Niching importance sampling yields a robust probability-of-failure estimator that avoids degeneracy on multi-modal performance functions by integrating evolutionary niching with importance sampling.
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KL-DNN uses low-rank SVD and nested Karhunen-Loeve expansions to enable scalable operator learning on large 3D GCS simulations, achieving 0.04% relative pressure error and two-order speedup over DeepONet.
An eigenvalue-based small-sample approximation to MCMC reduces required paths from up to 1,000,000 to as few as 10 while producing comparable steady-state distributions by Wasserstein distance and lower variance.
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A Trainable-by-Parts Operator Learning Framework: Bridging DeepONet and Karhunen-Loeve Expansions for Large-Scale Applications
KL-DNN uses low-rank SVD and nested Karhunen-Loeve expansions to enable scalable operator learning on large 3D GCS simulations, achieving 0.04% relative pressure error and two-order speedup over DeepONet.