3.4k citations · 27.2k across the 213 of their papers we have counts for
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Reliable extrapolation of deep neural operators informed by physics or sparse observations
Min Zhu, Handi Zhang, Anran Jiao +2
Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equ…
SMS: Spiking Marching Scheme for Efficient Long Time Integration of Differential Equations
Qian Zhang, Adar Kahana, George Em Karniadakis +1
We propose a Spiking Neural Network (SNN)-based explicit numerical scheme for long time integration of time-dependent Ordinary and Partial Differential Equations (ODEs, PDEs). The…
Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology
Zheyuan Hu, Ameya D. Jagtap, George Em Karniadakis +1
In this paper, we propose the augmented physics-informed neural network (APINN), which adopts soft and trainable domain decomposition and flexible parameter sharing to further impr…
On the Geometry Transferability of the Hybrid Iterative Numerical Solver for Differential Equations
Adar Kahana, Enrui Zhang, Somdatta Goswami +3
The discovery of fast numerical solvers prompted a clear and rapid shift towards iterative techniques in many applications, especially in computational mechanics, due to the increa…
How important are activation functions in regression and classification? A survey, performance comparison, and future directions
Ameya D. Jagtap, George Em Karniadakis
Inspired by biological neurons, the activation functions play an essential part in the learning process of any artificial neural network commonly used in many real-world problems.…
NeuralUQ: A comprehensive library for uncertainty quantification in neural differential equations and operators
Zongren Zou, Xuhui Meng, Apostolos F Psaros +1
Uncertainty quantification (UQ) in machine learning is currently drawing increasing research interest, driven by the rapid deployment of deep neural networks across different field…