A wide variety of applications in science and engineering, such as uncertainty quantification, inverse problems, or optimization approaches, depend on effectively and efficiently exploring high-dimensional parameter spaces. For such applications, creating an initial uniform, random sampling of the space to create a baseline of knowledge is the first step. Simulations evaluated at these samples are then used for subsequent processing. In its most generic form, the goal of sampling is to produce the maximal amount of information with the minimal number of samples. However, the quality of the initial sample designs is rarely analyzed or optimized, thus influencing the performance of the entire workflow.
Our project developed a new spectral sampling theory for analyzing and creating experiment designs in high-dimensional spaces. New algorithms for estimating sample properties and sample synthesis were designed. Finally, applications of the proposed spectral sampling tools in surrogate modeling, scientific machine learning, and image analysis were presented.
This project leveraged and supported Lawrence Livermore National Laboratory's core competencies in high-performance computing, simulation, and data science. Our results, due to their fundamental nature, broadly impact the Laboratory's mission focus areas. Better sampling strategies will lead to high quality results using significantly fewer resources with potential applications to uncertainty quantification for stockpile stewardship or weapon design, better weather or climate ensembles, optimizing the energy grid, and sensitivity analysis and inverse modeling in materials science and high-energy physics. The software library developed for this project enables a wider adoption of these tools in other mission-critical applications, and our work has attracted interest from industry partners.
Anirudh, R., et al. 2017. “Poisson Disk Sampling on the Grassmannian: Applications in Subspace Optimization.” Proceedings: IEEE Conference on Computer Vision and Pattern Recognition, Honolulu, HI, July 2017. LLNL-CONF-7303848 and LLNL-POST-735098.
Kailkhura, B., et al. 2016. "Theoretical Guarantees for Poison-Disk Sampling Using Pair Correlation Function." IEEE ICASSP. Shanghai, China, March 2016. LLNL-CONF-682297.
——— . 2016. “Stair Blue Noise Sampling.” ACM Transactions on Graphics 35(6): 248. LLNL-JRNL-703039.
——— . 2016. “Theoretical Guarantees for Poisson Disk Sampling Using Pair Correlation Function.” IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Shanghai, China, March 2016. LLNL-CONF-682297.
——— . 2018. "A Spectral Approach for the Design of Experiments: Design, Analysis and Algorithms." J. Mach Learn Res. 19. LLNL-JRNL-743060.
——— . 2019. “A Look at the Effect of Sample Design on Generalization through the Lens of Spectral Analysis.” Conference on Neural Information Processing Systems, Vancouver, Canada, December 2019. LLNL-CONF-7756799.
Song, H., et al., 2018. "Triplet Network with Attention for Speaker Diarization." Interspeech. LLNL-PROC-755003.
Thiagarajan, J., et al. 2016. "Spectral Sampling in High Dimensional Parameter Spaces." SIAM UQ. Lausanne, Switzerland, April 2016. LLNL-PRES-729358.
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