Decision Support Methods

The Decision Support Methods (DSM) research area encompasses fundamental research in uncertainty quantification (UQ), numerical optimization, and the mathematics of digital twins, focusing on enhancing the reliability and effectiveness of computational sciences. These methods are pivotal for quantifying confidence in simulations, refining AI training and inference processes, and addressing complex parameter and state estimation challenges inherent in scientific research across the Department of Energy.

Based on several decades of applied mathematics research with an eye toward partnership applications, the DSM team has developed a broad range of robust algorithmic approaches that are available through the FASTMath Software Catalog.  Novel applied mathematics research is expanding these methods across four themes:

• • Leveraging domain knowledge for more effective surrogate models and numerical optimization.

  • Estimating model fidelity to account for uncertainty (including model error) in both traditional and AI models.

  • Combining information from sources with different fidelities and modalities to develop efficient multi-fidelity UQ and surrogate modeling methods.

  • Advancing the mathematics of digital twins to provide more effective data assimilation and experimental design as well as knowledge transfer across families of systems. 

There are many synergies across these research themes. Multi-fidelity and multimodal approaches are crucial to the efficiency of digital twin operations, while estimating model fidelity and using domain knowledge enables effective multi-fidelity approaches. Likewise, multiple AI techniques are integrated directly into our methodologies to provide better accuracy in surrogate models, more effective dimensionality reduction into latent spaces, acceleration of outer-loop analyses, and enhanced model selection in digital twin and multi-fidelity approaches. In turn, our methods are also applied to assess the predictive fidelity of AI approaches, leading to a deep synergy between the field of AI and DSM.