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Found 12 papers, 5 papers with code
Large Language Model-Based Evolutionary Optimizer: Reasoning with elitism
Large Language Models (LLMs) have demonstrated remarkable reasoning abilities, prompting interest in their application as black-box optimizers.
RiemannONets: Interpretable Neural Operators for Riemann Problems
Developing the proper representations for simulating high-speed flows with strong shock waves, rarefactions, and contact discontinuities has been a long-standing question in numerical analysis.
Deep smoothness WENO scheme for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators
In this paper, we introduce an improved version of the fifth-order weighted essentially non-oscillatory (WENO) shock-capturing scheme by incorporating deep learning techniques.
A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions
This problem is also found in, and in some sense more difficult, with domain decomposition strategies such as temporal decomposition using XPINNs.
Learning stiff chemical kinetics using extended deep neural operators
Specifically, to train the DeepONet for the syngas model, we solve the skeletal kinetic model for different initial conditions.
Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology
We also show cases where XPINN is already better than PINN, so APINN can still slightly improve XPINN.
How important are activation functions in regression and classification? A survey, performance comparison, and future directions
For this purpose, we also discuss various requirements for activation functions that have been used in the physics-informed machine learning framework.
Error estimates for physics informed neural networks approximating the Navier-Stokes equations
We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier-Stokes equations with (extended) physics informed neural networks.
Physics-informed neural networks for inverse problems in supersonic flows
Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles.
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
Specifically, for general multi-layer PINNs and XPINNs, we first provide a prior generalization bound via the complexity of the target functions in the PDE problem, and a posterior generalization bound via the posterior matrix norms of the networks after optimization.
Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions
We propose a new type of neural networks, Kronecker neural networks (KNNs), that form a general framework for neural networks with adaptive activation functions.
Locally adaptive activation functions with slope recovery term for deep and physics-informed neural networks
Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.
