The workshop aimed to unite researchers from diverse fields of mathematics and statistics to explore the foundations of high-dimensional modeling and computational studies. It addressed recent advancements in numerical analysis, dynamical systems, and stochastic differential equations that support model reduction for large-scale complex systems. Incorporating targeted geometric structures, such as Riemannian manifolds, into large-scale statistical models is known to enhance the stability, reliability, and efficiency of numerical methods. However, algorithms are often presented in application contexts without adequate attention to their fundamental properties, limiting the adoption of these advanced modeling methods. The workshop emphasized understanding the fundamental properties of these structures, their impact on dynamics and stochastic dynamics, and the need to redesign algorithms to capture essential properties, aiming for robustness and suitability for high-performance computation. By bringing together numerical analysts, statisticians, and modelers, the workshop sought to improve the quality of methods and identify new model frameworks to guide future development.
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