High-Dimensional Uncertainty Quantification via Active and Rank-Adaptive Tensor Regression
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Uncertainty quantification based on stochastic spectral methods suffers from the curse of dimensionality. This issue was mitigated recently by low-rank tensor methods. However, there exist two fundamental challenges in low-rank tensor-based uncertainty quantification: how to automatically determine the tensor rank and how to pick the simulation samples. This paper proposes a novel tensor regression method to address these two challenges. Our method uses an ℓ_q/ ℓ_2-norm regularization to determine the tensor rank and an estimated Voronoi diagram to pick informative samples for simulation. The proposed framework is verified by a 19-dim phonics bandpass filter and a 57-dim CMOS ring oscillator, capturing the high-dimensional uncertainty well with only 90 and 290 samples respectively.
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