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cs.LG2026
A Trainable-by-Parts Operator Learning Framework: Bridging DeepONet and Karhunen-Loeve Expansions for Large-Scale Applications
Christian Munoz, Alexandre Tartakovsky
Training operator-learning models for large-scale problems governed by partial differential equations (PDEs) is challenging due to the curse of dimensionality, memory constraints,…
cs.LG2025
VAE-DNN: Energy-Efficient Trainable-by-Parts Surrogate Model For Parametric Partial Differential Equations
Yifei Zong, Alexandre M. Tartakovsky
We propose a trainable-by-parts surrogate model for solving forward and inverse parameterized nonlinear partial differential equations. Like several other surrogate and operator le…
cs.LG2025
Mathematics of Digital Twins and Transfer Learning for PDE Models
Yifei Zong, Alexandre Tartakovsky
We define a digital twin (DT) of a physical system governed by partial differential equations (PDEs) as a model for real-time simulations and control of the system behavior under c…