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stat.ML2025
Physics-informed Polynomial Chaos Expansion with Enhanced Constrained Optimization Solver and D-optimal Sampling
Qitian Lu, Himanshu Sharma, Michael D. Shields +1
Physics-informed polynomial chaos expansions (PC) provide an efficient physically constrained surrogate modeling framework by embedding governing equations and other physical c…
stat.ML2025
Polynomial Chaos Expansion for Operator Learning
Himanshu Sharma, Lukáš Novák, Michael D. Shields
Operator learning (OL) has emerged as a powerful tool in scientific machine learning (SciML) for approximating mappings between infinite-dimensional functional spaces. One of its m…
stat.ML2024
Physics-constrained polynomial chaos expansion for scientific machine learning and uncertainty quantification
Himanshu Sharma, Lukáš Novák, Michael D. Shields
We present a novel physics-constrained polynomial chaos expansion as a surrogate modeling method capable of performing both scientific machine learning (SciML) and uncertainty quan…