Scientific machine learning through physics–informed neural networks: Where we are and what's next
Abstract Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode
model equations, like Partial Differential Equations (PDE), as a component of the neural …
model equations, like Partial Differential Equations (PDE), as a component of the neural …
A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data
Neural operators can learn nonlinear mappings between function spaces and offer a new
simulation paradigm for real-time prediction of complex dynamics for realistic diverse …
simulation paradigm for real-time prediction of complex dynamics for realistic diverse …
Physics-informed machine learning: A survey on problems, methods and applications
Recent advances of data-driven machine learning have revolutionized fields like computer
vision, reinforcement learning, and many scientific and engineering domains. In many real …
vision, reinforcement learning, and many scientific and engineering domains. In many real …
Reliable extrapolation of deep neural operators informed by physics or sparse observations
Deep neural operators can learn nonlinear mappings between infinite-dimensional function
spaces via deep neural networks. As promising surrogate solvers of partial differential …
spaces via deep neural networks. As promising surrogate solvers of partial differential …
Wavelet neural operator for solving parametric partial differential equations in computational mechanics problems
T Tripura, S Chakraborty - Computer Methods in Applied Mechanics and …, 2023 - Elsevier
With massive advancements in sensor technologies and Internet-of-things (IoT), we now
have access to terabytes of historical data; however, there is a lack of clarity on how to best …
have access to terabytes of historical data; however, there is a lack of clarity on how to best …
Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport
Deep neural operators can learn operators mapping between infinite-dimensional function
spaces via deep neural networks and have become an emerging paradigm of scientific …
spaces via deep neural networks and have become an emerging paradigm of scientific …
Partial differential equations meet deep neural networks: A survey
Many problems in science and engineering can be represented by a set of partial differential
equations (PDEs) through mathematical modeling. Mechanism-based computation following …
equations (PDEs) through mathematical modeling. Mechanism-based computation following …
Learning two-phase microstructure evolution using neural operators and autoencoder architectures
Phase-field modeling is an effective but computationally expensive method for capturing the
mesoscale morphological and microstructure evolution in materials. Hence, fast and …
mesoscale morphological and microstructure evolution in materials. Hence, fast and …
Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems
Multiscale modeling is an effective approach for investigating multiphysics systems with
largely disparate size features, where models with different resolutions or heterogeneous …
largely disparate size features, where models with different resolutions or heterogeneous …
Wavelet neural operator: a neural operator for parametric partial differential equations
T Tripura, S Chakraborty - arXiv preprint arXiv:2205.02191, 2022 - arxiv.org
With massive advancements in sensor technologies and Internet-of-things, we now have
access to terabytes of historical data; however, there is a lack of clarity in how to best exploit …
access to terabytes of historical data; however, there is a lack of clarity in how to best exploit …