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Neural Combinatorial Wavelet Neural Operator (NCWNO)
Neural Combinatorial Wavelet Neural Operator (NCWNO)
Creation of Machine Learning models for each new Scientific Task from scratch remains a resource-intensive undertaking,
Creation of Machine Learning models for each new Scientific Task from scratch remains a resource-intensive undertaking,
demanding (i) Considerable Computational Time and (ii) Huge Memory Resources.
demanding (i) Considerable Computational Time and (ii) Huge Memory Resources.
We introduce the concept of the Neural Combinatorial Wavelet Neural Operator (NCWNO) as a foundational model for scientific computing in computational mechanics problems. "This model is specifically designed to excel in learning from a diverse spectrum of physics and continuously adapt to the solution operators associated with unseen parametric partial differential equations (PDEs)."
We introduce the concept of the Neural Combinatorial Wavelet Neural Operator (NCWNO) as a foundational model for scientific computing in computational mechanics problems. "This model is specifically designed to excel in learning from a diverse spectrum of physics and continuously adapt to the solution operators associated with unseen parametric partial differential equations (PDEs)."
Simultaneously Predicting for Six PDEs using a Pre-Trained NCWNO
Simultaneously Predicting for Six PDEs using a Pre-Trained NCWNO
Each time-step represents one-half of a second. The training is carried out on a 64 x 64 spatial grid.
The proposed foundational model offers two key advantages (see the pictorial demonstration below):
The proposed foundational model offers two key advantages (see the pictorial demonstration below):
(i) NCWNO can simultaneously learn solution operators for multiple parametric PDEs.
(i) NCWNO can simultaneously learn solution operators for multiple parametric PDEs.
(ii) NCWNO can swiftly generalize to new parametric PDEs with minimal fine-tuning.
(ii) NCWNO can swiftly generalize to new parametric PDEs with minimal fine-tuning.
The proposed NCWNO is the first foundational operator learning algorithm distinguished by
The proposed NCWNO is the first foundational operator learning algorithm distinguished by
(i) Its robustness against catastrophic forgetting.
(i) Its robustness against catastrophic forgetting.
(ii) The maintenance of positive transfer for new parametric PDEs.
(ii) The maintenance of positive transfer for new parametric PDEs.
(iii) The facilitation of knowledge transfer across dissimilar tasks.
(iii) The facilitation of knowledge transfer across dissimilar tasks.
Neural Network Architecture of NCWNO
Neural Network Architecture of NCWNO
*** The source codes for reproducing the results presented in this paper will be made available publicly upon acceptance ***
Performance on 1D PDEs
Performance on 1D PDEs
The Pre-training is done on a 256 spatial grid.
Relative L2 norm of Prediction error in Sequential Learning in 1D PDEs
Relative L2 norm of Prediction error in Sequential Learning in 1D PDEs
Relative L2 norm of Prediction error in Sequential Learning in 2D PDEs
Relative L2 norm of Prediction error in Sequential Learning in 2D PDEs
Out-of-Distribution Generalization to New 1D PDEs
Out-of-Distribution Generalization to New 1D PDEs
Out-of-Distribution Generalization to New 2D PDEs
Out-of-Distribution Generalization to New 2D PDEs
Overview of the Prediction Error on Multiple PDEs in a Single Frame
Overview of the Prediction Error on Multiple PDEs in a Single Frame
Evolution of Prediction error for Out-of-Distribution Parameters
Evolution of Prediction error for Out-of-Distribution Parameters
Zero-Shot Prediction on Sub- and Super-resolutions
Zero-Shot Prediction on Sub- and Super-resolutions
(Train on a given resolution and Test on a different resolution)
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