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Found 12 papers, 2 papers with code
Rethinking materials simulations: Blending direct numerical simulations with neural operators
This methodology is based on the integration of a community numerical solver with a U-Net neural operator, enhanced by a temporal-conditioning mechanism that enables accurate extrapolation and efficient time-to-solution predictions of the dynamics.
Randomized Forward Mode of Automatic Differentiation For Optimization Algorithms
The probability distribution of the random vector determines the statistical properties of RFG.
AI-Aristotle: A Physics-Informed framework for Systems Biology Gray-Box Identification
The proposed framework -- named AI-Aristotle -- combines eXtreme Theory of Functional Connections (X-TFC) domain-decomposition and Physics-Informed Neural Networks (PINNs) with symbolic regression (SR) techniques for parameter discovery and gray-box identification.
Tackling the Curse of Dimensionality with Physics-Informed Neural Networks
We demonstrate in various diverse tests that the proposed method can solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schr\"{o}dinger equations in tens of thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach.
Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs
Subsequently, the closed form dependency of parameter values found by PINN on the initial radii and contact angles are given using symbolic regression.
MyCrunchGPT: A chatGPT assisted framework for scientific machine learning
To demonstrate the flow of the MyCrunchGPT, and create an infrastructure that can facilitate a broader vision, we built a webapp based guided user interface, that includes options for a comprehensive summary report.
A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data
In addition, symbolic regression is employed to determine the closed form of the unknown part of the equation from the data, and the results confirm the accuracy of the X-PINNs based approach.
Learning bias corrections for climate models using deep neural operators
In this study, we replace the bias correction process with a surrogate model based on the Deep Operator Network (DeepONet).
Deep neural operators can serve as accurate surrogates for shape optimization: A case study for airfoils
Deep neural operators, such as DeepONets, have changed the paradigm in high-dimensional nonlinear regression from function regression to (differential) operator regression, paving the way for significant changes in computational engineering applications.
Scalable algorithms for physics-informed neural and graph networks
For more complex systems or systems of systems and unstructured data, graph neural networks (GNNs) present some distinct advantages, and here we review how physics-informed learning can be accomplished with GNNs based on graph exterior calculus to construct differential operators; we refer to these architectures as physics-informed graph networks (PIGNs).
BIG-bench Machine Learning
Physics-informed machine learning
Learning two-phase microstructure evolution using neural operators and autoencoder architectures
We utilize the convolutional autoencoder to provide a compact representation of the microstructure data in a low-dimensional latent space.
Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks
The ultrasonic surface wave data is represented as a surface deformation on the top surface of a metal plate, measured by using the method of laser vibrometry.
