM (FAnSSIE) project led by Los Alamos National Laboratory, calibrates ice sheet models to historical observations of Antarctic and quantifies the uncertainties in projected future sea level rise.

As part of Brookhavenâ€™s Four-Dimensional Atmospheric Sensing and Simulation (FASSt) initiative, we are developing a mathematical and computational framework for optimal observing system design based on the principles of Bayesian optimal experimental design.

Digital twins are virtual computational representations of real-world systems that integrate measurements and other information to improve prediction and control in those systems. In the M2dt project, we are building and applying digital twins for the self-assembly of thin polymer films relevant to semiconductor and battery design and ice shelf-ocean cavities that are trigger points for sea level rise.

The Objective-Driven Data Reduction for Scientific Workflows (ODDR) project is developing rigorous theoretical foundations for effective reduction of scientific data and implementing practical algorithms that can significantly reduce the data generated by complex experimental or computational systems.

Led by Brookhaven Lab with partners Los Alamos and Lawrence Berkeley National Laboratories, the RADIUM project is developing a computational framework for optimal decision-making under uncertainty subject to the constraints of limited existing data and a narrow ability to acquire new data; finite computing resources allocated optimally toward achieving specific goals; and confined time frames to generate insight on which to base a decision.

In a multi-institutional collaboration led by the Oregon Health & Science University, we are investigating the calibration of spatial tumor models to experimental data as a first step in determining the clinical utility of a modeling approach to recommend drug combinations.

This project examines the role of uncertainty in GMD computational pipelines. We are exploring systems biology pathway models of cellular protein-protein interactions to assess the probability that a given drug candidate will kill a cancer cell through the application of Bayesian parameter estimation in systems of ordinary differential equations.