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Gopalakrishnan Meena, Murali

Publications and source records attributed to Gopalakrishnan Meena, Murali.

4 records
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DOE OSTI2024

Learning the boundary-to-domain mapping using Lifting Product Fourier Neural Operators for partial differential equations

Neural operators such as the Fourier Neural Operator (FNO) have been shown to provide resolution-independent deep learning models that can learn mappings between function spaces. For example, an initial condition can be mapped to the solution of a partial differential equation (PDE) at a future time-step using a neural operator. Despite the popularity of neural operators, their use to predict solution functions over a domain given only data over the boundary (such as a spatially varying Dirichlet boundary condition) remains unexplored. In this paper, we refer to such problems as boundary-to-domain problems; they have a wide range of applications in areas such as fluid mechanics, solid mechanics, heat transfer etc. We present a novel FNO-based architecture, named Lifting Product FNO (or LP-FNO) which can map arbitrary boundary functions defined on the lower-dimensional boundary to a solution in the entire domain. Specifically, two FNOs defined on the lower-dimensional boundary are lifted into the higher dimensional domain using our proposed lifting product layer. We demonstrate the efficacy and resolution independence of the proposed LP-FNO for the 2D Poisson equation.

Kashi, Aditya↗
DOE OSTI2024

Efficient Distributed Sequence Parallelism for Transformer-Based Image Segmentation

We introduce an efficient distributed sequence parallel approach for training transformer-based deep learning image segmentation models. The neural network models are comprised of a combination of a Vision Transformer encoder with a convolutional decoder to provide image segmentation mappings. The utility of the distributed sequence parallel approach is especially useful in cases where the tokenized embedding representation of image data are too large to fit into standard computing hardware memory. To demonstrate the performance and characteristics of our models trained in sequence parallel fashion compared to standard models, we evaluate our approach using a 3D MRI brain tumor segmentation dataset. We show that training with a sequence parallel approach can match standard sequential model training in terms of convergence. Furthermore, we show that our sequence parallel approach has the capability to support training of models that would not be possible on standard computing resources.

Lyngaas, Isaac↗
DOE OSTI2023

Entropy-driven Optimal Sub-sampling of Fluid Dynamics for Developing Machine-learned Surrogates

Optimal sub-sampling of large datasets from fluid dynamics simulations is essential for training reduced-order machine learned models. A method using Shannon entropy was developed to weight flow features according to their level of information content, such that the most informative features can be extracted and used for training a surrogate model. The method is demonstrated in the canonical flow over a cylinder problem simulated with OpenFOAM. Both time-independent predictions and temporal forecasting were investigated as well as two types of prediction targets: local per-grid-point predictions and global per-time-step predictions. When tested on training a surrogate model, results indicate that our entropy-based sampling method typically outperforms random sampling and yields more reproducible results in less iterations. Finally, the method was used to train a surrogate model for modeling turbulence in magnetohydrodynamic flows, which revealed various challenges and opportunities for future research.

Brewer, Wes↗