1 citations · 2 across the 5 of their papers we have counts for
6 papers
Spectral Audit of In-Context Operator Networks
Zhiwei Gao, Liu Yang, George Em Karniadakis
Existing evaluations of neural operators and in-context operator learning rely primarily on prediction error, but accurate output prediction does not guarantee the correct local dy…
Nonlinear parametrization solver for fractional Burgers equations
Haojun Qin, Zhiwei Gao, Jinye Shen +1
Fractional Burgers equations pose substantial challenges for classical numerical methods due to the combined effects of nonlocality and shock-forming nonlinear dynamics. In particu…
Probabilistic Predictions of Process-Induced Deformation in Carbon/Epoxy Composites Using a Deep Operator Network
Elham Kiyani, Amit Makarand Deshpande, Madhura Limaye +7
Fiber reinforcement and polymer matrix respond differently to manufacturing conditions due to mismatch in coefficient of thermal expansion and matrix shrinkage during curing of the…
Safe cross-entropy-based importance sampling for rare event simulations
Zhiwei Gao, George Karniadakis
The Improved Cross-Entropy (ICE) method is a powerful tool for estimating failure probabilities in reliability analysis. Its core idea is to approximate the optimal importance-samp…
DeepSeek vs. ChatGPT vs. Claude: A Comparative Study for Scientific Computing and Scientific Machine Learning Tasks
Qile Jiang, Zhiwei Gao, George Em Karniadakis
Large Language Models (LLMs) have emerged as powerful tools for tackling a wide range of problems, including those in scientific computing, particularly in solving partial differen…
Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networks
Zhiwei Gao, George Em Karniadakis
Uncertainty quantification (UQ) plays a pivotal role in scientific machine learning, especially when surrogate models are used to approximate complex systems. Although multilayer p…