ameyajagtap Goto Github PK
Name: Ameya D. Jagtap
Type: User
Bio: Assistant Professor of Applied Mathematics (Research), Division of Applied Mathematics, Brown University, USA
Location: United States
Name: Ameya D. Jagtap
Type: User
Bio: Assistant Professor of Applied Mathematics (Research), Division of Applied Mathematics, Brown University, USA
Location: United States
How important are How important are activation functions in regression and classification? A survey, performance comparison, and future directions
We proposed the simple adaptive activation functions deep neural networks. The proposed method is simple and easy to implement in any neural networks architecture.
We propose a conservative physics-informed neural network (cPINN) on decompose domains for nonlinear conservation laws. The conservation property of cPINN is obtained by enforcing the flux continuity in the strong form along the sub-domain interfaces.
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations
The first comprehensive theoretical analysis of PINNs (and XPINNs) for a prototypical nonlinear PDE, the Navier-Stokes equations are given.
Use Fourier transform to learn operators in differential equations.
Simplified implementation of locally adaptive activation functions (LAAF) with slope recovery for deep and physics-informed neural networks (PINNs) in PyTorch.
Python codes for Locally Adaptive Activation Function (LAAF) used in deep neural networks. Please cite this work as "A D Jagtap, K Kawaguchi, G E Karniadakis, Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 20200334, 2020. (http://dx.doi.org/10.1098/rspa.2020.0334)".
Short course on physics-informed deep learning
Physics Informed Deep Learning: Data-driven Solutions and Discovery of Nonlinear Partial Differential Equations
POD-PINN code and manuscript
We propose Deep Kronecker Neural Network, which is a general framework for neural networks with adaptive activation functions. In particular we proposed Rowdy activation functions that inject sinusoidal fluctuations thereby allows the optimizer to exploit more and train the network faster. Various test cases ranging from function approximation, inferring the PDE solution, and the standard deep learning benchmarks like MNIST, CIFAR-10, CIFAR-100, SVHN etc are solved to show the efficacy of the proposed activation functions.
Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
XPINN code written in TensorFlow 2
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