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A Bayesian Multiscale Deep Learning Framework for Flows in Random Media
Govinda Anantha Padmanabha, Nicholas Zabaras
Fine-scale simulation of complex systems governed by multiscale partial differential equations (PDEs) is computationally expensive and various multiscale methods have been develope…
Solving inverse problems using conditional invertible neural networks
Govinda Anantha Padmanabha, Nicholas Zabaras
Inverse modeling for computing a high-dimensional spatially-varying property field from indirect sparse and noisy observations is a challenging problem. This is due to the complex…
Multi-fidelity Generative Deep Learning Turbulent Flows
Nicholas Geneva, Nicholas Zabaras
In computational fluid dynamics, there is an inevitable trade off between accuracy and computational cost. In this work, a novel multi-fidelity deep generative model is introduced…
Integration of adversarial autoencoders with residual dense convolutional networks for estimation of non-Gaussian hydraulic conductivities
Shaoxing Mo, Nicholas Zabaras, Xiaoqing Shi +1
Inverse modeling for the estimation of non-Gaussian hydraulic conductivity fields in subsurface flow and solute transport models remains a challenging problem. This is mainly due t…
Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks
Nicholas Geneva, Nicholas Zabaras
In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems. However, in their…
Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data
Yinhao Zhu, Nicholas Zabaras, Phaedon-Stelios Koutsourelakis +1
Surrogate modeling and uncertainty quantification tasks for PDE systems are most often considered as supervised learning problems where input and output data pairs are used for tra…