Quickly determining the dynamic response of complex structures, such as buildings and bridges, when faced with uncertainties that can include, but are not limited to, actual member dimensions and loads they experience, is still a challenge for today's advanced computer modeling tools. Research funded by this award aims to create new methods for analyzing the behavior of complex engineering systems and structures in the presence of uncertainty, advancing scientific progress and improving civil infrastructure safety. Advances in experimental techniques and emerging technologies have led to increasingly complex mathematical models for large-scale systems. Current methods for solving these models exhibit either high accuracy or computational efficiency, but not both. This restriction limits the effectiveness of the methods for system analysis, design and optimization. This research will create a novel solution methodology that combines high accuracy with computational efficiency, enabling more reliable and efficient analysis of structural systems. The methodology will also impact emerging technologies like the use digital representations of actual structures, where accurate predictions of a system's future performance are critical for informed decision-making. Advancements from this research will enhance infrastructure resilience and support emerging industries. Additionally, the project includes innovative education, outreach, and community engagement activities to inspire the