2018-2020 Assessment of the Army Research Office (2021) / Chapter Skim
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4 Mathematical Sciences Division
4 Mathematical Sciences Division
Pages 36-44
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COMPUTATIONAL MATHEMATICS PROGRAM Overall Scientific Quality and Degree of Innovation The objectives of this program are to develop mathematical characterizations and computational models for (1) common themes in anomalous physics; (2)
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Significant Accomplishments The Computational Mathematics Program had some significant scientific advances. For example, the work on fast solvers for fractional partial differential equations represents a significant advance in the field.
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There may be opportunities to increase the feedback and cooperation of managers of other programs for projects with intellectual themes that cross over into other areas of the mathematical sciences. Significant Accomplishments Most researchers appear to be accomplishing stated research goals.
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MODELING OF COMPLEX SYSTEMS PROGRAM Overall Scientific Quality and Degree of Innovation Starting from a hypothesis that direct simulation approaches (e.g., computational partial differential equations) are insufficient for effective characterization of the systems of Army/DoD interest, this program has chosen to focus its activities on the nascent fields of geometric and topological analysis of complex systems.
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Relevance/Transitions Funded projects have led to tangible benefit to the Army such as the work on environment reconstruction delivered to the ARL Survivability and Analysis Directorate or the work on improved facial recognition delivered to the ARL Sensors and Electron Devices Directorate. In addition to these direct transitions, funding has led to efficient identification of adversarial groups from topological considerations (work by a Small Business Innovation Research program researcher for the Psychological Operations Group at Fort Bragg)
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As an example, quantum communication and information processing would seem a prime candidate for a joint funding mechanism. The collaboration of NSF/NIH in the joint Division of Mathematical Sciences/National Institute of General Medical Sciences program could serve as a useful role model and allow the ARO to leverage limited funds with more impact.
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Overall Scientific Quality and Innovation The PIs and research outcomes are of generally high quality. There are many examples of the PIs receiving prestigious academic recognition, including Presidential Early Career Awards for Scientists and Engineers (PECASE)
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The division's program might be strengthened if such short-term funding were used as part of an entrepreneurial model with the goal of developing a diverse set of competing technical approaches to high-opportunity topics. Promising areas for the expansion of the scientific program include statistical methods and reinforcement learning in biology and learning combined with computational partial differential equations.
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programs at ARO support centers whose efforts intersect more than one traditional research specialty, typically at $1.25 million per year for 5 years. Research topics increasingly benefit from such multidisciplinary participation, even in pairs or small sets of investigators and over shorter time periods.
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