Scientific observations, experiments, and simulations are producing data at rates beyond our capacity to store, analyze, stream, and archive the data in raw form. Of necessity, many research groups have already begun reducing the size of their data sets via techniques such as compression, reduced order models, experiment-specific triggers, filtering, and feature extraction. Once reduced in size, transporting, storing, and analyzing the data is still a considerable challenge a reality that motivates SCs Integrated Research Infrastructure (IRI) program [1] and necessitates further innovation in data-reduction methods. These further efforts should continue to increase the level of mathematical rigor in scientific data reduction to ensure that scientifically-relevant constraints on quantities of interest are satisfied, that methods can be integrated into scientific workflows, and that methods are implemented in a manner that inspires trust that the desired information is preserved. Moreover, as the scientific community continues to drive innovation in artificial intelligence (AI), important opportunities to apply AI methods to the challenges of scientific data reduction and apply data-reduction techniques to enable scientific AI, continue to present themselves [2-4].The drivers for data reduction techniques constitute a broad and diverse set of scientific disciplines that cover every aspect of the DOE scientific mission. An incomplete list includes light sources, accelerators, radio astronomy, cosmology, fusion, climate, materials, combustion, the power grid, and genomics, all of which have either observatories, experimental facilities, or simulation needs that produce unwieldy amounts of raw data. ASCR is interested in algorithms, techniques, and workflows that can reduce the volume of such data, and that have the potential to be broadly applied to more than one application. Applicants who submit a pre-application that focuses on a single science application may be discouraged from submitting a full proposal.Accordingly, a virtual DOE workshop entitled Data Reduction for Science was held in January of 2021, resulting in a brochure [5] detailing four priority research directions (PRDs) identified during the workshop. These PRDs are (1) effective algorithms and tools that can be trusted by scientists for accuracy and efficiency, (2) progressive reduction algorithms that enable data to be prioritized for efficient streaming, (3) algorithms which can preserve information in features and quantities of interest with quantified uncertainty, and (4) mapping techniques to new architectures and use cases. For additional background, see [6-9].The principal focus of this FOA is to support applied mathematics and computer science approaches that address one or more of the identified PRDs. Research proposed may involve methods primarily applicable to high-performance computing, to scientific edge computing, or anywhere scientific data must be collected or processed. Significant innovations will be required in the development of effective paradigms and approaches for realizing the full potential of data reduction for science. Proposed research should not focus only on particular data sets from specific applications, but rather on creating the body of knowledge and understanding that will inform future scientific advances. Consequently, the funding from this FOA is not intended to incrementally extend current research in the area of the proposed project. Rather, the proposed projects must reflect viable strategies toward the potential solution of challenging problems in data reduction for science. It is expected that the proposed projects will significantly benefit from the exploration of innovative ideas or from the development of unconventional approaches. Proposed approaches may include innovative research with one or more key characteristics, such as compression, reduced order models, experiment-specific triggers, filtering, and feature extraction, and may focus on cross-cutting concepts such as artificial intelligence or trust. Preference may be given to pre-applications that include reduction estimates for at least two science applications.