Learning Where the Physics Is: Probabilistic Adaptive Sampling for Stiff PDEs

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References (12)

[1]
Deep vs. Shallow: Benchmarking Physics-Informed Neural Architectures on the Biharmonic Equation
2025Akshay Govind Srinivasan, Vikas Dwivedi et al.
[2]
ADVANCED NUMERICAL METHODS FOR SOLVING NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS IN FLUID MECHANICS: APPLICATIONS IN AEROSPACE ENGINEERING
2025D. M. Madhavi, Mir Sohail et al.
[3]
Kernel-Adaptive PI-ELMs for Forward and Inverse Problems in PDEs with Sharp Gradients
2025Vikas Dwivedi, Balaji Srinivasan et al.
[4]
Curriculum Learning-Driven PIELMs for Fluid Flow Simulations
2025Vikas Dwivedi, Bruno Sixou et al.
[5]
Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations
2024Nick McGreivy, Ammar Hakim
[6]
Solving inverse problems in physics by optimizing a discrete loss: Fast and accurate learning without neural networks
2022P. Karnakov, S. Litvinov et al.
[7]
DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations
2021Keju Tang, X. Wan et al.
[8]
When and why PINNs fail to train: A neural tangent kernel perspective
2020Sifan Wang, Xinling Yu et al.
[9]
Physics Informed Extreme Learning Machine (PIELM) - A rapid method for the numerical solution of partial differential equations
2019Vikas Dwivedi, B. Srinivasan
[10]
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
2019M. Raissi, P. Perdikaris et al.
[11]
Extreme learning machine: Theory and applications
2006G. Huang, Q. Zhu et al.
[12]
Robust Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion-Reaction and Flow Problems
1996H. Roos, M. Stynes et al.

Founder's Pitch

"A probabilistic framework improving the efficiency of Physics-Informed Extreme Learning Machines for modeling stiff PDEs."

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